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Quantum Electronic StructureJune 16, 2023

Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level
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Dávid Mester*
Dávid Mester
Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
ELKH-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
*E-mail: [email protected]
More by Dávid Mester
https://orcid.org/0000-0001-6570-2917
Mihály Kállay*
Mihály Kállay
Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
ELKH-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
*E-mail: [email protected]
More by Mihály Kállay
https://orcid.org/0000-0003-1080-6625

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Journal of Chemical Theory and Computation

Cite this: J. Chem. Theory Comput. 2023, 19, 13, 3982–3995

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https://doi.org/10.1021/acs.jctc.3c00363

Published June 16, 2023

CC-BY 4.0 .

Abstract

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The double-hybrid (DH) time-dependent density functional theory is extended to vertical ionization potentials (VIPs) and electron affinities (VEAs). Utilizing the density fitting approximation, efficient implementations are presented for the genuine DH ansatz relying on the perturbative second-order correction, while an iterative analogue is also elaborated using our second-order algebraic-diagrammatic construction [ADC(2)]-based DH approach. The favorable computational requirements of the present schemes are discussed in detail. The performance of the recently proposed spin-component-scaled and spin-opposite-scaled (SOS) range-separated (RS) and long-range corrected (LC) DH functionals is comprehensively assessed, while popular hybrid and global DH approaches are also discussed. For the benchmark calculations, up-to-date test sets are selected with high-level coupled-cluster references. Our results show that the ADC(2)-based SOS-RS-PBE-P86 approach is the most accurate and robust functional. This method consistently outperforms the excellent SOS-ADC(2) approach for VIPs, although the results are somewhat less satisfactory for VEAs. Among the genuine DH functionals, the SOS-ωPBEPP86 approach is also recommended for describing ionization processes, but its performance is even less reliable for electron-attached states. In addition, surprisingly good results are attained by the LC hybrid ωB97X-D functional, where the corresponding occupied (unoccupied) orbital energies are retrieved as VIPs (VEAs) within the present formalism.

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Subjects

1. Introduction

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Vertical ionization potentials (VIPs) and electron affinities (VEAs) are crucial parameters that are used to characterize the electronic structure of molecular systems. The accurate prediction of VIPs, for example, can provide insights into the properties of semiconducting materials used in solar cell devices. Therefore, understanding the relationship between VIPs and photovoltaic efficiency is of great importance in the development of next-generation solar cells. (1−3) Furthermore, ionizing radiations can cause damage to DNA, with secondary electron attachment resulting in various forms of DNA degradation, making it important to understand the role of electron-attached states in genetics, biochemistry, and health sciences. (4−10) The reliable prediction of these parameters for extended molecular systems is still a challenging task that requires accurate and efficient theoretical methods.

To obtain the total energy of a given system, the most commonly used approaches are based on the cost-effective density functional theory (DFT). (11) Within DFT, the highest occupied Kohn–Sham (KS) orbital energy of an n-electron system can also be interpreted as the negative of the exact ionization potential; (12−14) however, these values are often underestimated in comparison with the experimental results. (12,15) Consequently, the use of the more advanced wave function-based methods is desired, but a good alternative could also be offered by the efficient double-hybrid (DH) DFT approaches, which combine KS-DFT with second-order wave function approximations. (16−21)

Concerning the wave function methods, the equation-of-motion coupled-cluster (EOM-CC) formalism (22−26) is a popular computational tool for calculating electronic excited states of molecules. It is based on the similarity transformation of the electronic Hamiltonian, and the resulting effective operator is diagonalized to produce final state wave functions and energies. One of the most significant advantages of the EOM-CC approach is its ability to systematically include electron correlation effects in the calculations, enabling one to achieve arbitrary accuracy within the hierarchical expansion. However, as the methods become more advanced, they also become more expensive. The EOM-CC formalism can describe a qualitatively different set of final states for an n-electron reference system. For instance, ionization processes can be studied by diagonalizing the corresponding operator in a basis of determinants containing n – 1 electrons, (27−31) while electron-attached states correspond to the diagonal representation in the n + 1 particle space. (32,33)

Another promising approach in the field is the algebraic-diagrammatic construction (ADC) formalism. (34) This method is based on the diagrammatic perturbation expansion of the polarization propagator and the Møller–Plesset (MP) partitioning of the Hamiltonian. Similar to the EOM-CC approach, the ADC formalism also permits the indirect inclusion of orbital relaxation effects through couplings to higher-excited configurations. Originally, for VIP and VEA calculations, the ADC methods were elaborated based on the perturbative self-energy expansion of the Dyson equation. (35) However, this led to computationally inefficient schemes as the electron attachment and detachment parts of the propagator are coupled. To address this issue, non-Dyson ADC schemes were later proposed, (36,37) which allow for independent calculations of VIPs and VEAs. The effective implementation and comprehensive investigation of the ADC methods is still an active research field. (38−44)

Further Dyson propagator methods must also be mentioned, (45) which are not strictly related to the ADC formalism. These methods are based on an approximation of the self-energy matrix, where the diagonal elements of the corresponding matrix represent a correlated, energy-dependent potential which is felt by the electrons assigned to canonical molecular orbitals (MOs). In the simplest approaches, the mixing of canonical orbitals in the Feynman–Dyson amplitudes is prevented by neglecting the non-diagonal elements of the self-energy matrix. (46,47) Later, several renormalized methods with more flexible non-diagonal self-energies have also been developed. (47−50) The performance of such methods has been demonstrated in excellent studies. (47,51)

In the previously mentioned methods, VIPs and VEAs are calculated directly in a single calculation. The so-called energy difference or Δ-approaches, however, follow a significantly different scheme, where the corresponding quantities are obtained as the difference between the total energy of the neutral and charged system computed in two separate calculations using the ground-state approximation. Depending on the applied method, several different approaches can be defined, such as the self-consistent field (ΔSCF), (52−54) ΔMP, (52) and ΔCC (55−57) methods. The major drawback of these approaches is that the optimization of the non-Aufbau determinant can easily lead to variational collapse. Moreover, the resulting excited states are not orthogonal to the ground state, which means that the evaluation of transition matrix elements is highly problematic. In addition, higher-order Δ-approaches often require additional calculations to help the selection of the reference determinant for a desired state. In order to avoid misunderstandings, we would like to note that other ΔMP methods have also been developed. (58,59) In these cases, the VIPs and VEAs are defined as the difference in the MP correlation energy between the natural and charged systems, which both are described with the orbitals and orbitals energies obtained for the n-electron system.

Concerning DH DFT, so far the most widespread option to compute VIPs and VEAs has been to employ this simple but less favorable approach. The performance of DHs for VIPs and VEAs utilizing the Δ-approach is well-documented in the literature. For the interested reader, we recommend the diverse GMTKN55 benchmark study, (60) where the performance of several popular DHs is tested for well-established benchmark compilations using theoretically back-corrected experimental reference values (61,62) and is also assessed against numerous pure and hybrid functionals. At the same time, we would like to note that numerous developments have taken place in the field recently. One of the most notable attempts is the orbital-optimized DH scheme using the optimized-effective-potential method, (63) for which a range-separated version was also elaborated. (64) In these cases, the VIPs and VEAs are obtained by calculating derivatives of the total energy by finite differences using fractional electron numbers. (65−67) Another direct method has also been developed (68) which is based on a more general extension of the second-order energy derivative with respect to occupation numbers, (69) while the combination of the extended Koopmans’ theorem and the adiabatic connection formalism is also noteworthy. (70)

In this paper, a somewhat different route is followed, and the time-dependent DFT (TDDFT) formalism is extended to directly calculate VIPs and VEAs within the DH theory. We first provide a brief overview of the time-dependent approaches used, including a discussion of the genuine formalism of DH TDDFT theory and a more advanced iterative scheme. Thereafter, the corresponding working equations and efficient implementations for VIPs and VEAs are presented in detail. As we will see, the presented perturbative approach can be considered as a simplified version of the scheme introduced in ref (63). Finally, state-of-the-art and popular functionals are tested on benchmark compilations, and the performances of the methods are comprehensively assessed.

2. Theoretical Overview

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2.1. Double-Hybrid Density Functional Theory for Excitations

The DH theory surpasses popular hybrid TDDFT calculations by incorporating the impact of double excitations. Similar to ground-state calculations, (16) excitation energies within the genuine formalism (71) are obtained in a two-step manner. First, in the most common and convenient approach, a Hermitian eigenvalue equation relying on the Tamm–Dancoff approximation (TDA) (72) is solved as

A^{D H} c = ω^{T D A} c

(1)

where A^DH denotes the corresponding DH Jacobian, c is the singles excitation vector, and ω^TDA is the TDA excitation energy. Using the spatial-orbital representation, the elements of the Jacobian are defined by

A_{i a, j b}^{D H} = (ε_{a} - ε_{i}) δ_{i j} δ_{a b} + 2 (i a | j b) - α_{X} (i j | a b) + (1 - α_{X}) (i a | f_{X} | j b) + (1 - α_{C}) (i a | f_{C} | j b)

(2)

where i, j, ... (a, b, ...) denote occupied (unoccupied) molecular orbitals, and ε_a and ε_i are the corresponding orbital energies. (ia|jb) is a two-electron repulsion integral in Mulliken’s convention, whereas (ia|f_X|jb) and (ia|f_C|jb) are the integrals of the exchange and correlation kernels, respectively. The above expression contains two adjustable parameters: the ratio of the Hartree–Fock (HF) and DFT contributions to the exchange energy is handled by α_X, while the DFT correlation part is scaled by 1 – α_C. The excitation energies obtained in this way have just hybrid quality. With the solution of eq 1 at hand, in the second step, the second-order correction is calculated perturbatively relying on the configuration interaction singles (CIS) (73) with perturbative doubles [CIS(D)] (74) approach. Accordingly, the improved excitation energy at the DH level is obtained as

ω^{D H} = ω^{T D A} + α_{C} ω^{(D)}

(3)

where ω^(D) is the perturbative correction. The thorough theoretical background of genuine excited-state DH approaches has been presented in excellent papers, (71,75−77) while the efficient calculation of the second-order terms invoking the density fitting (DF) approximation has been detailed in our previous work. (78)

Nowadays, one of the most prominent second-order approaches is the second-order ADC [ADC(2)] method (79,80) as it offers an appropriate compromise between accuracy and computational cost. (81) In practice, a nonlinear eigenvalue equation is solved iteratively as

{\tilde{A}}^{A D C (2)} (ω^{A D C (2)}) c = ω^{A D C (2)} c

(4)

where

{\tilde{A}}^{A D C (2)}

is the so-called effective ADC(2) Jacobian and ω^ADC(2) denotes the ADC(2) excitation energy. The corresponding Jacobian can be split into two parts as

{\tilde{A}}^{A D C (2)} = A^{C I S} + A^{[2]}

(5)

where A^CIS is the CIS Jacobian, and all of the terms including second-order contributions are collected into matrix A^[2].

Similar to CIS(D), an ADC(2)-based DH analogue can also be defined. (82) In the former case, the CIS excitation energy and singles excitation vector are replaced by the quantities obtained by eq 1, and the second-order correction is scaled by an empirical factor and added to the final excitation energy. For the ADC(2)-based approach, the ADC(2) Jacobian is modified in a very similar way. That is, the CIS Jacobian in eq 5 is replaced by the DH Jacobian defined by eq 2, while the second-order terms are scaled by an empirical factor:

{\tilde{A}}^{D H - A D C (2)} = A^{D H} + α_{C} A^{[2]}

(6)

In contrast to the genuine formalism, where the doubles correction is added a posteriori to the TDA excitation energy, these excitations are treated iteratively in this ansatz. Thus, an improvement in the calculated excitation energies is expected. Additionally, the transition properties, such as oscillator strengths, can be calculated at a higher level using the presented approach. Needless to say, the computational cost also increases since the ADC(2)-based approach is iterative.

In recent years, significant developments have been made in the DH theory. First, the spin-scaling techniques have been extended to excited-state calculations as well. (76) In this case, the opposite-spin and same-spin contributions to the second-order correction are scaled separately, (83−88) which enables higher flexibility of the energy functional. It is also noteworthy that the computational scaling of the spin-opposite-scaled (SOS) variant, where the same-spin contributions are completely neglected, can be reduced to N⁴ invoking the DF approximation for the electron-repulsion integrals and Laplace transform-based techniques, (88) whereas the scaling of the original and spin-component-scaled (SCS) variants are N⁵, where N is a measure of the system size.

Later, to remedy the wrong long-range behavior of global exchange-correlation (XC) functionals, long-range corrected (LC) and range-separated (RS) DH functionals have been introduced. (78,89) In these approaches, the Coulomb operator is split into long- and short-range components using a range-separation parameter. For the RS-DH approaches, (78) both the exchange and correlation contributions are separated, while only the former one is split for LC DHs. (89) These approaches can arbitrarily be combined with spin-scaling techniques, (77,90) whereas their generalization to the ADC(2)-based formalism is also fairly straightforward. (91)

In the following sections, we discuss the extension of DH TDDFT theory to ionized and electron-attached states. Since a TDDFT calculation with a pure or hybrid functional just returns (the negative of) the corresponding orbital energies, this practically requires the generalization of the CIS(D) and ADC(2) methods to VIP and VEA calculations. We also present the working equations for an efficient, DF-based implementation. The adaptation of the approaches for spin-scaled and range-separated functionals is not discussed in detail; the derivation of the corresponding equations is straightforward based on our previous publications. (78,90,91)

2.2. VIP and VEA Calculations for CIS(D)

We start our proposition with the evaluation of the second-order correction for the ground state, which is required for the subsequent discussion of the excited-state corrections. Assuming a closed-shell system and spatial orbitals, the second-order MP (MP2) correlation energy is defined by

E^{M P 2} = ⟨ Φ_{0} | \hat{V} | {\hat{T}}_{2} Φ_{0} ⟩ = \sum_{i j a b} (i a | j b) (2 t_{i j}^{a b} - t_{j i}^{a b})

(7)

where the MP2 doubles amplitudes, t_ij^ab, can be obtained by acting the

{\hat{T}}_{2}

operator on the HF reference determinant, Φ₀:

{\hat{T}}_{2} Φ_{0} = \frac{1}{2} \sum_{i j a b} t_{i j}^{a b} Φ_{i j}^{a b} = \frac{1}{2} \sum_{i j a b} \frac{(i a | j b)}{ε_{i} + ε_{j} - ε_{a} - ε_{b}} Φ_{i j}^{a b} = \frac{1}{2} \sum_{i j a b} \frac{(i a | j b)}{D_{i j}^{a b}} Φ_{i j}^{a b}

(8)

where Φ_ij^ab is the corresponding double substitution, and the orbital energy differences D_ij^ab are constructed as ε_i + ε_j – ε_a – ε_b. Using the DF approximation, the four-center quantities can be recast as

(i a | j b) = \sum_{P Q} I_{i a}^{P} V_{P Q}^{- 1} I_{j b}^{Q}

(9)

where P and Q stand for the elements of the auxiliary basis, whereas I_ia^P and V_PQ are three- and two-center Coulomb integrals, respectively, and V_PQ^–1 is a simplified notation for the corresponding element of the inverse of the two-center Coulomb integral matrix. Usually, the matrix K with elements K_ia,jb = (ia|jb) is factorized as K = IV^–1/2V^–1/2I^T = JJ^T. Using the latter notation, the MP2 correlation energy can be expressed in the following simple form:

E^{M P 2} = \sum_{i j a b} (i a | j b) (2 t_{i j}^{a b} - t_{j i}^{a b}) = \sum_{i j a b} (i a | j b) {\tilde{t}}_{i j}^{a b} = \sum_{j b Q} J_{j b}^{Q} \sum_{i a} J_{i a}^{Q} {\tilde{t}}_{i j}^{a b} = \sum_{j b Q} J_{j b}^{Q} Y_{j b}^{Q}

(10)

where the intermediate Y_ia^Q is defined by the contraction of the three-center integrals and the antisymmetrized amplitudes.

For the extension of the genuine DH TDDFT approach to electron-attached/detached states, the generalization of CIS(D) to such states is required. First, we note that the CIS method (73) can formally be generalized to calculate VIPs and VEAs. Concerning the former, using a generic ionization operator,

{\hat{C}}_{1}

, the ionized state can be expanded as a linear combination of singly ionized determinants:

{\hat{C}}_{1} Φ_{0} = \sum_{i} c_{i} Φ_{i}

. Projecting onto the subspace of ionized determinants, the following eigenvalue equations are obtained:

⟨ Φ_{i} | \hat{H} | {\hat{C}}_{1} Φ_{0} ⟩ = - ε_{i} c_{i}

(11)

Here, the eigenvalues of this equation correspond to the negative occupied orbital energies as VIPs, while the eigenvectors are orthogonal unit vectors. The second-order (D) correction for the ionization of the k̅th orbital can be interpreted as a CIS(D) (74) calculation using the corresponding ionized determinant:

E_{\bar{k}}^{(D)} = ⟨ Φ_{n - 1} | \hat{V} | {\hat{C}}_{2} Φ_{0} ⟩ + ⟨ Φ_{n - 1} | \hat{V} | {\hat{T}}_{2} {\hat{C}}_{1} Φ_{0} ⟩

(12)

where the final state can be obtained as

Φ_{n - 1} = {\hat{C}}_{1} Φ_{0} = \sum_{i} δ_{i \bar{k}} Φ_{i} = Φ_{\bar{k}}

(13)

while the action of the double excitation operator on the reference yields

{\hat{C}}_{2} Φ_{0} = \sum_{i j a} c_{i j}^{a} Φ_{i j}^{a} = \sum_{i j a} \frac{⟨ Φ_{i j}^{a} | \hat{V} | {\hat{C}}_{1} Φ_{0} ⟩}{D_{i j}^{a} - ε_{\bar{k}}} Φ_{i j}^{a}

(14)

As the disconnected terms in the second contribution to eq 12 yield the MP2 energy, the final perturbative correction to the VIP is given as

ω_{\bar{k}}^{(D)} = E_{\bar{k}}^{(D)} - E^{M P 2} = \sum_{i j a} V_{i j}^{a} (2 c_{i j}^{a} - c_{j i}^{a}) - X = \sum_{i j a} V_{i j}^{a} {\tilde{c}}_{i j}^{a} - X

(15)

where the elements of the

{\hat{C}}_{2}

-related intermediate V_ij^a can be expressed as

V_{i j}^{a} = ⟨ Φ_{i j}^{a} | \hat{V} | {\hat{C}}_{1} Φ_{0} ⟩ = - (j a | i \bar{k}) = - \sum_{Q} J_{j a}^{Q} J_{i \bar{k}}^{Q}

(16)

while the remaining

{\hat{T}}_{2} {\hat{C}}_{1}

-related contribution of eq 12 is simply calculated as

X = \sum_{a Q} J_{\bar{k} a}^{Q} Y_{\bar{k} a}^{Q}

(17)

We note that these equations retrieve the second-order self-energies in the diagonal and frequency-independent approximations, which correspond to the ΔMP2 method. (58,59,92,93) Accordingly, a similar DH ansatz is recovered from the optimized-effective-potential method of Toulouse and co-workers (63,64) if the variation of the orbitals and orbital energies in the MP2 correlation energy is neglected when taking the derivative of the total energy with respect to n.

As can be seen, in contrast to the standard excited-state CIS(D) equations, the most demanding operations are proportional to N⁴. Since one of the occupied indices on the right-hand side of eq 16 is restricted to the ionized orbital, the computation of V_ij^a scales as N_occ²N_unoccN_aux, where N_occ, N_unocc, and N_aux are the number of occupied, unoccupied, and auxiliary orbitals, respectively. The rate-determining step of eq 17 is the evaluation of intermediate Y, which also requires only a fourth-power scaling operation due to the restriction. This means that the cost of the perturbative second-order correction is comparable to a single iteration in a ground-state HF calculations. In addition, the unoccupied–unoccupied block of the three-center integrals is not required for the calculations, which is not true for standard CIS(D) calculations.

Similar equations are obtained for the electron-attached states. In this case, for the first-order equations, the energy of the unoccupied orbitals is retrieved as VEAs. The second-order (D) correction for the c̅th orbital is calculated as

E_{\bar{c}}^{(D)} = ⟨ Φ_{n + 1} | \hat{V} | {\hat{C}}_{2} Φ_{0} ⟩ + ⟨ Φ_{n + 1} | \hat{V} | {\hat{T}}_{2} {\hat{C}}_{1} Φ_{0} ⟩

(18)

where the wave function of the n + 1-electron state is expressed as

Φ_{n + 1} = {\hat{C}}_{1} Φ_{0} = \sum_{a} δ_{a \bar{c}} Φ^{a} = Φ^{\bar{c}}

(19)

while the corresponding

{\hat{C}}_{2}

operator generates the higher-order excitations:

{\hat{C}}_{2} Φ_{0} = \sum_{i a b} c_{i}^{a b} Φ_{i}^{a b} = \sum_{i a b} \frac{⟨ Φ_{i}^{a b} | \hat{V} | {\hat{C}}_{1} Φ_{0} ⟩}{D_{i}^{a b} + ε_{\bar{c}}} Φ_{i}^{a b}

(20)

The final (D) correction to the VEA is obtained as

ω_{\bar{c}}^{(D)} = E_{\bar{c}}^{(D)} - E^{M P 2} = \sum_{i a b} V_{i}^{a b} {\tilde{c}}_{i}^{a b} - X

(21)

In this case, the intermediate V_i^ab can be written in the

V_{i}^{a b} = ⟨ Φ_{i}^{a b} | \hat{V} | {\hat{C}}_{1} Φ_{0} ⟩ = (i a | b \bar{c}) = \sum_{Q} J_{i a}^{Q} J_{b \bar{c}}^{Q}

(22)

form, while the intermediate X can be calculated as

X = \sum_{i Q} J_{i \bar{c}}^{Q} Y_{i \bar{c}}^{Q}

(23)

Again, the rate-determining steps of the above scheme, that is the calculation of V_i^ab and

Y_{i \bar{c}}^{Q}

, scale as N⁴.

2.3. VIP and VEA Calculations for ADC(2)

For the ADC(2) part of the DH calculation, we propose to employ the non-Dyson ADC approach of Schirmer and co-workers. (36,37) The working equations for VIPs within the non-Dyson ADC schemes up to third order have been previously presented in the literature. (38) However, an effective implementation relying on the DF approximation has not yet been published. Additionally, even though the derivation of the equations is fairly straightforward, the expressions for VEAs have not been presented. To remedy this, the most important expressions are collected herein.

For VIP calculations, the elements of the vector

σ^{A D C (2)} = {\tilde{A}}^{A D C (2)} c

are given as

\begin{array}{l} σ_{i}^{A D C (2)} = - ε_{i} c_{i} - \frac{1}{2} \sum_{j k a b} (i a | k b) T_{j k}^{a b} c_{j} - \frac{1}{2} \sum_{j k a b} (j a | k b) T_{i k}^{a b} c_{j} - \sum_{j k a} (i j | k a) C_{j k}^{a} \\ = - ε_{i} c_{i} - \frac{1}{2} \sum_{j a Q} (Y_{j a}^{Q} J_{i a}^{Q} + J_{j a}^{Q} Y_{i a}^{Q}) c_{j} - \sum_{j Q} J_{i j}^{Q} \sum_{k a} J_{k a}^{Q} C_{j k}^{a} \end{array}

(24)

The resulting terms are very similar to those obtained for CIS(D). However, as the solutions of the corresponding eigenvalue equation are not unit vectors, the final state is properly expanded as Φ_n–1 = ∑_ic_iΦ_i ≠ ∑_iδ_ijΦ_i. Accordingly, the elements of intermediate V_ij^a can be expressed as

V_{i j}^{a} = - \sum_{k} (j a | i k) c_{k} = - \sum_{Q} J_{j a}^{Q} \sum_{k} J_{i k}^{Q} c_{k}

(25)

In addition, the leading complexity of the expressions is somewhat higher compared to that obtained for CIS(D). That is, the rate-determining step of the above procedure is also the evaluation of intermediate Y, but the restriction regarding the ionized orbital cannot be applied in this case. This implies that the most expensive step is proportional to N⁵; however, it has to be carried out only once, regardless of the number of ionized states. The iterative procedure still scales as N⁴ since the intermediate in parentheses can be evaluated before it. In addition, the demanding J_ab^Q-type integrals are not required for the calculations.

For VEAs, the elements of the Jacobi matrix transformation read explicitly as

\begin{array}{l} σ_{a}^{A D C (2)} = ε_{a} c^{a} - \frac{1}{2} \sum_{j k b c} (j b | k c) T_{j k}^{a c} c^{b} - \frac{1}{2} \sum_{j k b c} (j a | k c) T_{j k}^{b c} c^{b} + \sum_{k b c} (a b | k c) C_{k}^{b c} \\ = ε_{a} c^{a} - \frac{1}{2} \sum_{j b Q} (J_{j b}^{Q} Y_{j a}^{Q} + Y_{j b}^{Q} J_{j a}^{Q}) c^{b} + \sum_{b Q} J_{a b}^{Q} \sum_{k c} J_{k c}^{Q} C_{k}^{b c} \end{array}

(26)

where V_i^ab is calculated as

V_{i}^{a b} = \sum_{c} (i a | b c) c^{c} = \sum_{Q} J_{i a}^{Q} \sum_{c} J_{b c}^{Q} c^{c}

(27)

As can be seen, similar findings can be stated regarding the scaling of the procedure as those obtained for VIPs.

The anticipated benefit of the ADC(2)-based formalism over the CIS(D)-based one is twofold. First, as the singles coefficients are relaxed during the iterative procedure, an improvement in the calculated VIPs and VEAs is expected. Second, other quantities, such as Dyson orbitals and pole strengths, (94−96) can be calculated at a higher level taking into account the effect of double excitations. As the perturbative (D) correction is only an energy correction for the CIS(D)-based approaches, the aforementioned quantities have only hybrid quality. This implies that pole strengths are always equal to unity in these cases. The calculation of pole strengths for ADC(2)-based DH approaches is fairly straightforward. Similar modifications for transition density matrices have already been discussed in ref (82). That is, the first-order contributions to the spectroscopic amplitude vector are kept unchanged, while all the second-order contributions are scaled by α_C. The working equations to calculate pole strengths for ADC(2) can be found in ref (38).

3. Computational Details

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3.1. Calculation of the Numerical Results

In this study, the Mrcc suite of quantum chemical programs (97) was used to calculate VIPs and VEAs, and TDDFT calculations were carried out using TDA. To tackle the corresponding ionized and electron-attached states, a modified Davidson algorithm using the root-following technique (98) was adopted. Dunning’s correlation consistent basis sets (cc-pVXZ, where X = D and T) (99,100) and their diffuse function augmented variants (aug-cc-pVXZ) (101) were employed for the calculations, and the DF approximation was utilized for both the ground and attached/detached states. For this purpose, the corresponding auxiliary bases of Weigend and co-workers (102−104) were employed. The frozen core approximation was employed in a similar manner to the original benchmark studies (see Sect. 3.2) in the post-KS/HF steps. The convergence threshold for the energies was set to 10^–6 E_h, while the default adaptive integration grid of the Mrcc package was used for the XC contributions. (105)

For the calculations, the exchange and correlation functionals of Perdew, Burke, and Ernzerhof (PBE), (106) Becke’s 1988 exchange functional (B88), (107) the correlation functional of Lee, Yang, and Parr (LYP), (108) Perdew’s 1986 correlation functional (P86), (109) and Becke’s 1997 exchange and correlation functionals (B97) (110) were used. The built-in functionals of the Mrcc package were employed in all cases, except for the LC hybrid and LC-DH functionals, where the locally modified version of the Libxc library (111,112) was utilized. The attributes of the assessed DH functionals are collected in Table 1.

Table 1. Functionals Assessed in the Benchmark Calculations^a

Functional	Exchange	Correlation	Class	Number of parameters	References
SCS-RS-PBE-P86	PBE	P86	RS DH	4	(90)
SOS-RS-PBE-P86	PBE	P86	RS DH	3	(90)
SCS-ωPBEPP86	PBE	P86	LC DH	7	(77)
SOS-ωPBEPP86	PBE	P86	LC DH	5	(77)
DSD-PBEP86	PBE	P86	global DH	4	(113)
PBE0-2	PBE	PBE	global DH	2	(114)
SOS-PBE0-2	PBE	PBE	global DH	3	(115)
PBE-QIDH	PBE	PBE	global DH	2	(116)
B2GPPLYP	B88	LYP	global DH	2	(117)
ωB97X-D	B97	B97	LC hybrid	18	(118)
CAM-B3LYP	B88	LYP	LC hybrid	3	(119)
PBE0	PBE	PBE	global hybrid	1	(120)

^{^a}

Both the CIS(D)- and ADC(2)-based approaches are discussed for all the DH functionals, except for SOS/SCS-ωPBEPP86. For more details regarding the ADC(2)-based formalism, see refs (82) and (91).

To gain some insight into the performance of the corresponding methods for valence excitations, we recommend comprehensive benchmark studies (77,90,91,121) for the interested readers.

The errors utilized for the evaluation of the VIPs and VEAs are calculated by subtracting the reference values from the computed ones. The statistical error measures presented in the figures are the mean absolute errors (MAEs), standard deviations (SDs), and maximum absolute errors (MAXs). All the computed raw energies are available in the Supporting Information (SI). In addition, the mean errors, deviations spans, and root-mean-square errors are also included.

3.2. The Benchmark Sets

Three different benchmark sets were selected from the literature to assess the performance of the methods, and currently, these compilations are regarded as the most comprehensive ones for VIP and VEA calculations. First, we discuss the benchmark compilation of Sherrill et al., (122) which contains 24 medium-sized organic acceptor molecules. This test set incorporates the first VIPs and VEAs of the corresponding systems. References obtained at the CCSD(T)/aug-cc-pVDZ level are used in this study, invoking the frozen core approximation.

Thereafter, the test set originally compiled by Bartlett and co-workers is analyzed. (123) Since this compilation was later simplified by Ortiz et al., (47) it is hereafter referred to as the BO benchmark set. The final set includes 170 valence ionized states of 33 small molecules using CCSDT/cc-pVTZ results as the reference. As can be seen, this test set contains several VIPs associated also with lower-lying valence orbitals. In contrast to the statistics presented in ref (124), all the VIPs are considered in this study. Similar to the original work, (123) the core electrons were correlated during the calculations.

Finally, the performance of the functionals for biochemically relevant systems is assessed. A benchmark compilation containing nucleobases was proposed by Śmiga and co-workers. (125) Recently, high-level VIPs and VEAs were computed by Tajti et al. (124) using a composite reference at the complete basis set (CBS) limit. As the CBS extrapolation is not trivial for DH-TDDFT calculations, in this study, values obtained at the CCSD(T)(a)*/cc-pVDZ level are used as the references. The benchmark set incorporates six electron-attached/detached states of five different molecules.

4. Results and Discussion

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In this section, the performance of the considered functionals is assessed. The results are discussed mainly from two aspects. First, the benefits of the ADC(2)-based formalism are compared with the CIS(D)-based one. Second, the effects of the DH formalism are examined in comparison with the corresponding wave function-based approaches. The importance of the spin-scaling techniques has already been emphasized by Tajti et al. (124) Accordingly, we do not discuss the outcomes from this aspect, especially for the wave function-based methods.

4.1. The Acceptor Test Set

The acceptor test set of Sherrill and co-workers (122) is discussed first. The error measures corresponding to the VIPs are visualized in Figure 1. Upon examining the MAEs, one can see that the highest accuracy is achieved by CCSD, with a MAE of 0.07 eV. These error measures for the SOS variant of ADC(2) and CIS(D), which are around 0.22 and 0.25 eV, respectively, are also acceptable. Among the ADC(2)-based DH methods, the best performances are attained by the spin-scaled RS-DH functionals. The MAEs for the SOS and SCS variants are 0.16 and 0.18 eV, respectively, while for SOS-PBE0-2, it is still around 0.30 eV. However, for the remaining functionals, the error exceeds 0.50 eV. It is somewhat surprising for DSD-PBEP86, which also contains spin-scaling parameters. Regarding the CIS(D)-based DH approaches, it can be concluded that the ADC(2)-based counterpart consistently outperforms the genuine variants. Nevertheless, SCS/SOS-ωPBEPP86 yields excellent results with MAEs of 0.12 and 0.15 eV. In addition, ωB97X-D is also outstanding with a MAE of 0.16 eV, while the error is significantly larger for CAM-B3LYP. A somewhat more balanced performance can be observed for the ADC(2)- and CIS(D)-based variants if the SDs and MAXs are considered. In this case, the SDs for the ADC(2)-based approaches range between 0.12 and 0.18 eV, while for the CIS(D)-based ones, they are between 0.14 and 0.22 eV. The MAXs for the most reliable DH methods are approximately 0.50 eV. These results can be achieved by ωB97X-D as well. In general, we can conclude that the error measures for the best functionals are lower in comparison with the corresponding wave function-based counterpart.

Figure 1. Error measures for the VIPs of the acceptor test set (122) using the aug-cc-pVDZ basis set with the corresponding auxiliary bases. The MAEs (SDs) are visualized by colored (black) bars, while MAXs are presented by dots. For the sake of clarity, some outliers are omitted. The wave function (first group), ADC(2)-based DH (second group), CIS(D)-based DH (third group), and hybrid methods (fourth group) are presented in gray, blue, red, and orange, respectively. The CCSD values were taken from ref (124).

Continuing the previous study, the error measures regarding the VEAs are presented in Figure 2. As can be seen, it is difficult to compete with the CCSD, SOS-CIS(D), and SOS-ADC(2) approaches. The lowest MAE, precisely 0.05 eV, is attained by CCSD, while the errors are still around 0.10 eV for SOS-CIS(D) and SOS-ADC(2). Among the ADC(2)- and CIS(D)-based DH functionals, the best performances are provided by the SOS-RS-PBE-P86 functionals. Unfortunately, in these cases, the MAEs are 0.40 and 0.46 eV, respectively. Nevertheless, these values are somewhat lower than those obtained for the standard ADC(2) and CIS(D) methods. This is also true for SOS-PBE0-2, while the remaining DH functionals have significantly higher MAEs. Acceptable performance is achieved by ωB97X-D, with a MAE of 0.44 eV. Inspecting the SDs, a somewhat more balanced picture can be obtained. The precision of CCSD is still outstanding with an SD of 0.06 eV; however, the other methods are very close to each other. That is, the SDs are 0.14 and 0.17 eV for ADC(2) and CIS(D), respectively, while they are around 0.13 eV for the SOS variants. The deviations do not exceed 0.15 eV for most of the DH functionals, while some of the best performers, such as the SOS-PBE0-2 functionals, have even lower SDs compared to the SOS-ADC(2) approach. A bit larger deviation, precisely 0.19 eV, is yielded by ωB97X-D. If the MAXs are considered, the performances are very similar to those obtained for the MAEs. Accordingly, the lowest MAXs, being 0.15, 0.24, and 0.27 eV, are achieved by CCSD, SOS-CIS(D), and SOS-ADC(2), respectively. These excellent results cannot be approached by any other methods. That is, the same measures are 0.85 and 0.97 eV for the standard ADC(2) and CIS(D) approaches, respectively. Among the DH functionals, the best results are provided by the ADC(2)- and CIS(D)-based SOS-RS-PBE-P86, with MAXs of 0.69 and 0.77 eV, respectively, while it is 0.76 eV for ωB97X-D.

Figure 2. Error measures for the VEAs of the acceptor test set (122) using the aug-cc-pVDZ basis set with the corresponding auxiliary bases. See the caption of Figure 1 for further details.

4.2. The Bartlett/Ortiz Test Set

Thereafter, the comprehensive BO benchmark set (47,123) is assessed. The main error measures are collected in Figure 3. Upon inspection of the error bars, we can conclude that the best results are achieved by the CCSD and ADC(2)-based SOS-RS-PBE-P86 approaches, with MAEs of 0.24 eV. The performance of the SOS-ADC(2) and the SCS variant of the former functional is also outstanding, with error measures that do not exceed 0.30 eV. In addition, the CIS(D)-based variants of the SOS/SCS-RS-PBE-P86, SOS-PBE0-2, and SCS/SOS-ωPBEPP86 functionals can also be deemed reliable. Overall, the CIS(D)-based approaches are slightly outperformed by the ADC(2)-based ones. For this benchmark set, the ωB97X-D functional is not outstanding at all. The MAE is 1.10 eV, which is significantly higher in comparison with the best DH approaches. Similar rankings can be determined when considering SDs. Among the wave function-based methods, the most precise results are provided by CCSD, with an SD of 0.23 eV, while an SD of 0.34 eV is obtained for the SOS-ADC(2) approach. In this regard, the performance is more balanced for the DH functionals. The lowest SD, which is 0.29 eV, is attained by the ADC(2)-based SOS-RS-PBE-P86 method, while an SD of around 0.35 eV is achieved by the remaining best performers. Again, this error measure is noticeably higher for ωB97X-D, with an SD of 0.51 eV. Upon examination of the MAXs, the lowest value of 1.32 eV is obtained for the ADC(2)-based SOS-PBE0-2 approach, while a MAX of 1.33 eV is attained by SOS-ADC(2). The ADC(2)-based SOS-RS-PBE-P86 is also outstanding, with an error of 1.53 eV, but most of the DH functionals are reliable, as the MAXs do not exceed 2.00 eV, whereas it is 1.81 for CCSD. A somewhat higher value, precisely 2.64 eV, is obtained for ωB97X-D.

Figure 3. Error measures for the VIPs of the BO test set (47,123) using the cc-pVTZ basis set with the corresponding auxiliary bases. See the caption of Figure 1 for further details.

4.3. Nucleobases

Finally, the performances for the nucleobases (124,125) are discussed. The error measures corresponding to the VIPs are presented in Figure 4. On the basis of the numerical results, surprisingly, the ADC(2)-based SOS-PBE0-2 and ωB97X-D are the best performers, with MAEs of 0.11 eV. Similarly, outstanding accuracy is achieved by the SOS-ADC(2) and ADC(2)-based SOS-RS-PBE-P86 methods, while the CCSD and SOS-ωPBEPP86 approaches also seem to be reliable. In these cases, the MAEs are below 0.15 eV. Comparing the ADC(2)- and CIS(D)-based functionals, again, the former ones outperform the latter ones. When examining the SDs, similar conclusions can be drawn. That is, excellent precision is observed for the SOS-PBE0-2 functionals, with deviations of around 0.06 eV, and CCSD also achieves a similar result. In this regard, the ADC(2)-based methods provide more balanced values. The SD is approximately 0.15 eV for the remaining DH functionals, which is highly acceptable, while a bit larger values are obtained for the ωB97X-D and the CIS(D)-based approaches, except for SOS-ωPBEPP86. The MAXs are also well-balanced for the best DHs, ranging between 0.24 and 0.36 eV, while it is 0.64 eV for ωB97X-D.

Figure 4. Error measures for the VIPs of the nucleobases (124,125) using the cc-pVDZ basis set with the corresponding auxiliary bases. See the caption of Figure 1 for further details.

The results for the electron-attached states of the nucleobases are collected in Figure 5. As can be seen, again, CCSD and the SOS variants of the wave function-based methods outperform the DH functionals. However, the differences are somewhat less pronounced than those obtained for the acceptor test set. That is, the lowest MAE, 0.06 eV, is attained by CCSD, while the SOS-ADC(2) and SOS-CIS(D) approaches achieve MAEs of 0.16 and 0.19 eV, respectively. Among the DH methods, the most accurate approach is the ADC(2)-based SOS-RS-PBE-P86, with a MAE of 0.30 eV. In addition, the CIS(D)-based counterpart is also superior in its class. The SCS variant of the former functionals, as well as the SOS-PBE0-2 and SCS/SOS-ωPBEPP86 methods provide acceptable performance. In these cases, the MAEs do not exceed 0.50 eV. For the remaining DH functionals, significantly higher errors are obtained, while the MAE is 0.37 eV for the ωB97X-D method. Upon examining the SDs, an interesting behavior can be observed. Regarding the DH approaches, the lowest deviations are yielded by the methods that are the most inaccurate. For instance, B2GPPLYP has an SD of 0.13 eV, while this value is larger even for SOS-ADC(2). The deviations are around 0.26 eV for the most accurate ADC(2)-based approaches, while they are approximately 0.30 eV for the CIS(D)-based counterparts. A similar precision is achieved by ωB97X-D, with an SD of 0.35 eV. The lowest MAX, being 0.22 eV, is reached by CCSD, while SOS-ADC(2) and SOS-CIS(D) are also outstanding in this regard. The maximum errors are 0.40 eV for the SOS second-order wave function methods. The performance of the best DH functionals is well-balanced within each class. The MAXs are around 0.70 eV for the ADC(2)-based approaches, while they are roughly 0.85 eV for the CIS(D)-based ones. For the hybrid functionals, the lowest MAX, precisely 0.93 eV, is attained by ωB97X-D.

Figure 5. Error measures for the VEAs of the nucleobases (124,125) using the cc-pVDZ basis set with the corresponding auxiliary bases. See the caption of Figure 1 for further details.

For this benchmark set, the effect of the second-order correction is also assessed. This study is also intriguing due to the fact that orbital energies can be interpreted as VIPs and VEAs within Koopmans’ theorem. However, it is important to keep in mind that these values only offer a simplified approximation of the corresponding quantities as the relaxation effects are neglected. For the VIPs, the mean errors are collected in Figure 6, while the corresponding chart for the VEAs can be found in the SI. Considering the negative values of occupied orbital energies, it can generally be concluded that VIPs are consistently overestimated. This is also true for the wave function-based methods. The second-order correction, to some extent, systematically reduces the VIP values. As can be seen, the methods that are least accurate inspecting the orbital energies, such as SOS-ADC(2), ADC(2)-based SOS-RS-PBE-P86, and SCS-ωPBEPP86, actually provide the most accurate VIPs in terms of the final result. In contrast, for methods where VIPs can be precisely described by the negative of orbital energies, such as DSD-PBEP86 and B2GPPLYP, the second-order correction significantly reduces the corresponding values, leading to inaccurate results for the DH calculations. Similar findings can be reported if VEAs are inspected; however, the effects are opposite to what was observed for VIPs. For the most precise methods, virtual orbital energies significantly underestimate VEAs, and the second-order correction systematically increases their values. For the (SOS-)PBE0-2 and DSD-PBEP86 methods, VEAs can be precisely described by the virtual orbital energies, while for the least accurate methods, such as B2GPPLYP, the orbital energies are already overestimated.

Figure 6. Mean errors for the VIPs of the nucleobases using the aug-cc-pVDZ basis sets with the corresponding auxiliary bases. Errors calculated from the orbital energies (final DH results) are visualized by the darker (lighter) bars. The wave function (first group), ADC(2)-based DH (second group), and CIS(D)-based DH (third group) methods are presented in gray, blue, and red, respectively.

4.4. Overall Performance

It is hard to characterize the performance of the methods with a single measure. Recently, a very simple procedure was suggested by Casanova-Páez and Goerigk. (77) In their original paper, the MAEs obtained for the benchmark sets were simply averaged. In this study, we use the same measure separately for VIPs and VEAs. From a practical point of view, the computational cost of the approaches is also important. In order to help with the selection of methods worth applying, the overall performance of the best approaches and the rate-determining steps of the calculations are collected in Table 2. Inspecting the results, we can conclude that the most reliable method is the most expensive CCSD, while the SOS-ADC(2) approach is also outstanding. Among the functionals, the most robust performance is attained by the ADC(2)-based SOS-RS-PBE-P86 method. For ionization potentials, it outperforms SOS-ADC(2), and almost CCSD quality can be achieved. This method also provides the lowest overall MAE for VEAs; however, the accuracy is far below that obtained for CCSD or SOS-ADC(2). As a cost-effective alternative, SOS-ωPBEPP86 is also recommended for VIPs, but its performance is even less reliable for electron-attached states.

Table 2. Averaged MAEs for VIPs and VEAs, as Well as the Number of Independent Parameters and the Scaling of the Rate-Determining Steps on Top of the KS/HF Solution for the Best Performers

		MAE			Scaling
Class	Method	VIP	VEA	Number of parameters	Ground state	VIP/VEA
wave function-based	CCSD	0.153	0.051	–	iterative N⁶	iterative N⁵
	SOS-ADC(2)	0.211	0.135	1	perturbative N⁴	iterative N⁴
	SOS-CIS(D)	0.325	0.146	1	perturbative N⁴	perturbative N⁴
	ADC(2)	0.585	0.431	–	perturbative N⁵	iterative N⁴
	CIS(D)	0.834	0.492	–	perturbative N⁴	perturbative N⁴
ADC(2)-based DH	SCS-RS-PBE-P86	0.212	0.458	4	perturbative N⁵	iterative N⁴
	SOS-RS-PBE-P86	0.182	0.354	3	perturbative N⁴	iterative N⁴
	SOS-PBE0-2	0.300	0.506	3	perturbative N⁴	iterative N⁴
CIS(D)-based DH	SCS-RS-PBE-P86	0.328	0.511	4	perturbative N⁴	perturbative N⁴
	SOS-RS-PBE-P86	0.306	0.396	3	perturbative N⁴	perturbative N⁴
	SCS-ωPBEPP86	0.256	0.683	7	perturbative N⁴	perturbative N⁴
	SOS-ωPBEPP86	0.226	0.552	5	perturbative N⁴	perturbative N⁴
	SOS-PBE0-2	0.352	0.518	3	perturbative N⁴	perturbative N⁴
LC hybrid	ωB97X-D	0.457	0.406	18	–	–
	CAM-B3LYP	0.924	1.121	3	–	–

5. Conclusions

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In this study, double-hybrid time-dependent density functional theory has been extended to directly calculate vertical ionization potentials and electron affinities. The approach has been presented for the genuine variant of the DH TDDFT theory, (71) where the second-order correction is calculated perturbatively relying on the CIS(D) method. In addition, our ADC(2)-based DH variant (82) has also been considered, where the double excitations are treated iteratively. It has been demonstrated that the costs of the VIP and VEA calculations with the CIS(D)-based DHs are just comparable to one KS iteration step per state, while for the ADC(2)-based ones, the most demanding step is proportional to N⁵. However, it has to be carried out only once, regardless of the number of tackled states, and the iterative procedure still scales as N⁴. For a detailed comparison, state-of-the-art RS-DH and LC-DH methods, including spin-scaling techniques, were selected, as well as robust and popular hybrid and global DH approaches were also included. To assess the performance of the functionals, comprehensive benchmark calculations were carried out on the best available test sets. A total of 224 electron-detached and 54 electron-attached states were examined, with references provided by higher-order coupled-cluster calculations that include triple excitations.

The findings were analyzed from two main perspectives. First, the robustness of the ADC(2)-based ansatz was inspected in contrast to the CIS(D)-based approach. In this regard, the advantages of the more advanced formalism are clearly demonstrated. Second, the impact of the DH approach was assessed in comparison with the corresponding wave function-based methods. The excellent performance of SOS-ADC(2) had already been revealed by Tajti and co-workers. (124) Accordingly, the efficiency of the approaches is compared to this starting point. Our numerical results show that, among the functionals, the most robust performance is attained by the ADC(2)-based SOS-RS-PBE-P86 approach. This method consistently outperforms SOS-ADC(2) for ionization potentials; furthermore, CCSD quality can also be reached. Unfortunately, the results are not so encouraging for electron affinities. Even though the best performance is achieved by the above functional, the accuracy is far below that obtained for SOS-ADC(2). For ionization potentials, the CIS(D)-based SOS-ωPBEPP86 is also recommended, while SOS-PBE0-2 is identified as the most reliable global DH functional. The importance of spin-scaling techniques was confirmed by this study as well, though the performance of DSD-PBEP86 is found to be somewhat disappointing. In addition, surprisingly good results were revealed for ωB97X-D, where the VIPs/VEAs are associated with the corresponding Kohn–Sham orbital energies within the present formalism. Nevertheless, ωB97X-D does not outperform the DHs concerning robustness.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.3c00363.

Computed vertical ionization potentials and electron affinities (XLSX)

ct3c00363_si_001.xlsx (238.02 kb)

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Author Information

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Corresponding Authors
- Dávid Mester - Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary; ELKH-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary; MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary; https://orcid.org/0000-0001-6570-2917; Email: [email protected]
- Mihály Kállay - Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary; ELKH-BME Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary; MTA-BME Lendület Quantum Chemistry Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary; https://orcid.org/0000-0003-1080-6625; Email: [email protected]
Notes
The authors declare no competing financial interest.

Acknowledgments

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The work of D.M. is supported by the NKFIH PD142372 grant and the ÚNKP-22-4-II-BME-157 New National Excellence Program of the Ministry for Culture and Innovation from the source of the National Research, Development, and Innovation Fund. M.K. is grateful for the financial support from the National Research, Development, and Innovation Office (NKFIH, Grant No. KKP126451). The research reported in this paper is part of project BME-EGA-02, implemented with the support provided by the Ministry of Innovation and Technology of Hungary from the National Research, Development and Innovation Fund, financed under the TKP2021 funding scheme. The computing time granted on the Hungarian HPC Infrastructure at NIIF Institute, Hungary is gratefully acknowledged.

References

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This article references 125 other publications.

1
Yeh, N.; Yeh, P. Organic solar cells: Their developments and potentials. Renew. Sust. Energy Rev. 2013, 21, 421, DOI: 10.1016/j.rser.2012.12.046
Google Scholar
1
Organic solar cells: Their developments and potentials
Yeh, Naichia; Yeh, Pulin
Renewable & Sustainable Energy Reviews (2013), 21 (), 421-431CODEN: RSERFH; ISSN:1364-0321. (Elsevier Ltd.)
This paper aims to review the developments and the potentials of org. photovoltaic, which has caught the attention of researchers of optoelectronics. The paper briefly introduces the physics underlying org. photovoltaic devices of donor-acceptor interfaces. It examines a variety of materials and architectures that benefit the performance of the org. photovoltaic cell; along with the important photogeneration factors including the exciton diffusion length as well as charge transport, sepn., and collection. The authors have reviewed the recent understanding of the mechanisms that govern these photocurrent generation steps and sketched out the search for alternative materials and device architectures. The review also discusses areas where active researches should be directed for cell efficiency improvement and outlines the issues to be resolved in order to speed up the commercialization.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXksFags78%253D&md5=5b1dad002a9c806cbc670b98ce8a8ccf
2
Poelking, C.; Benduhn, J.; Spoltore, D.; Schwarze, M.; Roland, S.; Piersimoni, F.; Neher, D.; Leo, K.; Vandewal, K.; Andrienko, D. Open-circuit voltage of organic solar cells: interfacial roughness makes the difference. Commun. Phys. 2022, 5, 307, DOI: 10.1038/s42005-022-01084-x
Google Scholar
2
Open-circuit voltage of organic solar cells: interfacial roughness makes the difference
Poelking, Carl; Benduhn, Johannes; Spoltore, Donato; Schwarze, Martin; Roland, Steffen; Piersimoni, Fortunato; Neher, Dieter; Leo, Karl; Vandewal, Koen; Andrienko, Denis
Communications Physics (2022), 5 (1), 307CODEN: CPOHDJ; ISSN:2399-3650. (Nature Portfolio)
Org. photovoltaics (PV) is an energy-harvesting technol. that offers many advantages, such as flexibility, low wt. and cost, as well as environmentally benign materials and manufg. techniques. Despite growth of power conversion efficiencies to around 19% in the last years, org. PVs still lag behind inorg. PV technologies, mainly due to high losses in open-circuit voltage. Understanding and improving open circuit voltage in org. solar cells is challenging, as it is controlled by the properties of a donor-acceptor interface where the optical excitations are sepd. into charge carriers. Here, we provide an electrostatic model of a rough donor-acceptor interface and test it exptl. on small mol. PV materials systems. The model provides concise relationships between the open-circuit voltage, photovoltaic gap, charge-transfer state energy, and interfacial morphol. In particular, we show that the electrostatic bias generated across the interface reduces the photovoltaic gap. This neg. influence on open-circuit voltage can, however, be circumvented by adjusting the morphol. of the donor-acceptor interface.
>> More from SciFinder ^®
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3
Delgado, J. L.; Bouit, P.-A.; Filippone, S.; Herranz, M. A. Á.; Martín, N. Organic photovoltaics: a chemical approach. Chem. Commun. 2010, 46, 4853, DOI: 10.1039/c003088k
Google Scholar
3
Organic photovoltaics: a chemical approach
Delgado, Juan Luis; Bouit, Pierre-Antoine; Filippone, Salvatore; Herranz, Ma. Angeles; Martin, Nazario
Chemical Communications (Cambridge, United Kingdom) (2010), 46 (27), 4853-4865CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
A review. The fundamental contribution of chem. to the multidisciplinary field of org. photovoltaics is presented in a systematic way through the wide variety of org. compds. synthesized to be successfully used in photovoltaic devices. Basic processes in org. solar cells, bulk heterojunction plastic solar cells based on semiconducting π-conjugated polymers and fullerenes, mol. bulk heterojunction solar cells based on π-conjugated oligomers or dyes and fullerenes, and org. solar cells with innovative carbon nanostructures are discussed.
>> More from SciFinder ^®
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Alizadeh, E.; Sanche, L. Precursors of Solvated Electrons in Radiobiological Physics and Chemistry. Chem. Rev. 2012, 112, 5578, DOI: 10.1021/cr300063r
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Precursors of Solvated Electrons in Radiobiological Physics and Chemistry
Alizadeh, Elahe; Sanche, Leon
Chemical Reviews (Washington, DC, United States) (2012), 112 (11), 5578-5602CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
A review. The following topics are discussed: Secondary electrons in water; low-energy electrons (LEEs) and damage to cellular constituents (DNA, protein subunits, amino acids, peptides); LEEs in Radiobiol. and radiation therapy; Prehydrated electrons interacting with biomols.
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Alizadeh, E.; Orlando, T. M.; Sanche, L. Biomolecular Damage Induced by Ionizing Radiation: The Direct and Indirect Effects of Low-Energy Electrons on DNA. Annu. Rev. Phys. Chem. 2015, 66, 379, DOI: 10.1146/annurev-physchem-040513-103605
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Biomolecular damage induced by ionizing radiation: the direct and indirect effects of low-energy electrons on DNA
Alizadeh, Elahe; Orlando, Thomas M.; Sanche, Leon
Annual Review of Physical Chemistry (2015), 66 (), 379-398CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)
Many exptl. and theor. advances have recently allowed the study of direct and indirect effects of low-energy electrons (LEEs) on DNA damage. In an effort to explain how LEEs damage the human genome, researchers have focused efforts on LEE interactions with bacterial plasmids, DNA bases, sugar analogs, phosphate groups, and longer DNA moieties. Here, we summarize the current understanding of the fundamental mechanisms involved in LEE-induced damage of DNA and complex biomol. films. Results obtained by several labs. on films prepd. and analyzed by different methods and irradiated with different electron-beam current densities and fluencies are presented. Despite varied conditions (e.g., film thicknesses and morphologies, intrinsic water content, substrate interactions, and extrinsic atm. compns.), comparisons show a striking resemblance in the types of damage produced and their yield functions. The potential of controlling this damage using mol. and nanoparticle targets with high LEE yields in targeted radiation-based cancer therapies is also discussed.
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Kumar, A.; Becker, D.; Adhikary, A.; Sevilla, M. D. Reaction of Electrons with DNA: Radiation Damage to Radiosensitization. Int. J. Mol. Sci. 2019, 20, 3998, DOI: 10.3390/ijms20163998
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Reaction of electrons with DNA: radiation damage to radiosensitization
Kumar, Anil; Becker, David; Adhikary, Amitava; Sevilla, Michael D.
International Journal of Molecular Sciences (2019), 20 (16), 3998CODEN: IJMCFK; ISSN:1422-0067. (MDPI AG)
This review article provides a concise overview of electron involvement in DNA radiation damage. The review begins with the various states of radiation-produced electrons: Secondary electrons (SE), low energy electrons (LEE), electrons at near zero kinetic energy in water (quasi-free electrons, (e-qf)) electrons in the process of solvation in water (presolvated electrons, e-pre), and fully solvated electrons (e-aq). a current summary of the structure of e-aq, and its reactions with DNA-model systems is presented. Theor. works on redn. potentials of DNA-bases were found to be in agreement with expts. This review points out the proposed role of LEE-induced frank DNA-strand breaks in ion-beam irradiated DNA. The final section presents radiation-produced electron-mediated site-specific formation of oxidative neutral aminyl radicals from azidonucleosides and the evidence of radiosensitization provided by these aminyl radicals in azidonucleoside-incorporated breast cancer cells.
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Zheng, Y.; Cloutier, P.; Hunting, D. J.; Sanche, L.; Wagner, J. R. Chemical Basis of DNA Sugar–Phosphate Cleavage by Low-Energy Electrons. J. Am. Chem. Soc. 2005, 127, 16592, DOI: 10.1021/ja054129q
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Chemical basis of DNA sugar-phosphate cleavage by low-energy electrons
Zheng, Yi; Cloutier, Pierre; Hunting, Darel J.; Sanche, Leon; Wagner, J. Richard
Journal of the American Chemical Society (2005), 127 (47), 16592-16598CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
DNA damage by low-energy electrons (LEE) was examd. using a novel system in which thin solid films of oligonucleotide tetramers (CGTA and GCAT) were irradiated with monoenergetic electrons (10 eV) under ultrahigh vacuum. The products of irradn. were examd. by HPLC. These analyses permitted the quantitation of 16 nonmodified nucleobase, nucleoside, and nucleotide fragments of each tetramer resulting from the cleavage of phosphodiester and N-glycosidic bonds. The distribution of nonmodified products suggests a mechanism of damage involving initial electron attachment to nucleobase moieties, followed by electron transfer to the sugar-phosphate backbone, and subsequent dissocn. of the phosphodiester bond. Moreover, virtually all the nonmodified fragments contained a terminal phosphate group at the site of cleavage. These results demonstrate that the phosphodiester bond breaks by a distinct pathway in which the neg. charge localizes on the phosphodiester bond giving rise to nonmodified fragments with an intact phosphate group. Conversely, the radical must localize on the sugar moiety to give as yet unidentified modifications. In summary, the reaction of LEE with simple tetramers involved dissociative electron attachment leading to phosphodiester bond cleavage and the formation of nonmodified fragments.
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Dong, Y.; Gao, Y.; Liu, W.; Gao, T.; Zheng, Y.; Sanche, L. Clustered DNA Damage Induced by 2–20 eV Electrons and Transient Anions: General Mechanism and Correlation to Cell Death. J. Phys. Chem. Lett. 2019, 10, 2985, DOI: 10.1021/acs.jpclett.9b01063
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Clustered DNA Damage Induced by 2-20 eV Electrons and Transient Anions: General Mechanism and Correlation to Cell Death
Dong, Yanfang; Gao, Yingxia; Liu, Wenhui; Gao, Ting; Zheng, Yi; Sanche, Leon
Journal of Physical Chemistry Letters (2019), 10 (11), 2985-2990CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
The mechanisms of action of low-energy electrons (LEEs) generated in large quantities by ionizing radiation constitute an essential element of our understanding of early events in radiolysis and radiobiol. We present the 2-20 eV electron energy dependence of the yields of base damage (BD), BD-related crosslinks (CLs), and non-double-strand break (NDSB) clustered damage induced in DNA. These new yield functions are generated by the impact of LEEs on plasmid DNA films. The damage is analyzed by gel electrophoresis with and without enzyme treatment. Maxima at 5 and 10 eV in BDs and BD-related CLs yield functions, and two others, at 6 and 10 eV, in those of NDSB clustered damage are ascribed to core-excited transient anions that decay into bond-breaking channels. The mechanism causing all types of DNA damages can be attributed to the capture of a single electron by a base followed by multiple different electron transfer pathways.
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Mukherjee, M.; Tripathi, D.; Brehm, M.; Riplinger, C.; Dutta, A. K. Efficient EOM-CC-based Protocol for the Calculation of Electron Affinity of Solvated Nucleobases: Uracil as a Case Study. J. Chem. Theory Comput. 2021, 17, 105, DOI: 10.1021/acs.jctc.0c00655
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Efficient EOM-CC-based Protocol for the Calculation of Electron Affinity of Solvated Nucleobases: Uracil as a Case Study
Mukherjee, Madhubani; Tripathi, Divya; Brehm, Martin; Riplinger, Christoph; Dutta, Achintya Kumar
Journal of Chemical Theory and Computation (2021), 17 (1), 105-116CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
We present an explicit solvation protocol for the calcn. of electron affinity values of the solvated nucleobases. The protocol uses a quantum mechanics/mol. mechanics (QM/MM) approach based on the newly implemented domain-based pair natural orbital EOM-CCSD (equation-of-motion coupled-cluster single-double) method. The stability of the solvated nucleobase anion is sensitive to the local distribution of the water mols. around the nucleobase, and the calcd. electron affinity values converge slowly with respect to the no. of snapshots and the size of the water box. The use of nonpolarizable water mols. leads to an overestimation of the electron affinity and makes the result sensitive to the size of the QM region in the QM/MM calcn. The electron affinity values, although sensitive to the size of the basis set, lead to an almost const. blue shift of the electron affinity upon the increase in the basis set. The present protocol allows for a controllable description of the various parameters affecting the electron affinity value, and the calcd. adiabatic electron affinity values are in excellent agreement with exptl. results.
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Verma, P.; Ghosh, D.; Dutta, A. K. Electron Attachment to Cytosine: The Role of Water. J. Phys. Chem. A 2021, 125, 4683, DOI: 10.1021/acs.jpca.0c10199
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Electron Attachment to Cytosine: The Role of Water
Verma, Pooja; Ghosh, Debashree; Dutta, Achintya Kumar
Journal of Physical Chemistry A (2021), 125 (22), 4683-4694CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
We present an EOM-CCSD-based quantum mech./mol. mech. (QM/MM) study on the electron attachment process to solvated cytosine. The electron attachment in the bulk solvated cytosine occurs through a doorway mechanism, where the initial electron is localized on water. The electron is subsequently transferred to cytosine by the mixing of electronic and nuclear degrees of freedom, which occurs on an ultrafast time scale. The bulk water environment stabilizes the cytosine-bound anion by an extensive hydrogen-bond network and drastically enhances the electron transfer rate from that obsd. in the gas phase. Microhydration studies cannot reproduce the effect of the bulk water environment on the electron attachment process, and one needs to include a large no. of water mols. in the calcn. to obtain converged results. The predicted adiabatic electron affinity and electron transfer rate obtained from our QM/MM calcns. are consistent with the available exptl. results.
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Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133, DOI: 10.1103/PhysRev.140.A1133
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Zhan, C.-G.; Nichols, J. A.; Dixon, D. A. Ionization Potential, Electron Affinity, Electronegativity, Hardness, and Electron Excitation Energy: Molecular Properties from Density Functional Theory Orbital Energies. J. Phys. Chem. A 2003, 107, 4184, DOI: 10.1021/jp0225774
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Ionization Potential, Electron Affinity, Electronegativity, Hardness, and Electron Excitation Energy: Molecular Properties from Density Functional Theory Orbital Energies
Zhan, Chang-Guo; Nichols, Jeffrey A.; Dixon, David A.
Journal of Physical Chemistry A (2003), 107 (20), 4184-4195CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
Representative at. and mol. systems, including various inorg. and org. mols. with covalent and ionic bonds, have been studied by using d. functional theory. The calcns. were done with the commonly used exchange-correlation functional B3LYP followed by a comprehensive anal. of the calcd. highest-occupied and lowest-unoccupied Kohn-Sham orbital (HOMO and LUMO) energies. The basis set dependence of the DFT results shows that the economical 6-31+G* basis set is generally sufficient for calcg. the HOMO and LUMO energies (if the calcd. LUMO energies are neg.) for use in correlating with mol. properties. The directly calcd. ionization potential (IP), electron affinity (EA), electronegativity (χ), hardness (η), and first electron excitation energy (τ) are all in good agreement with the available exptl. data. A generally applicable linear correlation relationship exists between the calcd. HOMO energies and the exptl./calcd. IPs. We have also found satisfactory linear correlation relationships between the calcd. LUMO energies and exptl./calcd. EAs (for the bound anionic states), between the calcd. av. HOMO/LUMO energies and χ values, between the calcd. HOMO-LUMO energy gaps and η values, and between the calcd. HOMO-LUMO energy gaps and exptl./calcd. first excitation energies. By using these linear correlation relationships, the calcd. HOMO and LUMO energies can be employed to semiquant. est. ionization potential, electron affinity, electronegativity, hardness, and first excitation energy.
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Perdew, J. P.; Levy, M. Comment on “Significance of the highest occupied Kohn–Sham eigenvalue. Phys. Rev. B 1997, 56, 16021, DOI: 10.1103/PhysRevB.56.16021
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Comment on "Significance of the highest occupied Kohn-Sham eigenvalue"
Perdew, John P.; Levy, Mel
Physical Review B: Condensed Matter (1997), 56 (24), 16021-16028CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
With more explanation than usual and without appeal to Janak's theorem, we discuss the statement and proof of the ionization potential theorems for the exact Kohn-Sham d.-functional theory of a many-electron system: (1) For any av. electron no. N between the integers Z - 1 and Z, and thus for N → Z from below, the highest occupied or partly occupied Kohn-Sham orbital energy is minus the ionization energy of the Z-electron system. (2) For Z - 1 < N < Z, the exact Kohn-Sham effective potential vs(r) tends to zero as |r| → ∞. We then argue that an objection to these theorems [L. Kleinman, Phys. Rev. B 56, 12042 (1997)] overlooks a crucial step in the proof of theorem (2): The asymptotic exponential decay of the exact electron d. of the Z-electron system is controlled by the exact ionization energy, but the decay of an approx. d. is not controlled by the approx. ionization energy. We discuss relevant evidence from the numerical construction of the exact Kohn-Sham potential. In particular, we point out a model two-electron problem for which the ionization potential theorems are exactly confirmed. Finally, we comment on related issues: the self-interaction correction, the discontinuity of the exact Kohn-Sham potential as N passes through the integer Z, and the generalized sum rule on the exchange-correlation hole.
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Levy, M.; Perdew, J. P.; Sahni, V. Exact differential equation for the density and ionization energy of a many-particle system. Phys. Rev. A 1984, 30, 2745, DOI: 10.1103/PhysRevA.30.2745
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Zhang, G.; Musgrave, C. B. Comparison of DFT Methods for Molecular Orbital Eigenvalue Calculations. J. Phys. Chem. A 2007, 111, 1554, DOI: 10.1021/jp061633o
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Comparison of DFT Methods for Molecular Orbital Eigenvalue Calculations
Zhang, Gang; Musgrave, Charles B.
Journal of Physical Chemistry A (2007), 111 (8), 1554-1561CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
We report how closely the Kohn-Sham HOMO and LUMO eigenvalues of 11 d. functional theory (DFT) functionals, resp., correspond to the neg. ionization potentials (-IPs) and electron affinities (EAs) of a test set of mols. We also report how accurately the HOMO-LUMO gaps of these methods predict the lowest excitation energies using both time-independent and time-dependent DFT (TD-DFT). The 11 DFT functionals include the local spin d. approxn. (LSDA), five generalized gradient approxn. (GGA) functionals, three hybrid GGA functionals, one hybrid functional, and one hybrid meta GGA functional. We find that the HOMO eigenvalues predicted by KMLYP, BH and HLYP, B3LYP, PW91, PBE, and BLYP predict the -IPs with av. abs. errors of 0.73, 1.48, 3.10, 4.27, 4.33, and 4.41 eV, resp. The LUMOs of all functionals fail to accurately predict the EAs. Although the GGA functionals inaccurately predict both the HOMO and LUMO eigenvalues, they predict the HOMO-LUMO gap relatively accurately (∼0.73 eV). On the other hand, the LUMO eigenvalues of the hybrid functionals fail to predict the EA to the extent that they include HF exchange, although increasing HF exchange improves the correspondence between the HOMO eigenvalue and -IP so that the HOMO-LUMO gaps are inaccurately predicted by hybrid DFT functionals. We find that TD-DFT with all functionals accurately predicts the HOMO-LUMO gaps. A linear correlation between the calcd. HOMO eigenvalue and the exptl. -IP and calcd. HOMO-LUMO gap and exptl. lowest excitation energy enables us to derive a simple correction formula.
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Grimme, S. Semiempirical hybrid density functional with perturbative second-order correlation. J. Chem. Phys. 2006, 124, 034108, DOI: 10.1063/1.2148954
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Semiempirical hybrid density functional with perturbative second-order correlation
Grimme, Stefan
Journal of Chemical Physics (2006), 124 (3), 034108/1-034108/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A new hybrid d. functional for general chem. applications is proposed. It is based on a mixing of std. generalized gradient approxns. (GGAs) for exchange by Becke (B) and for correlation by Lee, Yang, and Parr (LYP) with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional contains only two global parameters that describe the mixt. of HF and GGA exchange (ax) and of the PT2 and GGA correlation (c), resp. The parameters are obtained in a least-squares-fit procedure to the G2/97 set of heat of formations. Opposed to conventional hybrid functionals, the optimum ax is found to be quite large (53% with c = 27%) which at least in part explains the success for many problematic mol. systems compared to conventional approaches. The performance of the new functional termed B2-PLYP is assessed by the G2/97 std. benchmark set, a second test suite of atoms, mols., and reactions that are considered as electronically very difficult (including transition-metal compds., weakly bonded complexes, and reaction barriers) and comparisons with other hybrid functionals of GGA and meta-GGA types. According to many realistic tests, B2-PLYP can be regarded as the best general purpose d. functional for mols. (e.g., a mean abs. deviation for the two test sets of only 1.8 and 3.2 kcal/mol compared to about 3 and 5 kcal/mol, resp., for the best other d. functionals). Very importantly, also the max. and minium errors (outliers) are strongly reduced (by about 10-20 kcal/mol). Furthermore, very good results are obtained for transition state barriers but unlike previous attempts at such a good description, this definitely comes not at the expense of equil. properties. Preliminary calcns. of the equil. bond lengths and harmonic vibrational frequencies for diat. mols. and transition-metal complexes also show very promising results. The uniformity with which B2-PLYP improves for a wide range of chem. systems emphasizes the need of (virtual) orbital-dependent terms that describe nonlocal electron correlation in accurate exchange-correlation functionals. From a practical point of view, the new functional seems to be very robust and it is thus suggested as an efficient quantum chem. method of general purpose.
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Goerigk, L.; Grimme, S. Double-hybrid density functionals. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2014, 4, 576, DOI: 10.1002/wcms.1193
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Double-hybrid density functionals
Goerigk, Lars; Grimme, Stefan
Wiley Interdisciplinary Reviews: Computational Molecular Science (2014), 4 (6), 576-600CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
Double-hybrid d. functionals (DHDFs) are reviewed in this study. In DHDFs parts of conventional d. functional theory (DFT) exchange and correlation are replaced by contributions from nonlocal Fock-exchange and second-order perturbative correlation. The latter portion is based on the well-known MP2 wave-function approach in which, however, Kohn-Sham orbitals are used to calc. its contribution. First, related methods preceding this idea are reviewed, followed by a thorough discussion of the first modern double-hybrid B2-PLYP. Parallels and differences between B2-PLYP and its various successors are then outlined. This discussion is rounded off with representative thermochem. examples demonstrating that DHDFs belong to the most robust and accurate DFT approaches currently available. This anal. also presents hitherto unpublished results for recently developed DHDFs. Finally, how double-hybrids can be combined with linear-response time-dependent DFT is also outlined and the value of this approach for electronically excited states is shown. WIREs Comput Mol Sci 2014, 4:576-600. doi: 10.1002/wcms.1193 For further resources related to this article, please visit the . Conflict of interest: The authors have declared no conflicts of interest for this article.
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Brémond, É.; Ciofini, I.; Sancho-García, J. C.; Adamo, C. Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists. Acc. Chem. Res. 2016, 49, 1503, DOI: 10.1021/acs.accounts.6b00232
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Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists
Bremond, Eric; Ciofini, Ilaria; Sancho-Garcia, Juan Carlos; Adamo, Carlo
Accounts of Chemical Research (2016), 49 (8), 1503-1513CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
A review. D. functional theory (DFT) emerged in the last two decades as the most reliable tool for the description and prediction of properties of mol. systems and extended materials, coupling in an unprecedented way high accuracy and reasonable computational cost. This success rests also on the development of more and more performing d. functional approxns. (DFAs). Indeed, the Achilles' heel of DFT is represented by the exchange-correlation contribution to the total energy, which, being unknown, must be approximated. Since the beginning of the 1990s, global hybrids (GH) functionals, where an explicit dependence of the exchange-correlation energy on occupied Kohn-Sham orbitals is introduced thanks to a fraction of Hartree-Fock-like exchange, imposed themselves as the most reliable DFAs for chem. applications. However, if these functionals normally provide results of sufficient accuracy for most of the cases analyzed, some properties, such as thermochem. or dispersive interactions, can still be significantly improved. A possible way out is represented by the inclusion, into the exchange-correlation functional, of an explicit dependence on virtual Kohn-Sham orbitals via perturbation theory. This leads to a new class of functionals, called double-hybrids (DHs). In this Account, we describe our nonempirical approach to DHs, which, following the line traced by the Perdew-Burke-Ernzerhof approach, allows for the definition of a GH (PBE0) and a DH (QIDH) model. In such a way, a whole family of nonempirical functionals, spanning on the highest rungs of the Perdew's quality scale, is now available and competitive with other-more empirical-DFAs. Discussion of selected cases, ranging from thermochem. and reactions to weak interactions and excitation energies, not only show the large range of applicability of nonempirical DFAs, but also underline how increasing the no. of theor. constraints parallels with an improvement of the DFA's numerical performances. This fact further consolidates the strong theor. framework of nonempirical DFAs.Finally, even if nonempirical DH approaches are still computationally expensive, relying on the fact that they can benefit of all tech. enhancements developed for speeding up post-Hartree-Fock methods, there is substantial hope for their near future routine application to the description and prediction of complex chem. systems and reactions.
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Martin, J. M. L.; Santra, G. Empirical Double-Hybrid Density Functional Theory: A ‘Third Way’ in Between WFT and DFT. Isr. J. Chem. 2020, 60, 787, DOI: 10.1002/ijch.201900114
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Empirical Double-Hybrid Density Functional Theory: A 'Third Way' in Between WFT and DFT
Martin, Jan M. L.; Santra, Golokesh
Israel Journal of Chemistry (2020), 60 (8-9), 787-804CODEN: ISJCAT; ISSN:0021-2148. (Wiley-VCH Verlag GmbH & Co. KGaA)
A review. Double hybrid d. functional theory arguably sits on the seamline between wavefunction methods and DFT: it represents a special case of Rung 5 on the "Jacob's Ladder" of John P. Perdew. For large and chem. diverse benchmarks such as GMTKN55, empirical double hybrid functionals with dispersion corrections can achieve accuracies approaching wavefunction methods at a cost not greatly dissimilar to hybrid DFT approaches, provided RI-MP2 and/or another MP2 acceleration techniques are available in the electronic structure code. Only a half-dozen or fewer empirical parameters are required. For vibrational frequencies, accuracies intermediate between CCSD and CCSD(T) can be achieved, and performance for other properties is encouraging as well. Organometallic reactions can likewise be treated well, provided static correlation is not too strong. Further prospects are discussed, including range-sepd. and RPA-based approaches.
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Su, N. Q.; Xu, X. The XYG3 Type of Doubly Hybrid Density Functionals. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2016, 6, 721, DOI: 10.1002/wcms.1274
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The XYG3 type of doubly hybrid density functionals
Su, Neil Qiang; Xu, Xin
Wiley Interdisciplinary Reviews: Computational Molecular Science (2016), 6 (6), 721-747CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
Doubly hybrid (DH) functionals have emerged as a new class of d. functional approxns. (DFAs), which not only have a nonlocal orbital-dependent component in the exchange part, but also incorporate the information of unoccupied orbitals in the correlation part, being at the top rung of Perdew's view of Jacob's ladder in DFAs. This review article focuses on the XYG3 type of DH (xDH) functionals, which use a low rung functional to perform the self-consistent-field calcn. to generate orbitals and densities, with which a top rung DH functional is used for final energy evaluation. We will discuss the theor. background of the xDH functionals, briefly reviewing the adiabatic connection formalism, coordinate scaling relations, and Goerling-Levy perturbation theory. General performance of the xDH functionals will be presented for both energies and structures. In particular, we will present the fractional charge behaviors of the xDH functionals, examg. the self-interaction errors, the delocalization errors and the deviation from the linearity condition, as well as their effects on the predicted ionization potentials, electron affinities and fundamental gaps. This provides a theor. rationale for the obsd. good performance of the xDH functionals. WIREs Comput Mol Sci 2016, 6:721-747. doi: 10.1002/wcms.1274 For further resources related to this article, please visit the .
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Sancho-García, J. C.; Adamo, C. Double-hybrid density functionals: Merging wavefunction and density approaches to get the best of both worlds. Phys. Chem. Chem. Phys. 2013, 15, 14581, DOI: 10.1039/c3cp50907a
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Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds
Sancho-Garcia, J. C.; Adamo, C.
Physical Chemistry Chemical Physics (2013), 15 (35), 14581-14594CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
A review. We review why and how double-hybrid d. functionals have become new leading actors in the field of computational chem., thanks to the combination of an unprecedented accuracy together with large robustness and reliability. Similar to their predecessors, the widely employed hybrid d. functionals, they are rooted in the Adiabatic Connection Method from which they emerge in a natural way. We present recent achievements concerning applications to chem. systems of the most interest, and current extensions to deal with challenging issues such as non-covalent interactions and excitation energies. These promising methods, despite a slightly higher computational cost than other typical d.-based models, are called to play a key role in the near future and can thus pave the way towards new discoveries or advances.
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Geertsen, J.; Rittby, M.; Bartlett, R. J. The equation-of-motion coupled-cluster method: Excitation energies of Be and CO. Chem. Phys. Lett. 1989, 164, 57, DOI: 10.1016/0009-2614(89)85202-9
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The equation-of-motion coupled-cluster method: excitation energies of beryllium and carbon monoxide
Geertsen, Jan; Rittby, Magnus; Bartlett, Rodney J.
Chemical Physics Letters (1989), 164 (1), 57-62CODEN: CHPLBC; ISSN:0009-2614.
The equation-of-motion coupled-cluster (EOM-CC) method for the calcn. of excitation energies is presented. The procedure is based upon representing an excited state as an excitation from a coupled-cluster ground state and the excitation energies are obtained by solving a non-Hermitian eigenvalue problem. Numerical applications are reported for Be and CO, and the compared to full CI, Fock space multi-ref. coupled-cluster, multi-ref. MBPT, and propagator results.
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Stanton, J. F.; Bartlett, R. J. The equation of motion coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties. J. Chem. Phys. 1993, 98, 7029, DOI: 10.1063/1.464746
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23
The equation-of-motion, coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited-state properties
Stanton, John F.; Bartlett, Rodney J.
Journal of Chemical Physics (1993), 98 (9), 7029-39CODEN: JCPSA6; ISSN:0021-9606.
A comprehensive overview of the equation of motion coupled-cluster (EOM-CC) method and its application to mol. systems is presented. By exploiting the biorthogonal nature of the theory, it is shown that excited-state properties and transition strengths can be evaluated via a generalized expectation-value approach that incorporates both the bra and ket state wave functions. Reduced d. matrixes defined by this procedure are given by closed form expressions. For the root of the EOM-CC effective Hamiltonian that corresponds to the ground state, the resulting equations are equiv. to the usual expressions for normal single-ref. CC d. matrixes. Thus, the method described in this paper provides a universal definition of coupled-cluster d. matrixes, providing a link between EOM-CC and traditional ground state CC theory. Excitation energy, oscillator strength, and property calcns. are illustrated by means of several numerical examples, including comparisons with full CI calcns. and a detailed study of the 10 lowest electronically excited states of the cyclic isomer of C4.
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Watts, J. D.; Bartlett, R. J. The inclusion of connected triple excitations in the equation-of-motion coupled-cluster method. J. Chem. Phys. 1994, 101, 3073, DOI: 10.1063/1.467620
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The inclusion of connected triple excitations in the equation-of-motion coupled-cluster method
Watts, John D.; Bartlett, Rodney
Journal of Chemical Physics (1994), 101 (4), 3073-8CODEN: JCPSA6; ISSN:0021-9606.
The implementation of connected triple excitations in the equation-of-motion (EOM) coupled-cluster (CC) method for excitation energies is reported for the first time. The ref. state is described by the complete CC singles, doubles, and triples (CCSDT) method. Excited states are generated from the ref. state wave function by the action of a linear excitation operator including single, double, and triple excitations. The excited state wave functions and energies are obtained by diagonalizing the effective Hamiltonian e-THeT, where T is the cluster operator for the ref. state, in the space of singly, doubly, and triply excited determinants. Comparison is made with full CI excitation energies for several examples (CH+, Be, SiH2, and CH2). These show that EOM-CCSDT is able to describe states which are doubly excited relative to the ref. state, as well as singly excited states. Calcns. of several excitation energies of BH using an extended basis set are also reported, and show good agreement with expt.
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Bartlett, R. J. Coupled-cluster theory and its equation-of-motion extensions. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 126, DOI: 10.1002/wcms.76
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25
Coupled-cluster theory and its equation-of-motion extensions
Bartlett, Rodney J.
Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (1), 126-138CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
A review. Coupled-cluster theory offers today's ref. quantum chem. method for most of the problems encountered in electronic structure theory. It has been instrumental in establishing the now well-known paradigm of converging, many-body methods, MBPT2 < CCD < CCSD < MBPT4 < CCSD(T) < CCSDT-n < CCSDT < CCSDT(Q) < CCSDTQ-n < CCSDTQ < fullCI. Many-body perturbation theory (MBPT) for second, MBPT2, and fourth-order MBPT4; and coupled-cluster (CC) theory for different categories of excitations, singles, doubles, triples, quadruples (SDTQ). Although built on the same basic concept as CI (CI), many-body methods fundamentally improve upon CI approxns. by introducing the property of size extensivity, meaning that contrary to any truncated CI all terms properly scale with the no. of electrons in the problem. This fundamental aspect of many-electron methods leads to the exceptional performance of CC theory and its finite-order MBPT approxns. plus its equation-of-motion extensions for excited, ionized, and electron attached states. This brief overview will describe formal aspects of the theory which should be understood by perspective users of CC methods. We will also comment on some current developments that are improving the theory's accuracy or applicability.
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Sneskov, K.; Christiansen, O. Excited state coupled cluster methods. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 566, DOI: 10.1002/wcms.99
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Excited state coupled cluster methods
Sneskov, Kristian; Christiansen, Ove
Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (4), 566-584CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
We review coupled cluster (CC) theory for electronically excited states. We outline the basics of a CC response theory framework that allows the transfer of the attractive accuracy and convergence properties assocd. with CC methods over to the calcn. of electronic excitation energies and properties. Key factors affecting the accuracy of CC excitation energy calcns. are discussed as are some of the key CC models in this field. To aid both the practitioner as well as the developer of CC excited state methods, we also briefly discuss the key computational steps in a working CC response implementation. Approaches aimed at extending the application range of CC excited state methods either in terms of mol. size and phenomena or in terms of environment (soln. and proteins) are also discussed.
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Nooijen, M.; Bartlett, R. J. Similarity transformed equation-of-motion coupled-cluster theory: Details, examples, and comparisons. J. Chem. Phys. 1997, 107, 6812, DOI: 10.1063/1.474922
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27
Similarity transformed equation-of-motion coupled-cluster theory: Details, examples, and comparisons
Nooijen, Marcel; Bartlett, Rodney J.
Journal of Chemical Physics (1997), 107 (17), 6812-6830CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The similarity transformed equation-of-motion coupled-cluster (STEOM-CC) method is presented in full detail. Comparisons are made with the Fock space coupled-cluster (FSCC) method and the equation-of-motion coupled-cluster (EOM-CC) scheme. The role of implicit triple excitations and, relatedly, charge transfer separability in STEOM is discussed. The dependence on the choice of active space in STEOM is addressed and criteria for the selection of the active space are given. The evaluation of properties within STEOM is outlined and a large no. of illustrative examples of STEOM is presented.
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Stanton, J. F.; Gauss, J. Perturbative treatment of the similarity transformed Hamiltonian in equation-of-motion coupled-cluster approximations. J. Chem. Phys. 1995, 103, 1064, DOI: 10.1063/1.469817
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Perturbative treatment of the similarity transformed Hamiltonian in equation-of-motion coupled-cluster approximations
Stanton, John F.; Gauss, Juergen
Journal of Chemical Physics (1995), 103 (3), 1064-76CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A series of size-consistent approxns. to the equation-of-motion coupled cluster method in the singles and doubles approxn. (EOM-CCSD) are developed by subjecting the similarity transformed Hamiltonian ‾H = exp(-T)H exp(T) to a perturbation expansion. Attention is directed to N and N - 1 electron final state realizations of the method defined by truncation of ‾H at second order. Explicit spin-orbital equations for the energy and its first deriv. are documented for both approaches [EOMEE-CCSD(2) and EOMIP-CCSD(2), resp.], and have been implemented in a large-scale quantum chem. program. Vertical ionization potentials calcd. by EOMIP-CCSD(2) are shown to be equiv. to those of an approach presented recently by Nooijen and Snijders [J. Chem. Phys. 102, 1681,(1995)]. Applications of both EOMIP-CCSD(2) and EOMEE-CCSD(2) provide results for final state properties that compare favorably with those obtained in full EOM-CCSD calcns. Anal. of the computational aspects of the approx. and full EOM-CCSD methods shows that the cost of EOMIP-CCSD(2) energy and gradient calcns. scales in proportion to the fifth power of the basis set size, a significant savings over the sixth power dependence of EOMIP-CCSD. This feature is of great practical importance, as it shows that this N - 1 electron final state approach has a large domain of applicability and is therefore likely to become a valuable tool for application calcns. On the other hand, the same cannot be said for EOMEE-CCSD(2) since its asymptotic computational dependence and storage requirements are the same as the full EOMEE-CCSD method.
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Stanton, J. F.; Gauss, J. Analytic energy derivatives for ionized states described by the equation-of-motion coupled cluster method. J. Chem. Phys. 1994, 101, 8938, DOI: 10.1063/1.468022
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Analytical energy derivatives for ionized states described by the equation-of-motion coupled cluster method
Stanton, John F.; Gauss, Juergen
Journal of Chemical Physics (1994), 101 (10), 8938-44CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The theory for analytic energy derivs. of excited electronic states described by the equation-of-motion coupled cluster (EOM-CC) method has been generalized to treat cases in which ref. and final states differ in the no. of electrons. While this work specializes to the sector of Fock space that corresponds to ionization of the ref., the approach can be trivially modified for electron attached final states. Unlike traditional coupled cluster methods that are based on single determinant ref. functions, several electronic configurations are treated in a balanced way by EOM-CC. Therefore, this quantum chem. approach is appropriate for problems that involve important nondynamic electron correlation effects. Furthermore, a fully spin adapted treatment of doublet electronic states is guaranteed when a spin restricted closed shell ref. state is used-a desirable feature that is not easily achieved in std. coupled cluster approaches. The efficient implementation of analytic gradients reported here allows this variant of EOM-CC theory to be routinely applied to multidimensional potential energy surfaces for the first time. Use of the method is illustrated by an investigation of the formyloxyl radical (HCOO), which suffers from notorious symmetry breaking effects.
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Pieniazek, P. A.; Bradforth, S. E.; Krylov, A. I. Charge localization and Jahn–Teller distortions in the benzene dimer cation. J. Chem. Phys. 2008, 129, 074104, DOI: 10.1063/1.2969107
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Charge localization and Jahn-Teller distortions in the benzene dimer cation
Pieniazek, Piotr A.; Bradforth, Stephen E.; Krylov, Anna I.
Journal of Chemical Physics (2008), 129 (7), 074104/1-074104/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Jahn-Teller (JT) distortions and charge localization in the benzene dimer cation are analyzed using the equation-of-motion coupled cluster with single and double substitutions for ionization potential (EOM-IP-CCSD) method. Ionization of the dimer changes the bonding from noncovalent to covalent and induces significant geometrical distortions, e.g., shorter interfragment distance and JT displacements. Relaxation along interfragment coordinates lowers the energy of the t-shaped and displaced sandwich isomers by 0.07 and 0.23 eV, resp., whereas JT displacements result in addnl. 0.18 and 0.23 eV. Energetically, the effect of JT distortion on the dimer is similar to the monomer where JT relaxation lowers the energy by 0.18 eV. While the change in the interfragment distance has dramatic spectroscopic consequences, the JT distortion causes only a small perturbation in the electronic spectra. The two geometrical relaxations in the t-shaped isomer lead to opposing effects on hole localization. Intermol. relaxation leads to an increased delocalization, whereas JT ring distortion localizes the charge. In the sandwich isomers, breaking the symmetry by ring rotation does not induce considerable charge localization. The optimization and property calcns. were performed using a new implementation of EOM-IP-CCSD energies and gradients in the Q-CHEM electronic structure package. (c) 2008 American Institute of Physics.
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Musiał, M.; Kucharski, S. A.; Bartlett, R. J. Equation-of-motion coupled cluster method with full inclusion of the connected triple excitations for ionized states: IP-EOM-CCSDT. J. Chem. Phys. 2003, 118, 1128, DOI: 10.1063/1.1527013
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Equation-of-motion coupled cluster method with full inclusion of the connected triple excitations for ionized states: IP-EOM-CCSDT
Musial, Monika; Kucharski, Stanislaw A.; Bartlett, Rodney J.
Journal of Chemical Physics (2003), 118 (3), 1128-1136CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The equation-of-motion (EOM) coupled cluster (CC) method with full inclusion of the connected triple excitations for ionization energies has been formulated and implemented. Using proper factorization of the three- and four-body parts of the effective Hamiltonian, an efficient computational procedure has been proposed for IP-EOM-CCSDT which at the EOM level requires no-higher-than nocc3nvir4 scaling. The method is calibrated by the evaluation of the valence vertical ionization potentials for CO, N2, and F2 mols. for several basis sets up to 160 basis functions. At the basis set limit, errors vary from 0.0 to 0.2 eV, compared to "exptl." vertical ionization potentials.
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Nooijen, M.; Bartlett, R. J. Equation of motion coupled cluster method for electron attachment. J. Chem. Phys. 1995, 102, 3629, DOI: 10.1063/1.468592
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Equation of motion coupled cluster method for electron attachment
Nooijen, Marcel; Bartlett, Rodney J.
Journal of Chemical Physics (1995), 102 (9), 3629-47CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The electron attachment equation of motion coupled cluster (EA-EOMCC) method is derived which enables detn. of the various bound states of an (N+1)-electron system and the corresponding energy eigenvalues relative to the energy of an N-electron CCSD ref. state. Detailed working equations for the EA-EOMCC method are derived using diagrammatic techniques for both closed-shell and open-shell CCSD ref. states based upon a single determinant. The EA-EOMCC method is applied to a variety of different problems, the main purpose being to establish its prospects and limitations. The results from EA-EOMCC calcns. are compared to other EOMCC approaches, starting from different ref. states, as well as other theor. methods and exptl. values, where available. We have investigated electron affinities for a wide selection of both closed-shell and open-shell systems. Excitation spectra of atoms and mols. with an odd no. of electrons are obtained, taking the closed-shell ground state of the ion as a ref. in the EA-EOMCC calcn. Finally we consider excitation spectra of some closed-shell systems, and find in particular that the electron attachment approach is capable of yielding accurate triplet excitation energies in an efficient way.
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Musiał, M.; Bartlett, R. J. Equation-of-motion coupled cluster method with full inclusion of connected triple excitations for electron-attached states: EA-EOM-CCSDT. J. Chem. Phys. 2003, 119, 1901, DOI: 10.1063/1.1584657
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Equation-of-motion coupled cluster method with full inclusion of connected triple excitations for electron-attached states: EA-EOM-CCSDT
Musial, Monika; Bartlett, Rodney J.
Journal of Chemical Physics (2003), 119 (4), 1901-1908CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
We extend the full triples equation-of-motion (EOM) coupled cluster (CC) method to electron attached states. Proper factorization of the three- and four-body parts of the effective Hamiltonian makes it possible to achieve for the EA-EOM part a scaling no higher than nocc2nvir5. The method is calibrated by the evaluation of the valence vertical electron affinities for the C2 and O3 mols. for several basis sets up to 160 basis functions. For C2, EA-EOM-CCSDT gives 3.24 eV at the extrapolated basis limit, while the exptl. adiabatic EA is equal to 3.27 ± 0.008 eV. For O3 the agreement is ∼1.9 eV compared to an adiabatic value of 2.1 eV.
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Schirmer, J. Beyond the random-phase approximation: A new approximation scheme for the polarization propagator. Phys. Rev. A 1982, 26, 2395, DOI: 10.1103/PhysRevA.26.2395
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Beyond the random-phase approximation: A new approximation scheme for the polarization propagator
Schirmer, Jochen
Physical Review A: Atomic, Molecular, and Optical Physics (1982), 26 (5), 2395-416CODEN: PLRAAN; ISSN:0556-2791.
Within the framework of the many-body Green's-function method, a new approach is given to the polarization propagator for finite Fermi systems. This approach makes explicit use of the diagrammatic perturbation expansion for the polarization propagator, and reformulates the exact summation in terms of a simple algebraic scheme, referred to as the algebraic diagrammatic construction (ADC). The ADC defines in a natural way a set of approxn. schemes (nth-order ADC schemes) which represent infinite partial summations exact up to nth order of perturbation theory. In contrast to the random-phase-approxn. (RPA)-like schemes, the corresponding math. procedures are essentially Hermitian eigenvalue problems in limited configuration spaces of unperturbed excited configurations. Explicit equations for the 1st- and 2nd-order ADC schemes are derived. These schemes are thoroughly discussed and compared with the Tamm-Dancoff approxn. and RPA schemes.
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Schirmer, J.; Cederbaum, L. S.; Walter, O. New approach to the one-particle Green’s function for finite Fermi systems. Phys. Rev. A 1983, 28, 1237, DOI: 10.1103/PhysRevA.28.1237
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35
New approach to the one-particle Green's function for finite Fermi systems
Schirmer, J.; Cederbaum, L. S.; Walter, O.
Physical Review A: Atomic, Molecular, and Optical Physics (1983), 28 (3), 1237-59CODEN: PLRAAN; ISSN:0556-2791.
A new approach to the one-particle Green's functions G for finite electronic systems is presented. This approach is based on the diagrammatic perturbation expansions of the Green's function and of the dynamic self-energy part M related to G via the Dyson equation. The exact summation of the latter expansion is reformulated in terms of a simple algebraic form referred to as algebraic diagrammatic construction (ADC). The ADC defines in a systematic way a set of approxn. schemes (nth-order ADC schemes) that represent infinite partial summations for M and (via the Dyson equation) for G being complete through nth order of perturbation theory. The corresponding math. procedures are essentially Hermitian eigenvalue problems in restricted configuration spaces of unperturbed ionic configurations. Explicit equations for the second-, third-, and fourth-order ADC schemes are derived and analyzed.
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Schirmer, J.; Trofimov, A. B.; Stelter, G. A non-Dyson third-order approximation scheme for the electron propagator. J. Chem. Phys. 1998, 109, 4734, DOI: 10.1063/1.477085
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A non-Dyson third-order approximation scheme for the electron propagator
Schirmer, J.; Trofimov, A. B.; Stelter, G.
Journal of Chemical Physics (1998), 109 (12), 4734-4744CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
An efficient third-order propagator method to compute ionization potentials and electron affinities of atoms and mols. is presented. The development is based on the algebraic diagrammatic construction (ADC) representing a specific reformulation of the diagrammatic perturbation series of the electron propagator G(ω). In contrast with previous approxn. schemes, relying on the Dyson equation and approxns. for the self-energy part, the ADC procedure here is applied directly to the (N.-+.1)-electron parts G-(ω) and G+(ω), resp., of the electron propagator. This leads to decoupled secular equations for the ionization energies ((N-1)-electron part) and electron affinities ((N+1)-electron part), resp. In comparison with the Dyson-type approach, there is a substantial redn. of the secular matrix dimension opposed by a small addnl. expense in computing some second- and third-order contributions to the secular matrix elements. The relationship of the non-Dyson ADC(3) method to coupled cluster methods is outlined.
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Trofimov, A. B.; Schirmer, J. Molecular ionization energies and ground- and ionic-state properties using a non-Dyson electron propagator approach. J. Chem. Phys. 2005, 123, 144115, DOI: 10.1063/1.2047550
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37
Molecular ionization energies and ground- and ionic-state properties using a non-Dyson electron propagator approach
Trofimov, A. B.; Schirmer, J.
Journal of Chemical Physics (2005), 123 (14), 144115/1-144115/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
An earlier proposed propagator method for the treatment of mol. ionization is tested in first applications. The method referred to as the non-Dyson third-order algebraic-diagrammatic construction [nD-ADC(3)] approxn. for the electron propagator represents a computationally promising alternative to the existing Dyson ADC(3) method. The advantage of the nD-ADC(3) scheme is that the (N±1)-electronic parts of the one-particle Green's function are decoupled from each other and the corresponding equations can be solved sep. For a test of the method the nD-ADC(3) results for the vertical ionization transitions in C2H4, CO, CS, F2, H2CO, H2O, HF, N2, and Ne are compared with available exptl. and theor. data including results of full CI (FCI) and coupled cluster computations. The mean error of the nD-ADC(3) ionization energies relative to the exptl. and FCI results is about 0.2 eV. The nD-ADC(3) method, scaling as n5 with the no. of orbitals, requires the soln. of a relatively simple Hermitian eigenvalue problem. The method renders access to ground-state properties such as dipole moments. Moreover, also one-electron properties of (N±1) electron states can now be studied as a consequence of a specific intermediate-state representation (ISR) formulation of the nD-ADC approach. Corresponding second-order ISR equations are presented.
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Dempwolff, A. L.; Schneider, M.; Hodecker, M.; Dreuw, A. Efficient implementation of the non-Dyson third-order algebraic diagrammatic construction approximation for the electron propagator for closed- and open-shell molecules. J. Chem. Phys. 2019, 150, 064108, DOI: 10.1063/1.5081674
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Efficient implementation of the non-Dyson third-order algebraic diagrammatic construction approximation for the electron propagator for closed- and open-shell molecules
Dempwolff, Adrian L.; Schneider, Matthias; Hodecker, Manuel; Dreuw, Andreas
Journal of Chemical Physics (2019), 150 (6), 064108/1-064108/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A novel efficient implementation of the non-Dyson algebraic diagrammatic construction (ADC) scheme of the (N - 1)-part of the electron propagator up to third order of perturbation theory is presented. Due to the underlying spin-orbital formulation, for the first time, the computation of ionization potentials of open-shell radicals is thus possible via non-Dyson ADC schemes. Thorough evaluation of the accuracy, applicability, and capabilities of the new method reveals a mean error of 0.15 eV for closed- as well as open-shell atoms and mols. (c) 2019 American Institute of Physics.
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Banerjee, S.; Sokolov, A. Y. Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green’s function implementation. J. Chem. Phys. 2019, 151, 224112, DOI: 10.1063/1.5131771
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Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green's function implementation
Banerjee, Samragni; Sokolov, Alexander Yu.
Journal of Chemical Physics (2019), 151 (22), 224112/1-224112/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
We present implementation of second- and third-order algebraic diagrammatic construction (ADC) theory for efficient and accurate computations of mol. electron affinities (EA), ionization potentials (IP), and densities of states [EA-/IP-ADC(n), n = 2, 3]. Our work utilizes the non-Dyson formulation of ADC for the single-particle propagator and reports working equations and benchmark results for the EA-ADC(2) and EA-ADC(3) approxns. We describe two algorithms for solving EA-/IP-ADC equations: (i) conventional algorithm that uses iterative diagonalization techniques to compute low-energy EA, IP, and d. of states and (ii) Green's function algorithm (GF-ADC) that solves a system of linear equations to compute d. of states directly for a specified spectral region. To assess the accuracy of EA-ADC(2) and EA-ADC(3), we benchmark their performance for a set of atoms, small mols., and five DNA/RNA nucleobases. As our next step, we demonstrate the efficiency of our GF-ADC implementation by computing core-level K-, L-, and M-shell ionization energies of a zinc atom without introducing the core-valence sepn. approxn. Finally, we use EA- and IP-ADC methods to compute the bandgaps of equally spaced hydrogen chains Hn with n up to 150, providing their ests. near thermodn. limit. Our results demonstrate that EA-/IP-ADC(n) (n = 2, 3) methods are efficient and accurate alternatives to widely used electronic structure methods for simulations of electron attachment and ionization properties. (c) 2019 American Institute of Physics.
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Hodecker, M.; Dempwolff, A. L.; Schirmer, J.; Dreuw, A. Theoretical analysis and comparison of unitary coupled-cluster and algebraic-diagrammatic construction methods for ionization. J. Chem. Phys. 2022, 156, 074104, DOI: 10.1063/5.0070967
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Theoretical analysis and comparison of unitary coupled-cluster and algebraic-diagrammatic construction methods for ionization
Hodecker, Manuel; Dempwolff, Adrian L.; Schirmer, Jochen; Dreuw, Andreas
Journal of Chemical Physics (2022), 156 (7), 074104CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
This article describes a novel approach for the calcn. of ionization potentials (IPs), or, more generally, electron-detachment energies, based on a unitary coupled-cluster (UCC) parameterization of the ground-state wave function. Explicit working equations for a scheme referred to as IP-UCC3 are given, providing electron-detachment energies and spectroscopic amplitudes of electron-detached states dominated by one-hole excitations correct through third order. In the derivation, an expansion of the UCC transformed Hamiltonian involving Bernoulli nos. as expansion coeffs. is employed. Both the secular matrix and the effective transition moments are shown to be essentially equiv. to the strict third-order algebraic-diagrammatic construction scheme for the electron propagator (IP-ADC). Interestingly, due to the Bernoulli expansion, neglecting triple substitutions in the UCC expansion manifold does not affect the third-order consistency of the IP-UCC effective transition moments. Finally, the equivalence between ADC and UCC excited-state schemes is shown to not hold in fourth or higher order due to a different treatment of the correlated excited-state basis. (c) 2022 American Institute of Physics.
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Dempwolff, A. L.; Hodecker, M.; Dreuw, A. Vertical ionization potential benchmark for unitary coupled-cluster and algebraic-diagrammatic construction methods. J. Chem. Phys. 2022, 156, 054114, DOI: 10.1063/5.0079047
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Vertical ionization potential benchmark for unitary coupled-cluster and algebraic-diagrammatic construction methods
Dempwolff, Adrian L.; Hodecker, Manuel; Dreuw, Andreas
Journal of Chemical Physics (2022), 156 (5), 054114CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The performance of several methods for the calcn. of vertical ionization potentials (IPs) or, more generally, electron-detachment energies based on unitary coupled-cluster (UCC) theory and the algebraic-diagrammatic construction (ADC) scheme is evaluated with respect to benchmark data computed at the level of equation-of-motion coupled-cluster theory, including single, double, and triple excitations (IP-EOM-CCSDT). Based on a statistical evaluation of about 200 electron-detached states of 41 mols., the second-order methods IP-ADC(2) and IP-UCC2 show modest accuracies with IP-EOM-CCSDT as ref., exposing a mean signed error and a std. deviation of the error of -0.54 ± 0.50 and -0.49 ± 0.54 eV, resp., accompanied by a mean abs. error (MAE) of 0.61 and 0.58 eV, resp. The strict third-order IP-ADC method demonstrates an accuracy of 0.26 ± 0.35 eV (MAE = 0.35 eV), while the IP-UCC3 method is slightly more accurate with 0.24 ± 0.26 eV (MAE = 0.29 eV). Employing the static self-energy computed using the Dyson expansion method (DEM) improves the IP-ADC(3) performance to 0.27 ± 0.28 eV, with the mean abs. error of this method being 0.32 eV. However, employing the simpler improved fourth-order scheme Σ(4+) for the static self-energy provides almost identical results as the DEM. Based on the quality of the present benchmark results, it therefore appears not necessary to use the computationally more demanding DEM. (c) 2022 American Institute of Physics.
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Dempwolff, A. L.; Paul, A. C.; Belogolova, A. M.; Trofimov, A. B.; Dreuw, A. Intermediate state representation approach to physical properties of molecular electron-detached states. I. Theory and implementation. J. Chem. Phys. 2020, 152, 024113, DOI: 10.1063/1.5137792
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Intermediate state representation approach to physical properties of molecular electron-detached states. I. Theory and implementation
Dempwolff, Adrian L.; Paul, Alexander C.; Belogolova, Alexandra M.; Trofimov, Alexander B.; Dreuw, Andreas
Journal of Chemical Physics (2020), 152 (2), 024113CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The third-order non-Dyson algebraic-diagrammatic construction approach to the electron propagator [IP-ADC(3)] is extended using the intermediate state representation (ISR) formalism, allowing the wave functions and properties of mol. states with detached electron to be studied. The second-order ISR equations [ISR(2)] for the one-particle (transition) d. matrix have been derived and implemented in the Q-CHEM program. The approach is completely general and enables evaluation of arbitrary one-particle operators and interpretation of electron detachment processes in terms of d.-based quantities. The IP-ADC(3)/ISR(2) equations were implemented for Ŝz-adapted intermediate states, allowing open-shell mols. to be studied using UHF refs. As a first test for computations of ground state properties, dipole moments of various closed- and open-shell mols. have been computed by means of electron detachment from the corresponding anions. The results are in good agreement with exptl. data. The potential of IP-ADC(3)/ISR(2) for the interpretation of photoelectron spectra is demonstrated for the galvinoxyl free radical. (c) 2020 American Institute of Physics.
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Dempwolff, A. L.; Paul, A. C.; Belogolova, A. M.; Trofimov, A. B.; Dreuw, A. Intermediate state representation approach to physical properties of molecular electron-detached states. II. Benchmarking. J. Chem. Phys. 2020, 152, 024125, DOI: 10.1063/1.5137794
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Intermediate state representation approach to physical properties of molecular electron-detached states. II. Benchmarking
Dempwolff, Adrian L.; Paul, Alexander C.; Belogolova, Alexandra M.; Trofimov, Alexander B.; Dreuw, Andreas
Journal of Chemical Physics (2020), 152 (2), 024125CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The third-order algebraic-diagrammatic construction method for studies of electron detachment processes within the electron propagator framework [IP-ADC(3)] was extended to treat the properties of mol. states with a detached electron using the intermediate state representation (ISR) formalism. The second-order ISR(2) equations for the one-particle (transition) d. matrix have been derived and implemented as an extension of the IP-(U)ADC(3) method available in the Q-CHEM program. As a first systematic test of the present IP-(U)ADC(3)/ISR(2) method, the dipole moments of various electronic states of closed- and open-shell mols. have been computed and compared to full CI (FCI) results. The present study employing FCI benchmarks also provides the first rigorous ests. for the accuracy of electron detachment energies obtained using the IP-ADC(3) method. (c) 2020 American Institute of Physics.
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Dempwolff, A. L.; Belogolova, A. M.; Trofimov, A. B.; Dreuw, A. Intermediate state representation approach to physical properties of molecular electron-attached states: Theory, implementation, and benchmarking. J. Chem. Phys. 2021, 154, 104117, DOI: 10.1063/5.0043337
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Intermediate state representation approach to physical properties of molecular electron-attached states: Theory, implementation, and benchmarking
Dempwolff, Adrian L.; Belogolova, Alexandra M.; Trofimov, Alexander B.; Dreuw, Andreas
Journal of Chemical Physics (2021), 154 (10), 104117CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Computational schemes for comprehensive studies of mol. electron-attached states and the calcn. of electron affinities (EAs) are formulated and implemented employing the intermediate state representation (ISR) formalism and the algebraic-diagrammatic construction approxn. for the electron propagator (EA-ADC). These EA-ADC(n)/ISR(m) schemes allow for a consistent treatment of not only electron affinities and pole strengths up to third-order of perturbation theory (n = 3) but also one-electron properties of electron-attached states up to second order (m = 2). The EA-ADC/ISR equations were implemented in the Q-CHEM program for Ŝz-adapted intermediate states, allowing also open-shell systems to be studied using UHF refs. For benchmarking of the EA-(U)ADC/ISR schemes, EAs and dipole moments of various electron-attached states of small closed- and open-shell mols. were computed and compared to full CI data. As an illustrative example, EA-ADC(3)/ISR(2) has been applied to the thymine-thymine (6-4) DNA photolesion. (c) 2021 American Institute of Physics.
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Ortiz, J. V. Electron propagator theory: an approach to prediction and interpretation in quantum chemistry. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2013, 3, 123, DOI: 10.1002/wcms.1116
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Electron propagator theory: an approach to prediction and interpretation in quantum chemistry
Ortiz, Joseph Vincent
Wiley Interdisciplinary Reviews: Computational Molecular Science (2013), 3 (2), 123-142CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
A review. Electron propagator theory provides a practical means of calcg. electron binding energies, Dyson orbitals, and ground-state properties from first principles. This approach to ab initio electronic structure theory also facilitates the interpretation of its quant. predictions in terms of concepts that closely resemble those of one-electron theories. An explanation of the phys. meaning of the electron propagator's poles and residues is followed by a discussion of its couplings to more complicated propagators. These relationships are exploited in superoperator theory and lead to a compact form of the electron propagator that is derived by matrix partitioning. Expressions for ref.-state properties, relationships to the extended Koopmans's theorem technique for evaluating electron binding energies, and connections between Dyson orbitals and transition probabilities follow from this discussion. The inverse form of the Dyson equation for the electron propagator leads to a strategy for obtaining electron binding energies and Dyson orbitals that generalizes the Hartree-Fock equations through the introduction of the self-energy operator. All relaxation and correlation effects reside in this operator, which has an energy-dependent, nonlocal form that is systematically improvable. Perturbative arguments produce several, convenient (e.g. partial third order, outer valence Green's function, and second-order, transition-operator) approxns. for the evaluation of valence ionization energies, electron affinities, and core ionization energies. Renormalized approaches based on Hartree-Fock or approx. Brueckner orbitals are employed when correlation effects become qual. important. Ref.-state total energies based on contour integrals in the complex plane and gradients of electron binding energies enable exploration of final-state potential energy surfaces.
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Ortiz, J. V. Partial third-order quasiparticle theory: Comparisons for closed-shell ionization energies and an application to the borazine photoelectron spectrum. J. Chem. Phys. 1996, 104, 7599, DOI: 10.1063/1.471468
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Partial third-order quasiparticle theory: comparisons for closed-shell ionization energies and an application to the Borazine photoelectron spectrum
Ortiz, J. V.
Journal of Chemical Physics (1996), 104 (19), 7599-7605CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Valence ionization energies of a set closed-shell mols. calcd. in a partial 3rd-order (P3) quasiparticle approxn. of the electron propagator have an av. abs. error of 0.19 eV. Diagonal elements of the self-energy matrix include all 2nd-order and some 3rd-order self-energy diagrams. Because of its 5th power dependence on basis set size and its independence from electron repulsion integrals with four virtual indexes, this method has considerable potential for large mols. Formal and computational comparisons with other electron propagator techniques illustrate the advantages of the P3 procedure. Addnl. applications to benzene and borazine display the efficacy of the P3 propagator in assigning photoelectron spectra. In the borazine spectrum, 2E' and 2A2' final states are responsible for an obsd. feature at 14.76 eV. Another peak at 17.47 eV is assigned to a 2E' final state.
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Corzo, H. H.; Galano, A.; Dolgounitcheva, O.; Zakrzewski, V. G.; Ortiz, J. V. NR2 and P3+: Accurate, Efficient Electron-Propagator Methods for Calculating Valence, Vertical Ionization Energies of Closed-Shell Molecules. J. Phys. Chem. A 2015, 119, 8813, DOI: 10.1021/acs.jpca.5b00942
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NR2 and P3+: Accurate, Efficient Electron-Propagator Methods for Calculating Valence, Vertical Ionization Energies of Closed-Shell Molecules
Corzo, H. H.; Galano, Annia; Dolgounitcheva, O.; Zakrzewski, V. G.; Ortiz, J. V.
Journal of Physical Chemistry A (2015), 119 (33), 8813-8821CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
Two accurate and computationally efficient electron-propagator (EP) methods for calcg. the valence, vertical ionization energies (VIEs) of closed-shell mols. have been identified through comparisons with related approxns. VIEs of a representative set of closed-shell mols. were calcd. with EP methods using 10 basis sets. The most easily executed method, the diagonal, second-order (D2) EP approxn., produces results that steadily rise as basis sets are improved toward values based on extrapolated coupled-cluster singles and doubles plus perturbative triples calcns., but its mean errors remain unacceptably large. The outer valence Green function, partial third-order and renormalized partial third-order methods (P3+), which employ the diagonal self-energy approxn., produce markedly better results but have a greater tendency to overestimate VIEs with larger basis sets. The best combination of accuracy and efficiency with a diagonal self-energy matrix is the P3+ approxn., which exhibits the best trends with respect to basis-set satn. Several renormalized methods with more flexible nondiagonal self-energies also have been examd.: the two-particle, one-hole Tamm-Dancoff approxn. (2ph-TDA), the third-order algebraic diagrammatic construction or ADC(3), the renormalized third-order (3+) method, and the nondiagonal second-order renormalized (NR2) approxn. Like D2, 2ph-TDA produces steady improvements with basis set augmentation, but its av. errors are too large. Errors obtained with 3+ and ADC(3) are smaller on av. than those of 2ph-TDA. These methods also have a greater tendency to overestimate VIEs with larger basis sets. The smallest av. errors occur for the NR2 approxn.; these errors decrease steadily with basis augmentations. As basis sets approach satn., NR2 becomes the most accurate and efficient method with a nondiagonal self-energy.
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Ortiz, J. V. An efficient, renormalized self-energy for calculating the electron binding energies of closed-shell molecules and anions. Int. J. Quantum Chem. 2005, 105, 803, DOI: 10.1002/qua.20664
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An efficient, renormalized self-energy for calculating the electron binding energies of closed-shell molecules and anions
Ortiz, J. V.
International Journal of Quantum Chemistry (2005), 105 (6), 803-808CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)
The energy-dependent, nonlocal correlation potential known as the self-energy that appears in the Dyson equation has a pole and residue structure that enables renormalizations of its low-order, perturbative contributions to be estd. The partial third-order (P3) approxn. has been extensively applied to the ionization energies of closed-shell, org. mols. and is the most successful example of a low-order, self-energy method. A renormalization based on the P3 self-energy ests. higher-order contributions by scaling low-order terms that chiefly describe final-state relaxation. The resulting P3 + self-energy retains the accuracy and efficiency of the P3 approxn., but also improves the latter method's performance with respect to the calcn. of anion electron detachment energies without the introduction of adjustable parameters. An application to an anion that previously has yielded only to more intricate treatments of electron correlation demonstrates the power of this simple, new approxn.
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Ortiz, J. V. A nondiagonal, renormalized extension of partial third-order quasiparticle theory: Comparisons for closed-shell ionization energies. J. Chem. Phys. 1998, 108, 1008, DOI: 10.1063/1.475463
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49
A nondiagonal, renormalized extension of partial third-order quasiparticle theory: comparisons for closed-shell ionization energies
Ortiz, J. V.
Journal of Chemical Physics (1998), 108 (3), 1008-1014CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Valence ionization energies of a set closed-shell mols. calcd. in a nondiagonal, renormalized approxn. of the electron propagator have an av. abs. error of 0.17 eV. This procedure extends the partial third order, quasiparticle approxn. of J. Chem. Phys. 104, 7599 (1996) that has proven successful in many applications. Elements of the self-energy matrix include all second-order and many higher-order terms. Because of its fifth power dependence on basis set size and its independence from electron repulsion integrals with four virtual orbital indexes, this method has considerable promise for large mols. Formal and computational comparisons with renormalized electron propagator techniques that are complete through third-order illustrate the advantages of this procedure.
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Opoku, E.; Pawłowski, F.; Ortiz, J. V. A new generation of diagonal self-energies for the calculation of electron removal energies. J. Chem. Phys. 2021, 155, 204107, DOI: 10.1063/5.0070849
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A new generation of diagonal self-energies for the calculation of electron removal energies
Opoku, Ernest; Pawlowski, Filip; Ortiz, J. V.
Journal of Chemical Physics (2021), 155 (20), 204107CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A new generation of diagonal self-energy approxns. in ab initio electron propagator theory for the calcn. of electron removal energies of mols. and mol. ions has been derived from an intermediately normalized, Hermitized super-operator metric. These methods and widely used antecedents such as the outer valence Green's function and the approx. renormalized partial third order method are tested with respect to a dataset of vertical ionization energies generated with a valence, triple-ζ, correlation-consistent basis set and a converged series of many-body calcns. whose accuracy approaches that of full CI. Several modifications of the diagonal second-order self-energy, a version of G0W0 theory based on Tamm-Dancoff excitations and several non-diagonal self-energies are also included in the tests. All new methods employ canonical Hartree-Fock orbitals. No adjustable or empirical parameters appear. A hierarchy of methods with optimal accuracy for a given level of computational efficiency is established. Several widely used diagonal self-energy methods are rendered obsolete by the new hierarchy whose members, in order of increasing accuracy, are (1) the opposite-spin non-Dyson diagonal second-order or os-nD-D2, (2) the approx. renormalized third-order quasiparticle or Q3+ , (3) the renormalized third-order quasiparticle or RQ3, (4) the approx. renormalized linear third-order or L3+ , and (5) the renormalized linear third-order or RL3 self-energies. (c) 2021 American Institute of Physics.
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Opoku, E.; Pawłowski, F.; Ortiz, J. V. Electron Propagator Theory of Vertical Electron Detachment Energies of Anions: Benchmarks and Applications to Nucleotides. J. Phys. Chem. A 2023, 127, 1085, DOI: 10.1021/acs.jpca.2c08372
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Electron Propagator Theory of Vertical Electron Detachment Energies of Anions: Benchmarks and Applications to Nucleotides
Opoku, Ernest; Pawlowski, Filip; Ortiz, J. V.
Journal of Physical Chemistry A (2023), 127 (4), 1085-1101CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
A new generation of ab initio electron-propagator self-energy approxns. that is free of adjustable parameters is tested on a benchmark set of 55 vertical electron detachment energies of closed-shell anions. Comparisons with older self-energy approxns. indicate that several new methods that make the diagonal self-energy approxn. in the canonical Hartree-Fock orbital basis provide superior accuracy and computational efficiency. These methods, their acronyms, mean abs. errors (in eV) and arithmetic bottlenecks expressed in terms of occupied (O) and virtual (V) orbitals are the opposite-spin, non-Dyson, diagonal second-order method (os-nD-D2, 0.2, OV2), the approx. renormalized quasiparticle third-order method (Q3+ , 0.15, O2V3) and the approx. renormalized, non-Dyson, linear, third-order method (nD-L3+ , 0.1, OV4). The BD-T1 (Brueckner Doubles with Triple field operators) nondiagonal electron-propagator method provides such close agreement with coupled-cluster single, double and perturbative triple replacement total energy differences that it may be used as an alternative means of obtaining std. data. The new methods with diagonal self-energy matrixes are the foundation of a composite procedure for estg. basis-set effects. This model produces accurate predictions and clear interpretations based on Dyson orbitals for the photoelectron spectra of the nucleotides found in DNA.
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Gilbert, A. T. B.; Besley, N. A.; Gill, P. M. W. Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM). J. Phys. Chem. A 2008, 112, 13164, DOI: 10.1021/jp801738f
Google Scholar
52
Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM)
Gilbert, Andrew T. B.; Besley, Nicholas A.; Gill, Peter M. W.
Journal of Physical Chemistry A (2008), 112 (50), 13164-13171CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
We present a simple algorithm, which we call the max. overlap method (MOM), for finding excited-state solns. to SCF equations. Instead of using the aufbau principle, the algorithm maximizes the overlap between the occupied orbitals on successive SCF iterations. This prevents variational collapse to the ground state and guides the SCF process toward the nearest, rather than the lowest energy, soln. The resulting excited-state solns. can be treated in the same way as the ground-state soln. and, in particular, derivs. of excited-state energies can be computed using ground-state code. We assess the performance of our method by applying it to a variety of excited-state problems including the calcn. of excitation energies, charge-transfer states, and excited-state properties.
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53
Bagus, P. S. Self-Consistent-Field Wave Functions for Hole States of Some Ne-Like and Ar-Like Ions. Phys. Rev. 1965, 139, A619, DOI: 10.1103/PhysRev.139.A619
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53
Self-consistent-field wave functions for hole states of some Ne-like and Ar-like ions
Bagus, P. S.
Physical Review (1965), 139 (3A), 619-34CODEN: PHRVAO; ISSN:0031-899X.
Analytic self-consistent-field (SCF) wave functions were computed for the ground states of the closed-shell at. systems F-, Ne, and Na+ and Cl-, Ar, and K+; and for those ground and excited states of the open-shell systems which are obtained by removing a single electron from any one of the occupied shells of these closed-shell systems. Details of the calcn. of the functions are presented, with emphasis on a justification of the procedures used for the calcns. for excited states. A high accuracy is obtained; the calcns. for the closed-shell systems give the most accurate analytic SCF wave functions which have yet been reported. Ionization potentials are compared with exptl. values. Computed ionization potentials for the removal of a 2s electron from Cl-, Ar, and K+, for which no direct exptl. data are available, are estd. to be accurate to 1%. The removal of an electron from the outermost s shell increases the correlation energy, in contradiction to the predictions of a recently proposed semi- empirical scheme for estg. the correlation energy. For example, the magnitude of the correlation energy of the lowest 2S state of Ar+ is ∼4 ev. greater than the magnitude of the correlation energy of neutral Ar. The effect of the nonzero off-diagonal Lagrangian multipliers is important for the inner shell hole states.
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Triguero, L.; Pettersson, L. G. M.; Ågren, H. Calculations of near-edge x-ray-absorption spectra of gas-phase and chemisorbed molecules by means of density-functional and transition-potential theory. Phys. Rev. B 1998, 58, 8097, DOI: 10.1103/PhysRevB.58.8097
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Calculations of near-edge x-ray-absorption spectra of gas-phase and chemisorbed molecules by means of density-functional and transition-potential theory
Triguero, L.; Pettersson, L. G. M.; Agren, H.
Physical Review B: Condensed Matter and Materials Physics (1998), 58 (12), 8097-8110CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
The authors explore the utility of d.-functional theory (DFT) in conjunction with the transition-potential (TP) method to simulate x-ray-absorption spectra. Calcns. on a set of small C-contg. mols. and chemisorbed species show that this provides a viable option for obtaining excitation energies and oscillator strengths close to the exptl. accuracy of core-valence transitions. Systematic variations in energy positions and intensities of the different spectra in the test series were studied, and comparison is made with respect to the static exchange-, SCF, and explicit electron-correlation methods. The choice between std. exchange-correlation functionals is of little consequence for the valence resonant, here π*, parts of the x-ray-absorption spectra, while the long-range behavior of presently available functionals is found not to be completely satisfactory for Rydberg-like transitions. Implementing a basis set augmentation technique, DFT methods still account well for most of the salient features in the near-edge x-ray-absorption spectra, save for the multielectron transitions in the near continuum, and for some loss of Rydberg structure. For clusters modeling surface adsorbates, the DFT transition potential method reproduces well the spectral compression and intensity redn. for the valence level absorption compared to the free phase, provided fairly large clusters are taken into account. While for near-edge x-ray-absorption fine-structure (NEXAFS) spectra of free mols. the DFT-TP and Hartree-Fock/static exchange methods have complementary advantages, the DFT-TP method is clearly to be preferred when using clusters to simulate NEXAFS spectra of surface adsorbates.
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Lee, J.; Small, D. W.; Head-Gordon, M. Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states. J. Chem. Phys. 2019, 151, 214103, DOI: 10.1063/1.5128795
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Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states
Lee, Joonho; Small, David W.; Head-Gordon, Martin
Journal of Chemical Physics (2019), 151 (21), 214103/1-214103/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
In this work, we revisited the idea of using the coupled-cluster (CC) ground state formalism to target excited states. Our main focus was targeting doubly excited states and double core hole states. Typical equation-of-motion (EOM) approaches for obtaining these states struggle without higher-order excitations than doubles. We showed that by using a non-Aufbau determinant optimized via the max. overlap method, the CC ground state solver can target higher energy states. Furthermore, just with singles and doubles (i.e., CCSD), we demonstrated that the accuracy of ΔCCSD and ΔCCSD(T) (triples) far surpasses that of EOM-CCSD for doubly excited states. The accuracy of ΔCCSD(T) is nearly exact for doubly excited states considered in this work. For double core hole states, we used an improved ansatz for greater numerical stability by freezing core hole orbitals. The improved methods, core valence sepn. (CVS)-ΔCCSD and CVS-ΔCCSD(T), were applied to the calcn. of the double ionization potential of small mols. Even without relativistic corrections, we obsd. qual. accurate results with CVS-ΔCCSD and CVS-ΔCCSD(T). Remaining challenges in ΔCC include the description of open-shell singlet excited states with the single-ref. CC ground state formalism as well as excited states with genuine multireference character. The tools and intuition developed in this work may serve as a stepping stone toward directly targeting arbitrary excited states using ground state CC methods. (c) 2019 American Institute of Physics.
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Meissner, L.; Balková, A.; Bartlett, R. J. Multiple solutions of the single-reference coupled-cluster method. Chem. Phys. Lett. 1993, 212, 177, DOI: 10.1016/0009-2614(93)87127-O
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Multiple solutions of the single-reference coupled-cluster method
Meissner, Leszek; Balkova, Anna; Bartlett, Rodney J.
Chemical Physics Letters (1993), 212 (1-2), 177-84CODEN: CHPLBC; ISSN:0009-2614.
The nonlinear coupled-cluster (CC) equations possess several solns. They describe various excited states as long as they contain a contribution from the ref. function. The authors study the addnl. solns. of the single-ref. CC equations and demonstrate that unlike the ground state, the approx. soln. for excited states in general does not satisfy the cluster condition nor the std. proof of extensivity. For such states that makes the CC approxn. poorer than that for the analogous CI.
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Zheng, X.; Cheng, L. Performance of Delta-Coupled-Cluster Methods for Calculations of Core-Ionization Energies of First-Row Elements. J. Chem. Theory Comput. 2019, 15, 4945, DOI: 10.1021/acs.jctc.9b00568
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Performance of Delta-Coupled-Cluster Methods for Calculations of Core-Ionization Energies of First-Row Elements
Zheng, Xuechen; Cheng, Lan
Journal of Chemical Theory and Computation (2019), 15 (9), 4945-4955CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
A thorough study of the performance of delta-coupled-cluster (ΔCC) methods for calcns. of core-ionization energies for elements of the first long row of the periodic table is reported. Inspired by the core-valence sepn. (CVS) scheme in response theories, a simple CVS scheme of excluding the vacant core orbital from the CC treatment has been adopted to solve the convergence problem of the CC equations for core-ionized states. Dynamic correlation effects have been shown to make important contributions to the computed core-ionization energies, esp. to chem. shifts of these quantities. The max. abs. error (MaxAE) and std. deviation (SD) of delta-Hartree-Fock results for chem. shifts of core-ionization energies with respect to the corresponding exptl. values amt. to more than 1.7 and 0.6 eV, resp. In contrast, the inclusion of electron correlation in ΔCC singles and doubles augmented with a noniterative triples correction [ΔCCSD(T)] method significantly reduces the corresponding deviations to around 0.3 and 0.1 eV. With the consideration of basis set effects and the corrections to the CVS approxn., ΔCCSD(T) has been shown to provide highly accurate results for abs. values of core-ionization energies, with a MaxAE of 0.22 eV and SD of 0.13 eV. To further demonstrate the usefulness of ΔCCSD(T), calcns. of carbon K-edge ionization energies of Et trifluoroacetate, a mol. of significant interest to the study of X-ray spectroscopy and dynamics, are reported.
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Hirata, S.; Hermes, M. R.; Simons, J.; Ortiz, J. V. General-Order Many-Body Green’s Function Method. J. Chem. Theory Comput. 2015, 11, 1595, DOI: 10.1021/acs.jctc.5b00005
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General-Order Many-Body Green's Function Method
Hirata, So; Hermes, Matthew R.; Simons, Jack; Ortiz, J. V.
Journal of Chemical Theory and Computation (2015), 11 (4), 1595-1606CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Electron binding energies are evaluated as differences in total energy between the N- and (N ± 1)-electron systems calcd. by the nth-order Moller-Plesset perturbation (MPn) theory using the same set of orbitals. The MPn energies up to n = 30 are, in turn, obtained by the determinant-based method of Knowles et al. (Chem. Phys. Lett.1985, 113, 8-12). The zeroth- through third-order electron binding energies thus detd. agree with those obtained by solving the Dyson equation in the diagonal and frequency-independent approxns. of the self-energy. However, as n → ∞, they converge at the exact basis-set solns. from the Dyson equation with the exact self-energy, which is nondiagonal and frequency-dependent. This suggests that the MPn energy differences define an alternative diagrammatic expansion of Koopmans-like electron binding energies, which takes into account the perturbation corrections from the off-diagonal elements and frequency dependence of the irreducible self-energy. Our anal. shows that these corrections are included as semireducible and linked-disconnected diagrams, resp., which are also found in a perturbation expansion of the electron binding energies of the equation-of-motion coupled-cluster methods. The rate of convergence of the electron binding energies with respect to n and its acceleration by Pade approximants are also discussed.
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Hirata, S.; Doran, A. E.; Knowles, P. J.; Ortiz, J. V. One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms. J. Chem. Phys. 2017, 147, 044108, DOI: 10.1063/1.4994837
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One-particle many-body Green's function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms
Hirata, So; Doran, Alexander E.; Knowles, Peter J.; Ortiz, J. V.
Journal of Chemical Physics (2017), 147 (4), 044108/1-044108/31CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A thorough anal. and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equiv. algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approxns. at 1 ≤ n ≤ 3 but converges at the full-configuration-interaction (FCI) limit at n = ∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approxn. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified math. using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approxns. at 1 ≤ n ≤ 3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams. (c) 2017 American Institute of Physics.
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Goerigk, L.; Hansen, A.; Bauer, C.; Ehrlich, S.; Najibi, A.; Grimme, S. A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions. Phys. Chem. Chem. Phys. 2017, 19, 32184, DOI: 10.1039/C7CP04913G
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A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions
Goerigk, Lars; Hansen, Andreas; Bauer, Christoph; Ehrlich, Stephan; Najibi, Asim; Grimme, Stefan
Physical Chemistry Chemical Physics (2017), 19 (48), 32184-32215CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
We present the GMTKN55 benchmark database for general main group thermochem., kinetics and noncovalent interactions. Compared to its popular predecessor GMTKN30, it allows assessment across a larger variety of chem. problems - with 13 new benchmark sets being presented for the first time - and it also provides ref. values of significantly higher quality for most sets. GMTKN55 comprises 1505 relative energies based on 2462 single-point calcns. and it is accessible to the user community via a dedicated website. Herein, we demonstrate the importance of better ref. values, and we re-emphasize the need for London-dispersion corrections in d. functional theory (DFT) treatments of thermochem. problems, including Minnesota methods. We assessed 217 variations of dispersion-cor. and -uncorrected d. functional approxns., and carried out a detailed anal. of 83 of them to identify robust and reliable approaches. Double-hybrid functionals are the most reliable approaches for thermochem. and noncovalent interactions, and they should be used whenever tech. feasible. These are, in particular, DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), and B2GPPLYP-D3(BJ). The best hybrids are ωB97X-V, M052X-D3(0), and ωB97X-D3, but we also recommend PW6B95-D3(BJ) as the best conventional global hybrid. At the meta-generalized-gradient (meta-GGA) level, the SCAN-D3(BJ) method can be recommended. Other meta-GGAs are outperformed by the GGA functionals revPBE-D3(BJ), B97-D3(BJ), and OLYP-D3(BJ). We note that many popular methods, such as B3LYP, are not part of our recommendations. In fact, with our results we hope to inspire a change in the user community's perception of common DFT methods. We also encourage method developers to use GMTKN55 for cross-validation studies of new methodologies.
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Goerigk, L.; Grimme, S. A general database for main group thermochemistry, kinetics, and noncovalent interactions – Assessment of common and reparameterized (meta-)GGA density functionals. J. Chem. Theory Comput. 2010, 6, 107, DOI: 10.1021/ct900489g
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A General Database for Main Group Thermochemistry, Kinetics, and Noncovalent Interactions - Assessment of Common and Reparameterized (meta-)GGA Density Functionals
Goerigk, Lars; Grimme, Stefan
Journal of Chemical Theory and Computation (2010), 6 (1), 107-126CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
We present a quantum chem. benchmark database for general main group thermochem., kinetics, and noncovalent interactions (GMTKN24). It is an unprecedented compilation of 24 different, chem. relevant subsets that either are taken from already existing databases or are presented here for the first time. The complete set involves a total of 1.049 at. and mol. single point calcns. and comprises 731 data points (relative chem. energies) based on accurate theor. or exptl. ref. values. The usefulness of the GMTKN24 database is shown by applying common d. functionals on the (meta-)generalized gradient approxn. (GGA), hybrid-GGA, and double-hybrid-GGA levels to it, including an empirical London dispersion correction. Furthermore, we refitted the functional parameters of four (meta-)GGA functionals based on a fit set contg. 143 systems, comprising seven chem. different problems. Validation against the GMTKN24 and the mol. structure (bond lengths) databases shows that the reparameterization does not change bond lengths much, whereas the description of energetic properties is more prone to the parameters' values. The empirical dispersion correction also often improves for conventional thermodn. problems and makes a functional's performance more uniform over the entire database. The refitted functionals typically have a lower mean abs. deviation for the majority of subsets in the proposed GMTKN24 set. This, however, is also often accompanied at the expense of poor performance for a few other important subsets. Thus, creating a broadly applicable (and overall better) functional by just reparameterizing existing ones seems to be difficult. Nevertheless, this benchmark study reveals that a reoptimized (i.e., empirical) version of the TPSS-D functional (oTPSS-D) performs well for a variety of problems and may meet the stds. of an improved functional. We propose validation against this new compilation of benchmark sets as a definitive way to evaluate a new quantum chem. method's true performance.
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Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. Gaussian-2 theory for molecular energies of first-and second-row compounds. J. Chem. Phys. 1991, 94, 7221, DOI: 10.1063/1.460205
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Gaussian-2 theory for molecular energies of first- and second-row compounds
Curtiss, Larry A.; Raghavachari, Krishnan; Trucks, Gary W.; Pople, John A.
Journal of Chemical Physics (1991), 94 (11), 7221-30CODEN: JCPSA6; ISSN:0021-9606.
The Gaussian-2 theor. procedure (G2 theory), based on ab-initio MO theory, for calcn. of mol. energies (atomization energies, ionization potentials, electron affinities, and proton affinities) of compds. contg. first- (Li-F) and second-row atoms (Na-Cl) is presented. This new theor. procedure adds three features to G1 theory (P., et al., 1989; C., et al., 1990), including a correction for nonadditivity of diffuse-sp and 2df basis-set extensions, a basis-set extension contg. a third d-function on nonhydrogen atoms and a second p-function on hydrogen atoms, and a modification of the higher level correction. G2 theory is a significant improvement over G1 theory, because it eliminates a no. of deficiencies present in G1 theory. Of particular importance is the improvement in atomization energies of ionic mols. such as LiF and hydrides such as C2H6,NH3, N2H4, H2O2, and CH3SH. The av. abs. deviation from expt. of atomization energies of 39 first-row compds. is reduced from 1.42 to 0.92 kcal/mol. In addn., G2 theory gives improved performance for hypervalent species and electron affinities of second-row species (the av. deviation from expt. of electron affinities of second-row species is reduced from 1.94 to 1.08 kcal/mol). Finally, G2 atomization energies for another 43 mols., not previously studied with G1 theory, many of which have uncertain exptl. data, are presented and differences with expt. are assessed.
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Śmiga, S.; Franck, O.; Mussard, B.; Buksztel, A.; Grabowski, I.; Luppi, E.; Toulouse, J. Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method. J. Chem. Phys. 2016, 145, 144102, DOI: 10.1063/1.4964319
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Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method
Smiga, Szymon; Franck, Odile; Mussard, Bastien; Buksztel, Adam; Grabowski, Ireneusz; Luppi, Eleonora; Toulouse, Julien
Journal of Chemical Physics (2016), 145 (14), 144102/1-144102/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
We introduce an orbital-optimized double-hybrid (DH) scheme using the optimized-effective-potential (OEP) method. The orbitals are optimized using a local potential corresponding to the complete exchange-correlation energy expression including the second-order Moller-Plesset correlation contribution. We have implemented a one-parameter version of this OEP-based self-consistent DH scheme using the BLYP d.-functional approxn. and compared it to the corresponding non-self-consistent DH scheme for calcns. on a few closed-shell atoms and mols. While the OEP-based self-consistency does not provide any improvement for the calcns. of ground-state total energies and ionization potentials, it does improve the accuracy of electron affinities and restores the meaning of the LUMO orbital energy as being connected to a neutral excitation energy. Moreover, the OEP-based self-consistent DH scheme provides reasonably accurate exchange-correlation potentials and correlated densities. (c) 2016 American Institute of Physics.
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Śmiga, S.; Grabowski, I.; Witkowski, M.; Mussard, B.; Toulouse, J. Self-Consistent Range-Separated Density-Functional Theory with Second-Order Perturbative Correction via the Optimized-Effective-Potential Method. J. Chem. Theory Comput. 2020, 16, 211, DOI: 10.1021/acs.jctc.9b00807
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Self-Consistent Range-Separated Density-Functional Theory with Second-Order Perturbative Correction via the Optimized-Effective-Potential Method
Smiga Szymon; Grabowski Ireneusz; Witkowski Mateusz; Mussard Bastien; Toulouse Julien
Journal of chemical theory and computation (2020), 16 (1), 211-223 ISSN:.
We extend the range-separated double-hybrid RSH+MP2 method (Angyan, J. G.; et al. Phys. Rev. A2005, 72, 012510), combining long-range HF exchange and MP2 correlation with a short-range density functional to a fully self-consistent version using the optimized-effective-potential technique in which the orbitals are obtained from a local potential including the long-range HF and MP2 contributions. We test this approach, that we name RS-OEP2, on a set of small closed-shell atoms and molecules. For the commonly used value of the range-separation parameter μ = 0.5 bohr(-1), we find that self-consistency does not seem to bring any improvement for total energies, ionization potentials, and electronic affinities. However, contrary to the non-self-consistent RSH+MP2 method, the present RS-OEP2 method gives a LUMO energy which physically corresponds to a neutral excitation energy and gives local exchange-correlation potentials which are reasonably good approximations to the corresponding Kohn-Sham quantities. At a finer scale, we find that RS-OEP2 gives largely inaccurate correlation potentials and correlated densities, which points to the need of further improvement of this type of range-separated double hybrids.
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Cohen, A. J.; Mori-Sánchez, P.; Yang, W. Second-Order Perturbation Theory with Fractional Charges and Fractional Spins. J. Chem. Theory Comput. 2009, 5, 786, DOI: 10.1021/ct8005419
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Second-Order Perturbation Theory with Fractional Charges and Fractional Spins
Cohen, Aron J.; Mori-Sanchez, Paula; Yang, Weitao
Journal of Chemical Theory and Computation (2009), 5 (4), 786-792CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
The behavior of MP2 for fractional occupations is investigated. The consideration of fractional charge behavior gives a simple derivation of an expression for the chem. potential (or the deriv. of energy with respect to the no. of electrons) of MP2. A generalized optimized effective potential formalism (OEP) has been developed in which the OEP is a nonlocal potential, which can be applied to explicit functionals of the orbitals and eigenvalues and also facilitates the evaluation of the chem. potential. The MP2 deriv. improves upon the corresponding Koopmans' theorem in Hartree-Fock theory for the ionization energy and also gives a good est. of the electron affinity. In strongly correlated systems with degeneracies and fractional spins, MP2 diverges, and another cor. second-order perturbative method ameliorates this failure for the energy but still does not recapture the correct behavior for the energy derivs. that yield the gap. Overall we present a view of wave function based methods and their behavior for fractional charges and spins that offers insight into the application of these methods to challenging chem. problems.
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Su, N. Q.; Yang, W.; Mori-Sánchez, P.; Xu, X. Fractional Charge Behavior and Band Gap Predictions with the XYG3 Type of Doubly Hybrid Density Functionals. J. Phys. Chem. A 2014, 118, 9201, DOI: 10.1021/jp5029992
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Fractional Charge Behavior and Band Gap Predictions with the XYG3 Type of Doubly Hybrid Density Functionals
Su, Neil Qiang; Yang, Weitao; Mori-Sanchez, Paula; Xu, Xin
Journal of Physical Chemistry A (2014), 118 (39), 9201-9211CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
In this work, we examine the fractional charge behaviors of doubly hybrid (DH) functionals. By plotting the ground-state energies E and energy derivs. for atoms and mols. with fractional electron nos. N, we directly quantify the delocalization errors of some representative DH functionals such as B2PLYP, XYG3, and XYGJ-OS. Numerical assessments on ionization potentials (IPs), electron affinities (EAs), and fundamental gaps, from either integer no. calcns. or energy deriv. calcns., are provided. It is shown that the XYG3 type of DH functionals gives good agreement between their energy derivs. and the exptl. IPs, EAs, and gaps, as expected from their nearly straight line fractional charge behaviors.
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Mussard, B.; Toulouse, J. Fractional-charge and fractional-spin errors in range-separated density-functional theory. Mol. Phys. 2017, 115, 161, DOI: 10.1080/00268976.2016.1213910
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Fractional-charge and fractional-spin errors in range-separated density-functional theory
Mussard, Bastien; Toulouse, Julien
Molecular Physics (2017), 115 (1-2), 161-173CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)
We investigate fractional-charge and fractional-spin errors in range-sepd. d.-functional theory (DFT). Specifically, we consider the range-sepd. hybrid (RSH) method which combines long-range Hartree-Fock (HF) exchange with a short-range semilocal exchange-correlation d. functional, and the RSH+MP2 method which adds long-range, second-order Moller-Plesset (MP2) correlation. Results on atoms and mols. show that the fractional-charge errors obtained in RSH are much smaller than in the std. Kohn-Sham (KS) scheme applied with semilocal or hybrid approxns., and also generally smaller than in the std. HF method. The RSH+MP2 method tends to have smaller fractional-charge errors than std. MP2 for the most diffuse systems, but larger fractional-charge errors for the more compact systems. Even though the individual contributions to the fractional-spin errors in the H atom coming from the short-range exchange and correlation d.-functional approxns. are smaller than the corresponding contributions for the full-range exchange and correlation d.-functional approxns., RSH gives fractional-spin errors that are larger than in the std. KS scheme and only slightly smaller than in std. HF. Adding long-range MP2 correlation only leads to infinite fractional-spin errors. This work clarifies the successes and limitations of range-sepd. DFT approaches for eliminating self-interaction and static-correlation errors.
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Su, N. Q.; Xu, X. Insights into Direct Methods for Predictions of Ionization Potential and Electron Affinity in Density Functional Theory. J. Phys. Chem. Lett. 2019, 10, 2692, DOI: 10.1021/acs.jpclett.9b01052
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Insights into Direct Methods for Predictions of Ionization Potential and Electron Affinity in Density Functional Theory
Su, Neil Qiang; Xu, Xin
Journal of Physical Chemistry Letters (2019), 10 (11), 2692-2699CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
Vertical ionization potential (IP) and electron affinity (EA) are fundamental mol. properties, while the Δ method and the direct method are the widely used approaches to compute these properties. The Δ method is calcd. by taking the total energy difference of the initial and final states, whose reliability is seriously affected by the issue assocd. with the imbalanced treatment of these two states. The direct method based on the derivs. involving only one single-state calcn. can yield a quasiparticle spectrum whose accuracy, on the other hand, is mostly affected by the levels of approx. mol. structure theories. Because of the aforementioned issues, EA prediction can be particularly problematic. Here we present, for the first time, an analytic theory on the derivation and realization of generalized Kohn-Sham (KS) eigenvalues of doubly hybrid (DH) functionals that depend on both occupied and unoccupied orbitals. The method based on the KS eigenvalues of neutral systems, termed the NKS method, is found to suffer little from the imbalance issue, while it is only the NKS method that can offer accurate EA prediction from a good functional approxn., such as the XYG3 type of DH functionals. Being less sensitive to the size of basis sets, the NKS method is of great significance for its application to large systems. The insights gained in this work are useful for the calcn. of properties assocd. with small energy differences while emphasizing the importance of the development of generalized functionals that rely on both occupied and unoccupied orbitals.
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Beste, A.; Vázquez-Mayagoitia, Á.; Ortiz, J. V. Direct ΔMBPT(2) method for ionization potentials, electron affinities, and excitation energies using fractional occupation numbers. J. Chem. Phys. 2013, 138, 074101, DOI: 10.1063/1.4790626
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Direct ΔMBPT(2) method for ionization potentials, electron affinities, and excitation energies using fractional occupation numbers
Beste, Ariana; Vazquez-Mayagoitia, Alvaro; Ortiz, J. V.
Journal of Chemical Physics (2013), 138 (7), 074101/1-074101/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A direct method (D-ΔMBPT(2)) to calc. 2nd-order ionization potentials (IPs), electron affinities (EAs), and excitation energies is developed. The ΔMBPT(2) method is defined as the correlated extension of the ΔHF method. Energy differences are obtained by integrating the energy deriv. with respect to occupation nos. over the appropriate parameter range. This is made possible by writing the 2nd-order energy as a function of the occupation nos. Relaxation effects are fully included at the SCF level. This is in contrast to linear response theory, which makes the D-ΔMBPT(2) applicable not only to single excited but also higher excited states. We show the relationship of the D-ΔMBPT(2) method for IPs and EAs to a 2nd-order approxn. of the effective Fock-space coupled-cluster Hamiltonian and a 2nd-order electron propagator method. We also discuss the connection between the D-ΔMBPT(2) method for excitation energies and the CIS-MP2 method. Finally, as a proof of principle, we apply our method to calc. ionization potentials and excitation energies of some small mols. For IPs, the ΔMBPT(2) results compare well to the 2nd-order soln. of the Dyson equation. For excitation energies, the deviation from equation of motion coupled cluster singles and doubles increases when correlation becomes more important. When using the numerical integration technique, we encounter difficulties that prevented us from reaching the ΔMBPT(2) values. Most importantly, relaxation beyond the Hartree-Fock level is significant and needs to be included in future research. (c) 2013 American Institute of Physics.
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Gu, Y.; Xu, X. Extended Koopmans’ theorem in the adiabatic connection formalism: Applied to doubly hybrid density functionals. J. Chem. Phys. 2020, 153, 044109, DOI: 10.1063/5.0010743
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Extended Koopmans' theorem in the adiabatic connection formalism: Applied to doubly hybrid density functionals
Gu, Yonghao; Xu, Xin
Journal of Chemical Physics (2020), 153 (4), 044109CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A rigorous framework that combines the extended Koopmans' theorem (EKT) with the adiabatic connection (AC) formalism of d. functional theory is developed here, namely, EKT-AC, to calc. the vertical ionization potentials (IPs) of mol. systems. When applied to the doubly hybrid d. functional approxns. (DH-DFAs), the EKT-DH approach is established for the B2PLYP-type DHs with one-parameter and two-parameters, as well as the XYG3-type DHs. Based on EKT-DH, an approxn. of the KT type is introduced, leading to the KT-DH approach. The IP-condition that the calcd. vertical IPs with EKT-DH or KT-DH are to reproduce the exptl. IPs closely is applied to investigate the commonly used DH-DFAs for such a purpose and is utilized as a principle for DH-DFA developments. Considering the systematic improvements, as well as its numeric stability, we recommend the KT-B2GPPLYP approach as a pragmatic way for vertical IP calcns. (c) 2020 American Institute of Physics.
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Grimme, S.; Neese, F. Double-hybrid density functional theory for excited electronic states of molecules. J. Chem. Phys. 2007, 127, 154116, DOI: 10.1063/1.2772854
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Double-hybrid density functional theory for excited electronic states of molecules
Grimme, Stefan; Neese, Frank
Journal of Chemical Physics (2007), 127 (15), 154116/1-154116/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Double-hybrid d. functionals are based on a mixing of std. generalized gradient approxns. (GGAs) for exchange and correlation with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional (dubbed B2PLYP) contains only two empirical parameters that describe the mixt. of HF and GGA exchange (ax) and of the PT2 and GGA correlation (ac), resp. Extensive testing has recently demonstrated the outstanding accuracy of this approach for various ground state problems in general chem. applications. The method is extended here without any further empirical adjustments to electronically excited states in the framework of time-dependent d. functional theory (TD-DFT) or the closely related Tamm-Dancoff approxn. (TDA-DFT). In complete analogy to the ground state treatment, a scaled second-order perturbation correction to CI with singles (CIS(D)) wave functions developed some years ago by Head-Gordon et al. is computed on the basis of d. functional data and added to the TD(A)-DFT/GGA excitation energy. The method is implemented by applying the resoln. of the identity approxn. and the efficiency of the code is discussed. Extensive tests for a wide variety of mols. and excited states (of singlet, triplet, and doublet multiplicities) including electronic spectra are presented. In general, rather accurate excitation energies (deviations from ref. data typically <0.2 eV) are obtained that are mostly better than those from std. functionals. Still, systematic errors are obtained for Rydberg (too low on av. by about 0.3 eV) and charge-transfer transitions but due to the relatively large ax parameter (0.53), B2PLYP outperforms most other functionals in this respect. Compared to conventional HF-based CIS(D), the method is more robust in electronically complex situations due to the implicit account of static correlation effects by the GGA parts. The (D) correction often works in the right direction and compensates for the overestimation of the transition energy at the TD level due to the elevated fraction of HF exchange in the hybrid GGA part. Finally, the limitations of the method are discussed for challenging systems such as transition metal complexes, cyanine dyes, and multireference cases.
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Hirata, S.; Head-Gordon, M. Time-dependent density functional theory within the Tamm–Dancoff approximation. Chem. Phys. Lett. 1999, 314, 291, DOI: 10.1016/S0009-2614(99)01149-5
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Time-dependent density functional theory within the Tamm-Dancoff approximation
Hirata, S.; Head-Gordon, M.
Chemical Physics Letters (1999), 314 (3,4), 291-299CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
A computationally simple method for mol. excited states, namely, the Tamm-Dancoff approxn. to time-dependent d. functional theory, is proposed and implemented. This method yields excitation energies for several closed- and open-shell mols. that are essentially of the same quality as those obtained from time-dependent d. functional theory itself, when the same exchange-correlation functional is used.
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Foresman, J. B.; Head-Gordon, M.; Pople, J. A.; Frisch, M. J. Toward a systematic molecular orbital theory for excited states. J. Phys. Chem. 1992, 96, 135, DOI: 10.1021/j100180a030
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Toward a systematic molecular orbital theory for excited states
Foresman, James B.; Head-Gordon, Martin; Pople, John A.; Frisch, Michael J.
Journal of Physical Chemistry (1992), 96 (1), 135-49CODEN: JPCHAX; ISSN:0022-3654.
The methodol. and computational considerations necessary for the detn. of the ab initio energy, wave function, and gradient of a mol. in an electronically excited state using MO theory are discussed. A fundamental level of theory is reexamd. which was employed several years ago for the interpretation of the electronic spectra of simple org. mols.: CI (CI) among all singly substituted determinants using a Hartree-Fock ref. state. Several new enhancements to this general theory are given. First, it is shown how the "CI-singles" wave function can be used to compute efficiently the analytic first deriv. of the energy in order to obtain accurate properties and optimized geometries for a wide range of mols. in their excited states. Secondly, a computer program is described which allows these computations to be done in a "direct" fashion, with no disk storage required for the two-electron repulsion integrals. This allows investigations of systems with large nos. of atoms (or large nos. of basis functions). Thirdly it is shown how the CI-singles approxn. can be cor. via second-order Moeller-Plesset perturbation theory to produce a level of theory for excited states which further includes some effects of electronic correlation. The relative success of the model as a function of basis set indicates that a judicious choice of basis set is needed in order to evaluate its performance adequately. Application of the method to the excited states of formaldehyde, ethylene, pyridine, and porphin demonstrates the utility of CI-singles theory.
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Head-Gordon, M.; Rico, R. J.; Oumi, M.; Lee, T. J. A doubles correction to electronic excited states from configuration interaction in the space of single substitutions. Chem. Phys. Lett. 1994, 219, 21, DOI: 10.1016/0009-2614(94)00070-0
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A doubles correction to electronic excited states from configuration interaction in the space of single substitutions
Head-Gordon, Martin; Rico, Rudolph J.; Oumi, Manabu; Lee, Timothy J.
Chemical Physics Letters (1994), 219 (1-2), 21-9CODEN: CHPLBC; ISSN:0009-2614.
A perturbative correction to the method of CI with single substitutions (CIS) is presented. This CIS(D) correction approx. introduces the effect of double substitutions which are absent in CIS excited states. CIS(D) is a second-order perturbation expansion of the coupled-cluster excited state method, restricted to single and double substitutions, in a series in which CIS is zeroth order, and the first-order correction vanishes. CIS(D) excitation energies are size consistent and the calculational complexity scales with the fifth power of mol. size, akin to second-order Moeller-Plesset theory for the ground state. Calcns. on singlet excited states of ethylene, formaldehyde, acetaldehyde, butadiene and benzene show that CIS(D) is a uniform improvement over CIS. CIS(D) appears to be a promising method for examg. excited states of large mols., where more accurate methods are not feasible.
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Ottochian, A.; Morgillo, C.; Ciofini, I.; Frisch, M. J.; Scalmani, G.; Adamo, C. Double hybrids and time-dependent density functional theory: An implementation and benchmark on charge transfer excited states. J. Comput. Chem. 2020, 41, 1242, DOI: 10.1002/jcc.26170
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Double hybrids and time-dependent density functional theory: An implementation and benchmark on charge transfer excited states
Ottochian, Alistar; Morgillo, Carmela; Ciofini, Ilaria; Frisch, Michael J.; Scalmani, Giovanni; Adamo, Carlo
Journal of Computational Chemistry (2020), 41 (13), 1242-1251CODEN: JCCHDD; ISSN:0192-8651. (John Wiley & Sons, Inc.)
In this paper we present the implementation and benchmarking of a Time Dependent D. Functional Theory approach in conjunction with Double Hybrid (DH) functionals. We focused on the anal. of their performance for through space charge-transfer (CT) excitations which are well known to be very problematic for commonly used functionals, such as global hybrids. Two different families of functionals were compared, each of them contg. pure, hybrid and double-hybrid functionals. The results obtained show that, beside the robustness of the implementation, these functionals provide results with an accuracy comparable to that of adjusted range-sepd. functionals, with the relevant difference that for DHs no parameter is tuned on specific compds. thus making them more appealing for a general use. Furthermore, the algorithm described and implemented is characterized by the same computational cost scaling as that of the ground state algorithm employed for MP2 and double hybrids.
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Schwabe, T.; Goerigk, L. Time-Dependent Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling. J. Chem. Theory Comput. 2017, 13, 4307, DOI: 10.1021/acs.jctc.7b00386
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Time-Dependent Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling
Schwabe, Tobias; Goerigk, Lars
Journal of Chemical Theory and Computation (2017), 13 (9), 4307-4323CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
For the first time, we combine time-dependent double-hybrid d. functional approxns. (TD-DHDFAs) for the calcn. of electronic excitation energies with the concepts of spin-component and spin-opposite scaling (SCS/SOS) of electron-pair contributions to their nonlocal correlation components. Different flavors of this idea, ranging from std. SCS parameters to fully fitted parameter sets, are presented and tested on six different parent DHDFAs. For cross-validation, we assess those methods on three benchmark sets that cover small- to medium-sized chromophores (up to 78 atoms) and different excitation types. For this purpose, we also introduce new CC3 ref. values for the popular Gordon benchmark set that we recommend using in future studies. Our results confirm that already the (unscaled) parent TD-DHDFAs are accurate and outperform some wave function methods. Further introduction of SCS/SOS eliminates extreme outliers, reduces deviation spans from ref. values by up to 0.5 eV, aligns the performance of the Tamm-Dancoff approxn. (TDA) to that of full TD calcns., and also enables a more balanced description of different excitation types. The best-performing TD-based methods in our cross validation have mean abs. deviations as low as 0.14 eV compared to the time- and resource-intensive CC3 approach. A very important finding is that we also obtained SOS variants with excellent performance, contrary to wave function based methods. This opens a future pathway to highly efficient methods for the optimization of excited-state geometries, particularly when paired with computing strategies such as the Laplace transform. We recommend our SCS- and SOS-based variants for further testing and subsequent applications.
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Casanova-Páez, M.; Goerigk, L. Time-Dependent Long-Range-Corrected Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling: A Comprehensive Analysis of Singlet–Singlet and Singlet–Triplet Excitation Energies. J. Chem. Theory Comput. 2021, 17, 5165, DOI: 10.1021/acs.jctc.1c00535
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Time-Dependent Long-Range-Corrected Double-Hybrid Density Functionals with Spin-Component and Spin-Opposite Scaling: A Comprehensive Analysis of Singlet-Singlet and Singlet-Triplet Excitation Energies
Casanova-Paez, Marcos; Goerigk, Lars
Journal of Chemical Theory and Computation (2021), 17 (8), 5165-5186CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Following the work on spin-component and spin-opposite scaled (SCS/SOS) global double hybrids for singlet-singlet excitations by Schwabe and Goerigk [J. Chem. Theory Comput., 20217, 13, 4307] and our own works on new long-range cor. (LC) double hybrids for singlet-singlet and singlet-triplet excitations [J. Chem. Theory Comput., 2019, 15, 4735], we present new LC double hybrids with SCS/SOS that demonstrate further improvement over previously published results and methods. We introduce new unscaled and scaled versions of different global and LC double hybrids based on Becke88 or PBE exchange combined with LYP, PBE, or P86 correlation. For singlet-singlet excitations, we cross-validate them on six benchmark sets that cover small to medium-sized chromophores with different excitation types (local-valence, Rydberg, and charge transfer). For singlet-triplet excitations, we perform the cross-validation on three different benchmark sets following the same anal. as in our previous work in 2020. In total, 203 excitations are analyzed. Our results confirm and extend those of Schwabe and Goerigk regarding the superior performance of SCS and SOS variants compared to their unscaled parents by decreasing mean abs. deviations, root-mean-square deviations, or error spans by more than half and bringing abs. mean deviations closer to zero. Our SCS/SOS variants are shown to be highly efficient and robust for the computation of vertical excitation energies, which even outperform specialized double hybrids that also contain an LC in their perturbative part. In particular, our new SCS/SOS-ωPBEPP86 and SCS/SOS-ωB88PP86 functionals are four of the most accurate and robust methods tested in this work, and we fully recommend them for future applications. However, if the relevant SCS and SOS algorithms are not available to the user, we suggest ωPBEPP86 as the best unscaled method in this work.
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Mester, D.; Kállay, M. A simple range-separated double-hybrid density functional theory for excited states. J. Chem. Theory Comput. 2021, 17, 927, DOI: 10.1021/acs.jctc.0c01135
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A Simple Range-Separated Double-Hybrid Density Functional Theory for Excited States
Mester, David; Kallay, Mihaly
Journal of Chemical Theory and Computation (2021), 17 (2), 927-942CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
A simple and robust range-sepd. (RS) double-hybrid (DH) time-dependent d. functional approach is presented for the accurate calcn. of excitation energies of mols. within the Tamm-Dancoff approxn. The scheme can be considered as an excited-state extension of the ansatz proposed by Toulouse and co-workers [J. Chem. Phys. 2018, 148, 164105], which is based on the two-parameter decompn. of the Coulomb potential, for which both the exchange and correlation contributions are range-sepd. A flexible and efficient implementation of the new scheme is also presented, which facilitates its extension to any combination of exchange and correlation functionals. The performance of the new approxn. is tested for singlet excitations on several benchmark compilations and thoroughly compared to that of representative DH, RS hybrid, and RS DH functionals. The one-electron basis set dependence and computation times are also assessed. Our results show that the new approach improves on std. DHs in most cases, and it can provide a more robust and accurate alternative. In addn., on av., it noticeably surpasses the existing RS hybrid and RS DH functionals.
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Schirmer, J.; Trofimov, A. B. Intermediate state representation approach to physical properties of electronically excited molecules. J. Chem. Phys. 2004, 120, 11449, DOI: 10.1063/1.1752875
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Intermediate state representation approach to physical properties of electronically excited molecules
Schirmer, J.; Trofimov, A. B.
Journal of Chemical Physics (2004), 120 (24), 11449-11464CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Propagator methods provide a direct approach to energies and transition moments for (generalized) electronic excitations from the ground state, but they do not usually allow 1 to det. excited state wave functions and properties. Using a specific intermediate state representation (ISR) concept, the authors here show how this restriction can be overcome in the case of the algebraic-diagrammatic construction (ADC) propagator approach. In the ISR reformulation of the theory the basic ADC secular matrix is written as a representation of the Hamiltonian (or the shifted Hamiltonian) in terms of explicitly constructible states, referred to as intermediate (or ADC) states. Similar intermediate state representations can be derived for operators other than the Hamiltonian. Together with the ADC eigenvectors, the intermediate states give rise to an explicit formulation of the excited wave functions and allow 1 to calc. phys. properties of excited states as well as transition moments for transitions between different excited states. As for the ground-state excitation energies and transition moments, the ADC excited state properties are size consistent so that the theory is suitable for applications to large systems. The established hierarchy of higher-order [ADC(n)] approxns., corresponding to systematic truncations of the IS configuration space and the perturbation-theor. expansions of the ISR matrix elements, can readily be extended to the excited state properties. Explicit ISR matrix elements for arbitrary 1-particle operators were derived and coded at the 2nd-order [ADC(2)] level of theory. As a 1st computational test of the method the authors have carried out ADC(2) calcns. for singlet and triplet excited state dipole moments in H2O and HF, where comparison to full CI results can be made. The potential of the ADC(2) method is further demonstrated in an exploratory study of the excitation energies and dipole moments of the low-lying excited states of para-nitroaniline. Four triplet states, T1-T4, and 2 singlet states, S1 and S2, lie (vertically) below the prominent charge transfer (CT) excitation, S3. The dipole moment of the S3 state (17.0 D) is distinctly larger than that of the corresponding T3 triplet state (11.7 D).
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Wormit, M.; Rehn, D. R.; Harbach, P. H. P.; Wenzel, J.; Krauter, C. M.; Epifanovsky, E.; Dreuw, A. Investigating Excited Electronic States using the Algebraic Diagrammatic Construction (ADC) Approach of the Polarisation Propagator. Mol. Phys. 2014, 112, 774, DOI: 10.1080/00268976.2013.859313
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Investigating excited electronic states using the algebraic diagrammatic construction (ADC) approach of the polarisation propagator
Wormit, Michael; Rehn, Dirk R.; Harbach, Philipp H. P.; Wenzel, Jan; Krauter, Caroline M.; Epifanovsky, Evgeny; Dreuw, Andreas
Molecular Physics (2014), 112 (5-6), 774-784CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)
The development of reliable theor. methods and the provision of efficient computer programs for the investigation of optical spectra and photochem. of large mols. in general is one of the most important tasks of contemporary theor. chem. Here, we present an overview of the current features of our implementation of the algebraic diagrammatic construction scheme of the polarisation propagator, which is a versatile and robust approach for the theor. investigation of excited states and their properties.
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Véril, M.; Scemama, A.; Caffarel, M.; Lipparini, F.; Boggio-Pasqua, M.; Jacquemin, D.; Loos, P.-F. QUESTDB: A database of highly accurate excitation energies for the electronic structure community. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1517 DOI: 10.1002/wcms.1517
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QUESTDB and A database of highly accurate excitation energies for the electronic structure community
Veril, Mickael; Scemama, Anthony; Caffarel, Michel; Lipparini, Filippo; Boggio-Pasqua, Martial; Jacquemin, Denis; Loos, Pierre-Francois
Wiley Interdisciplinary Reviews: Computational Molecular Science (2021), 11 (5), e1517CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
We describe our efforts of the past few years to create a large set of more than 500 highly accurate vertical excitation energies of various natures (π → π*, n → π*, double excitation, Rydberg, singlet, doublet, triplet, etc.) in small- and medium-sized mols. These values have been obtained using an incremental strategy which consists in combining high-order coupled cluster and selected CI calcns. using increasingly large diffuse basis sets in order to reach high accuracy. One of the key aspects of the so-called QUEST database of vertical excitations is that it does not rely on any exptl. values, avoiding potential biases inherently linked to expts. and facilitating theor. cross comparisons. Following this composite protocol, we have been able to produce theor. best ests. (TBEs) with the aug-cc-pVTZ basis set for each of these transitions, as well as basis set cor. TBEs (i.e., near the complete basis set limit) for some of them. The TBEs/aug-cc-pVTZ have been employed to benchmark a large no. of (lower-order) wave function methods such as CIS(D), ADC(2), CC2, STEOM-CCSD, CCSD, CCSDR(3), CCSDT-3, ADC(3), CC3, NEVPT2, and so on (including spin-scaled variants). In order to gather the huge amt. of data produced during the QUEST project, we have created a website () where one can easily test and compare the accuracy of a given method with respect to various variables such as the mol. size or its family, the nature of the excited states, the type of basis set, and so on. We hope that the present review will provide a useful summary of our effort so far and foster new developments around excited-state methods. This article is categorized under:Electronic Structure Theory > Ab Initio Electronic Structure Methods.
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Mester, D.; Kállay, M. Combined density functional and algebraic-diagrammatic construction approach for accurate excitation energies and transition moments. J. Chem. Theory Comput. 2019, 15, 4440, DOI: 10.1021/acs.jctc.9b00391
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Combined Density Functional and Algebraic-Diagrammatic Construction Approach for Accurate Excitation Energies and Transition Moments
Mester, David; Kallay, Mihaly
Journal of Chemical Theory and Computation (2019), 15 (8), 4440-4453CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
A composite of time-dependent d. functional theory (TDDFT) and the second-order algebraic-diagrammatic construction [ADC(2)] approach is presented for efficient calcn. of spectral properties of mols. Our method can be regarded as a new excited-state double-hybrid (DH) approach or a dressed TDDFT scheme, but it can also be interpreted as an empirically tuned ADC(2) model. Several combinations of exchange-correlation functionals and spin-scaling schemes are explored. Our best-performing method includes the Perdew, Burke, and Ernzerhof exchange and Perdew's 1986 correlation functional and employs the scaled-opposite-spin approxn. for the higher-order terms. The computation time of the new method scales as the fourth power of the system size, and an efficient cost-redn. approach is also presented, which further speeds up the calcns. Our benchmark calcns. show that the proposed model outperforms not only the existing DH approaches and ADC(2) variants but also the considerably more expensive coupled-cluster methods.
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Grimme, S. Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies. J. Chem. Phys. 2003, 118, 9095, DOI: 10.1063/1.1569242
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Improved second-order Moller-Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies
Grimme, Stefan
Journal of Chemical Physics (2003), 118 (20), 9095-9102CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A simple modification of the second-order Moller-Plesset perturbation theory (MP2) to improve the description of mol. ground state energies is proposed. The total MP2 correlation energy is partitioned into parallel- and antiparallel-spin components which are sep. scaled. The two parameters (scaling factors), whose values can be justified by basic theor. arguments, were optimized on a benchmark set of 51 reaction energies composed of 74 first-row mols. The new method performs significantly better than std. MP2: the rms [mean abs. error (MAE)] deviation drops from 4.6 (3.3) to 2.3 (1.8) kcal/mol. The max. error is reduced from 13.3 to 5.1 kcal/mol. Significant improvements are esp. obsd. for cases which are usually known as MP2 pitfalls while cases already described well with MP2 remain almost unchanged. Even for 11 atomization energies not considered in the fit, uniform improvements [MAE: 8.1 kcal/mol (MP2) vs. 3.2 kcal/mol (new)] were found. The results are furthermore compared with those from d. functional theory (DFT/B3LYP) and quadratic CI [QCISD/QCISD(T)] calcns. Also for difficult systems including strong (nondynamical) correlation effects, the improved MP2 method clearly outperforms DFT/B3LYP and yields results of QCISD or sometimes QCISD(T) quality. Preliminary calcns. of the equil. bond lengths and harmonic vibrational frequencies for ten diat. mols. also show consistent enhancements. The uniformity with which the new method improves upon MP2, thereby rectifying many of its problems, indicates significant robustness and suggests it as a valuable quantum chem. method of general use.
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Jung, Y.; Lochan, R. C.; Dutoi, A. D.; Head-Gordon, M. Scaled opposite-spin second order Møller–Plesset correlation energy: An economical electronic structure method. J. Chem. Phys. 2004, 121, 9793, DOI: 10.1063/1.1809602
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Scaled opposite-spin second order Moller-Plesset correlation energy: An economical electronic structure method
Jung, Yousung; Lochan, Rohini C.; Dutoi, Anthony D.; Head-Gordon, Martin
Journal of Chemical Physics (2004), 121 (20), 9793-9802CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A simplified approach to treating the electron correlation energy is suggested in which only the α-β component of the second order Moller-Plesset energy is evaluated, and then scaled by an empirical factor which is suggested to be 1.3. This scaled opposite-spin second order energy (SOS-MP2), where MP2 is Moller-Plesset theory, yields results for relative energies and deriv. properties that are statistically improved over the conventional MP2 method. Furthermore, the SOS-MP2 energy can be evaluated without the fifth order computational steps assocd. with MP2 theory, even without exploiting any spatial locality. A fourth order algorithm is given for evaluating the opposite spin MP2 energy using auxiliary basis expansions, and a Laplace approach, and timing comparisons are given.
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Kozuch, S.; Gruzman, D.; Martin, J. M. L. DSD-BLYP: A General Purpose Double Hybrid Density Functional Including Spin Component Scaling and Dispersion Correction. J. Phys. Chem. C 2010, 114, 20801, DOI: 10.1021/jp1070852
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DSD-BLYP: A General Purpose Double Hybrid Density Functional Including Spin Component Scaling and Dispersion Correction
Kozuch, Sebastian; Gruzman, David; Martin, Jan M. L.
Journal of Physical Chemistry C (2010), 114 (48), 20801-20808CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)
We present a general purpose double-hybrid DFT parametrization based on the BLYP functional, spin-component scaled (SCS) MP2-like correlation and a dispersion correction, called DSD-BLYP. Six training sets were used, including main group and transition state thermochem., kinetics, and dispersion forces. This new parametrization is usually 10-15% more accurate than the already exceptional B2GP-PLYP double hybrid, at the same computational cost. Its principal benefit is greater robustness for systems with significant nondynamical correlation. If a scaling factor is included in the harmonic frequency calcns., B2GP-PLYP was found to give very accurate results for kinetics, thermochem., and frequencies.
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Rhee, Y. M.; Head-Gordon, M. Scaled Second-Order Perturbation Corrections to Configuration Interaction Singles: Efficient and Reliable Excitation Energy Methods. J. Phys. Chem. A 2007, 111, 5314, DOI: 10.1021/jp068409j
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Scaled Second-Order Perturbation Corrections to Configuration Interaction Singles: Efficient and Reliable Excitation Energy Methods
Rhee, Young Min; Head-Gordon, Martin
Journal of Physical Chemistry A (2007), 111 (24), 5314-5326CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
Two modifications of the perturbative doubles correction to CI with single substitutions (CIS(D)) are suggested, which are excited state analogs of ground state scaled second-order Moller-Plesset (MP2) methods. The first approach employs two parameters to scale the two spin components of the direct term of CIS(D), starting from the two-parameter spin-component scaled (SCS) MP2 ground state, and is termed SCS-CIS(D). An efficient resoln.-of-the-identity (RI) implementation of this approach is described. The second approach employs a single parameter to scale only the opposite-spin direct term of CIS(D), starting from the one-parameter scaled opposite-spin (SOS) MP2 ground state, and is called SOS-CIS(D). By utilizing auxiliary basis expansions and a Laplace transform, a fourth-order algorithm for SOS-CIS(D) is described and implemented. The parameters that describe SCS-CIS(D) and SOS-CIS(D) are optimized based on a training set that includes valence excitations of various org. mols. and Rydberg transitions of water and ammonia, and they significantly improve upon CIS(D) itself. The accuracy of the two methods is found to be comparable. This arises from a strong correlation between the same-spin and the opposite-spin portions of the excitation energy terms. The methods are successfully applied to the zincbacteriochlorin-bacteriochlorin charge-transfer transition, for which time-dependent d. functional theory, with presently available exchange-correlation functionals, is known to fail. The methods are also successfully applied to describe various electronic transitions outside of the training set. The efficiency of the SOS-CIS(D) and the auxiliary basis implementation of CIS(D) and SCS-CIS(D) are confirmed with a series of timing tests.
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Hellweg, A.; Grün, S. A.; Hättig, C. Benchmarking the performance of spin-component scaled CC2 in ground and electronically excited states. Phys. Chem. Chem. Phys. 2008, 10, 4119, DOI: 10.1039/b803727b
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87
Benchmarking the performance of spin-component scaled CC2 in ground and electronically excited states
Hellweg, Arnim; Gruen, Sarah A.; Haettig, Christof
Physical Chemistry Chemical Physics (2008), 10 (28), 4119-4127CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
A generalization of the spin-component scaling and scaled opposite-spin modifications of second-order Moller-Plesset perturbation theory to the approx. coupled-cluster singles-and-doubles model CC2 (termed SCS-CC2 and SOS-CC2) is discussed and a preliminary implementation of ground and excited state energies and analytic gradients is reported. The computational results for bond distances, harmonic frequencies, adiabatic and 0-0 excitation energies are compared with exptl. results to benchmark their performance. Both variants of the spin-scaling increase the robustness of CC2 against strong correlation effects and lead for this method even to somewhat larger improvements than those obsd. for second-order Moller-Plesset perturbation theory. The spin-component scaling also enhances systematically the accuracy of CC2 for 0-0 excitation energies for π → π* and n → π* transitions, if geometries are detd. at the same level.
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Winter, N. O. C.; Hättig, C. Scaled opposite-spin CC2 for ground and excited states with fourth order scaling computational costs. J. Chem. Phys. 2011, 134, 184101, DOI: 10.1063/1.3584177
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Scaled opposite-spin CC2 for ground and excited states with fourth order scaling computational costs
Winter, Nina O. C.; Haettig, Christof
Journal of Chemical Physics (2011), 134 (18), 184101/1-184101/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
An implementation of scaled opposite-spin CC2 (SOS-CC2) for ground and excited state energies is presented that requires only fourth order scaling computational costs. The SOS-CC2 method yields results with an accuracy comparable to the unscaled method. Furthermore the time-detg. fifth order scaling steps in the algorithm can be replaced by only fourth order scaling computational costs using a "resoln. of the identity" approxn. for the electron repulsion integrals and a Laplace transformation of the orbital energy denominators. This leads to a significant redn. of computational costs esp. for large systems. Timings for ground and excited state calcns. are shown and the error of the Laplace transformation is investigated. An application to a chlorophyll mol. with 134 atoms results in a speed-up by a factor of five and demonstrates how the new implementation extends the applicability of the method. A SOS variant of the algebraic diagrammatic construction through second order ADC(2), which arises from a simplification of the SOS-CC2 model, is also presented. The SOS-ADC(2) model is a cost-efficient alternative in particular for future extensions to spectral intensities and excited state structure optimizations. (c) 2011 American Institute of Physics.
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Casanova-Páez, M.; Dardis, M. B.; Goerigk, L. ωB2PLYP and ωB2GPPLYP: The First Two Double-Hybrid Density Functionals with Long-Range Correction Optimized for Excitation Energies. J. Chem. Theory Comput. 2019, 15, 4735, DOI: 10.1021/acs.jctc.9b00013
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ωB2PLYP and ωB2GPPLYP: The First Two Double-Hybrid Density Functionals with Long-Range Correction Optimized for Excitation Energies
Casanova-Paez, Marcos; Dardis, Michael B.; Goerigk, Lars
Journal of Chemical Theory and Computation (2019), 15 (9), 4735-4744CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Double-hybrid d. functionals are currently the most accurate d. functionals for ground-state properties and electronic excitations. Nevertheless, the lack of a long-range correction scheme makes them unreliable when it comes to long-range excitations. For this reason, we propose the first two time-dependent double-hybrid functionals with correct asymptotic long-range behavior named ωB2PLYP and ωB2GPPLYP. Herein, we demonstrate their excellent performance and show that they are the most accurate and robust time-dependent d. functional theory methods for electronic excitation energies. They provide a balanced description of local-valence, Rydberg, and charge-transfer states. They are also able to tackle the difficult first two transitions in polycyclic arom. hydrocarbons and show very promising results in a preliminary study on transition-metal compds., exemplified for titanium dioxide clusters. This work shows that double hybrids can be systematically improved also for excitation energies, and further work in this field is warranted.
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Mester, D.; Kállay, M. Spin-Scaled Range-Separated Double-Hybrid Density Functional Theory for Excited States. J. Chem. Theory Comput. 2021, 17, 4211, DOI: 10.1021/acs.jctc.1c00422
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90
Spin-Scaled Range-Separated Double-Hybrid Density Functional Theory for Excited States
Mester, David; Kallay, Mihaly
Journal of Chemical Theory and Computation (2021), 17 (7), 4211-4224CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Our recently presented range-sepd. (RS) double-hybrid (DH) time-dependent d. functional approach [J. Chem. Theory Comput.17, 927 (2021)] is combined with spin-scaling techniques. The proposed spin-component-scaled (SCS) and scaled-opposite-spin (SOS) variants are thoroughly tested for almost 500 excitations including the most challenging types. This comprehensive study provides useful information not only about the new approaches but also about the most prominent methods in the DH class. The benchmark calcns. confirm the robustness of the RS-DH ansatz, while several tendencies and deficiencies are pointed out for the existing functionals. Our results show that the SCS variant consistently improves the results, while the SOS variant preserves the benefits of the original RS-DH method reducing its computational expenses. It is also demonstrated that, besides our approaches, only the nonempirical functionals provide balanced performance for general applications, while particular methods are only suggested for certain types of excitations.
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Mester, D.; Kállay, M. Accurate Spectral Properties within Double-Hybrid Density Functional Theory: A Spin-Scaled Range-Separated Second-Order Algebraic-Diagrammatic Construction-Based Approach. J. Chem. Theory Comput. 2022, 18, 865, DOI: 10.1021/acs.jctc.1c01100
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91
Accurate Spectral Properties within Double-Hybrid Density Functional Theory: A Spin-Scaled Range-Separated Second-Order Algebraic-Diagrammatic Construction-Based Approach
Mester, David; Kallay, Mihaly
Journal of Chemical Theory and Computation (2022), 18 (2), 865-882CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Our second-order algebraic-diagrammatic construction [ADC(2)]-based double-hybrid (DH) ansatz [J. Chem. Theory Comput.15, 4440 (2019)] is combined with range-sepn. techniques. In the present scheme, both the exchange and the correlation contributions are range-sepd., while spin-scaling approaches are also applied. The new methods are thoroughly tested for the most popular benchmark sets including 250 singlet and 156 triplet excitations, as well as 80 oscillator strengths. It is demonstrated that the range sepn. for the correlation contributions is highly recommended for both the genuine and the ADC(2)-based DH approaches. Our results show that the latter scheme slightly but consistently outperforms the former one for single excitation dominated transitions. Furthermore, states with larger fractions of double excitations are assessed as well, and challenging charge-transfer excitations are also discussed, where the recently proposed spin-scaled long-range cor. DHs fail. The suggested iterative fourth-power scaling RS-PBE-P86/SOS-ADC(2) method, using only three adjustable parameters, provides the most robust and accurate excitation energies within the DH theory. In addn., the relative error of the oscillator strengths is reduced by 65% compared to the best genuine DH functionals.
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Śmiga, S.; Grabowski, I. Spin-Component-Scaled ΔMP2 Parametrization: Toward a Simple and Reliable Method for Ionization Energies. J. Chem. Theory Comput. 2018, 14, 4780, DOI: 10.1021/acs.jctc.8b00638
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Spin-Component-Scaled ΔMP2 Parametrization: Toward a Simple and Reliable Method for Ionization Energies
Smiga, Szymon; Grabowski, Ireneusz
Journal of Chemical Theory and Computation (2018), 14 (9), 4780-4790CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
A practical, accurate, and cost- and implementation-free method (ΔMP2-SOS(IP)) for the calcn. of vertical ionization potentials is proposed. The simple method is based on a single-step, a diagonal, frequency-independent approxn. to the second-order self-energy expression combined with the spin-component-scaled technique. The search for an optimal scaling factor is performed for a set of 50 moderately sized mols., and the quality of the method is addnl. assessed for a benchmark set of 24 org. acceptor mols. The proposed ΔMP2-SOS(IP) method provides the best results of valence ionization energies as compared to the several std. self-consistent variants of the electron propagator methods at the second and higher orders (EP2, SCS-EP2, EP3, OVGF) with almost CCSD(T) or IP-EOM-CCSD accuracy and the cost of only a single opposite-spin ΔMP2-type calcn. (O(N3)). For core ionization energies, our new methods outperform the std. ΔMP2 results due to a better balanced treatment of the correlation and relaxation term in the second-order self-energy.
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93
Pickup, B. T.; Goscinski, O. Direct calculation of ionization energies. Mol. Phys. 1973, 26, 1013, DOI: 10.1080/00268977300102261
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93
Direct calculation of ionization energies. I. Closed shells
Pickup, B. T.; Goscincki, O.
Molecular Physics (1973), 26 (4), 1013-35CODEN: MOPHAM; ISSN:0026-8976.
The advantages of the propagator formalism, as a direct method of calcg. ionization energies, are stressed. The propagator equations are derived for closed-shell systems using an operator method instead of the usual diagrammatic derivations. The equations enable the development of an interpretation of the ionization energies in terms of conceptually simple quantities, such as pair correlation energies and assocd. relaxation effects, and retain the idea of orbital ionization. Infinite summations appearing in the self-energy terms are replaced by finite expressions involving functions satisfying uncoupled inhomogeneous differential equations. Certain high-order propagator equations are derived, and a connection with the Bethe-Goldstone formulation of pair correlation is made. Several computational procedures are advocated as forming the basis for balanced calcns. of at. and mol. ionization energies.
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Vidal, M. L.; Krylov, A. I.; Coriani, S. Dyson orbitals within the fc-CVS-EOM-CCSD framework: theory and application to X-ray photoelectron spectroscopy of ground and excited states. Phys. Chem. Chem. Phys. 2020, 22, 2693, DOI: 10.1039/C9CP03695D
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94
Dyson orbitals within the fc-CVS-EOM-CCSD framework: theory and application to X-ray photoelectron spectroscopy of ground and excited states
Vidal, Marta L.; Krylov, Anna I.; Coriani, Sonia
Physical Chemistry Chemical Physics (2020), 22 (5), 2693-2703CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
We report on the implementation of Dyson orbitals within the recently introduced frozen-core (fc) core-valence sepd. (CVS) equation-of-motion (EOM) coupled-cluster singles and doubles (CCSD) method, which enables efficient and reliable characterization of core-level states. The ionization potential (IP) variant of fc-CVS-EOM-CCSD, in which the EOM target states have one electron less than the ref., gives access to core-ionized states thus enabling modeling of X-ray photoelectron spectra (XPS) and its time-resolved variant (TR-XPS). Dyson orbitals are reduced quantities that can be interpreted as correlated states of the ejected/attached electron; they enter the expressions of various exptl. relevant quantities. In the context of photoelectron spectroscopy, Dyson orbitals can be used to est. the strengths of photoionization transitions. We illustrate the utility of Dyson orbitals and fc-CVS-EOM-IP-CCSD by calcg. XPS of the ground state of adenine and TR-XPS of the excited states of uracil.
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Díaz-Tinoco, M.; Corzo, H. H.; Pawłowski, F.; Ortiz, J. V. Do Dyson Orbitals resemble canonical Hartree–Fock orbitals?. Mol. Phys. 2019, 117, 2275, DOI: 10.1080/00268976.2018.1535142
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95
Do Dyson Orbitals resemble canonical Hartree-Fock orbitals?
Diaz-Tinoco, Manuel; Corzo, Hector H.; Pawlowski, Filip; Ortiz, J. V.
Molecular Physics (2019), 117 (17), 2275-2283CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)
A review. Dyson orbitals are overlaps between states with N and N±1 electrons and provide conceptual links between transition probabilities of electron detachment or attachment, d. matrixes, total energies and general principles of chem. bonding. Canonical, Hartree-Fock orbitals are compared with Dyson orbitals obtained with electron-propagator calcns. that retain all elements of the self-energy matrix, wherein all orbital-relaxation and electron-correlation corrections to Koopmans results reside. For valence ionization energies and electron affinities of representative closed-shell mols., canonical, Hartree-Fock orbitals usually are excellent approxns. to Dyson orbitals, although there are some notable cases where the resemblance is not as strong. Numerical relationships between pole strengths and the Koopmans contributions to Dyson orbitals also are inferred from the data.
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96
Ortiz, J. V. Dyson-orbital concepts for description of electrons in molecules. J. Chem. Phys. 2020, 153, 070902, DOI: 10.1063/5.0016472
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96
Dyson-orbital concepts for description of electrons in molecules
Ortiz, J. V.
Journal of Chemical Physics (2020), 153 (7), 070902CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Dyson orbitals, their electron-binding energies, and probability factors provide descriptions of electrons in mols. that are exptl. verifiable and that generalize qual. useful concepts of uncorrelated, mol.-orbital theory to the exact limit of Schrodinger's time-independent equation. Dyson orbitals are defined as overlaps between initial, N-electron states and final states with N±1 electrons and therefore are useful in the prediction and interpretation of many kinds of spectroscopic and scattering expts. They also are characteristic of N-electron initial states and may be used to construct electron densities, one-electron properties, and total energies with correlated Aufbau procedures that include probability factors between zero and unity. Relationships with natural orbitals, Kohn-Sham orbitals, and Hartree-Fock orbitals facilitate insights into the descriptive capabilities of Dyson orbitals. Electron-propagator approxns. that employ the Dyson quasiparticle equation or super-operator secular equations enable direct detn. of Dyson orbitals and obviate the need for many-electron wavefunctions of initial or final states. Numerical comparisons of the amplitudes and probability factors of Dyson orbitals calcd. with several self-energy approxns. reveal the effects of electron correlation on these uniquely defined, one-electron wavefunctions. (c) 2020 American Institute of Physics.
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Kállay, M.; Nagy, P. R.; Mester, D.; Gyevi-Nagy, L.; Csóka, J.; Szabó, P. B.; Rolik, Z.; Samu, G.; Csontos, J.; Hégely, B.; Ganyecz, Á.; Ladjánszki, I.; Szegedy, L.; Ladóczki, B.; Petrov, K.; Farkas, M.; Mezei, P. D.; Horváth, R. A. Mrcc, a quantum chemical program suite. See https://www.mrcc.hu/ (accessed March 1, 2023).
Google Scholar
There is no corresponding record for this reference.
98
Butscher, W.; Kammer, W. E. Modification of Davidson’s Method for the Calculation of Eigenvalues and Eigenvectors of Large Real-Symmetric Matrices: “Root Homing Procedure”. J. Comput. Phys. 1976, 20, 313, DOI: 10.1016/0021-9991(76)90084-X
Google Scholar
There is no corresponding record for this reference.
99
Dunning, T. H., Jr. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90, 1007, DOI: 10.1063/1.456153
Google Scholar
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Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
Dunning, Thom H., Jr.
Journal of Chemical Physics (1989), 90 (2), 1007-23CODEN: JCPSA6; ISSN:0021-9606.
Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.
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Woon, D. E.; Dunning, T. H., Jr. Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon. J. Chem. Phys. 1993, 98, 1358, DOI: 10.1063/1.464303
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100
Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon
Woon, David E.; Dunning, Thom H., Jr.
Journal of Chemical Physics (1993), 98 (2), 1358-71CODEN: JCPSA6; ISSN:0021-9606.
Correlation consistent and augmented correlation consistent basis sets were detd. for the second row atoms. The methodol., originally developed for the first row atoms (T. H. D., Jr., 1989) is first applied to S. The exponents for the polarization functions (dfgh) are systematically optimized for a correlated wave function (HF+1+2). The (sp) correlation functions are taken from the appropriate HF primitive sets; these functions differ little from the optimum functions. Basis sets of double zeta [4s3p1d], triple zeta [5s4p2d1f], and quadruple zeta [6s5p3d2f1g] quality are defined. Each of these sets is then augmented with diffuse functions to better describe electron affinities and other mol. properties: s and p functions were obtained by optimization for the anion HF energy, while an addnl. polarization function for each symmetry present in the std. set was optimized for the anion HF+1+2 energy. The results for S are then used to assist in detg. double zeta, triple zeta, and quadruple zeta basis sets for the remainder of the second row of the p block.
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Kendall, R. A.; Dunning, T. H., Jr.; Harrison, R. J. Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions. J. Chem. Phys. 1992, 96, 6796, DOI: 10.1063/1.462569
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Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions
Kendall, Rick A.; Dunning, Thom H., Jr.; Harrison, Robert J.
Journal of Chemical Physics (1992), 96 (9), 6796-806CODEN: JCPSA6; ISSN:0021-9606.
The authors describe a reliable procedure for calcg. the electron affinity of an atom and present results for H, B, C, O, and F (H is included for completeness). This procedure involves the use of the recently proposed correlation-consistent basis sets augmented with functions to describe the more diffuse character of the at. anion coupled with a straightforward, uniform expansion of the ref. space for multireference singles and doubles configuration-interaction (MRSD-CI) calcns. A comparison is given with previous results and with corresponding full CI calcns. The most accurate EAs obtained from the MRSD-CI calcns. are (with exptl. values in parentheses): H 0.740 eV (0.754), B 0.258 (0.277), C 1.245 (1.263), O 1.384 (1.461), and F 3.337 (3.401). The EAs obtained from the MR-SDCI calcns. differ by less than 0.03 eV from those predicted by the full CI calcns.
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102
Weigend, F.; Köhn, A.; Hättig, C. Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations. J. Chem. Phys. 2002, 116, 3175, DOI: 10.1063/1.1445115
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102
Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations
Weigend, Florian; Kohn, Andreas; Hattig, Christof
Journal of Chemical Physics (2002), 116 (8), 3175-3183CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The convergence of the second-order Moller-Plesset perturbation theory (MP2) correlation energy with the cardinal no. X is investigated for the correlation consistent basis-set series cc-pVXZ and cc-pV(X+d)Z. For the aug-cc-pVXZ and aug-cc-pV(X+d)Z series the convergence of the MP2 correlation contribution to the dipole moment is studied. It is found that, when d-shell electrons cannot be frozen, the cc-pVXZ and aug-cc-pVXZ basis sets converge much slower for third-row elements then they do for first- and second-row elements. Based on the results of these studies criteria are deduced for the accuracy of auxiliary basis sets used in the resoln. of the identity (RI) approxn. for electron repulsion integrals. Optimized auxiliary basis sets for RI-MP2 calcns. fulfilling these criteria are reported for the sets cc-pVXZ, cc-pV(X+d)Z, aug-cc-pVXZ, and aug-cc-pV(X+d)Z with X=D, T, and Q. For all basis sets the RI error in the MP2 correlation energy is more than two orders of magnitude smaller than the usual basis-set error. For the auxiliary aug-cc-pVXZ and aug-cc-pV(X+d)Z sets the RI error in the MP2 correlation contribution to the dipole moment is one order of magnitude smaller than the usual basis set error. Therefore extrapolations towards the basis-set limit are possible within the RI approxn. for both energies and properties. The redn. in CPU time obtained with the RI approxn. increases rapidly with basis set size. For the cc-pVQZ basis an acceleration by a factor of up to 170 is obsd.
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Weigend, F.; Häser, M.; Patzelt, H.; Ahlrichs, R. RI-MP2: optimized auxiliary basis sets and demonstration of efficiency. Chem. Phys. Lett. 1998, 294, 143, DOI: 10.1016/S0009-2614(98)00862-8
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103
RI-MP2: optimized auxiliary basis sets and demonstration of efficiency
Weigend, Florian; Haser, Marco; Patzelt, Holger; Ahlrichs, Reinhart
Chemical Physics Letters (1998), 294 (1,2,3), 143-152CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
Applications of the RI-MP2 method require high-quality auxiliary basis sets employed to approx. charge distributions. A variational procedure is proposed and applied to optimize auxiliary bases for main group and transition metal atoms which are tested for more than 350 mols. The RI approxn. affects mol. MP2 energies by less than 60 μEh per atom and equil. distances by less than 0.2 pm. We further comment on the extension from RHF to UHF and the exploitation of mol. symmetry. Applications to (Cu2S)n clusters and hydrocarbons CnH2n+2 document a significant redn. of computation times which allows for calcns. with up to 1000 basis functions in C1 symmetry.
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104
Weigend, F. Hartree–Fock Exchange Fitting Basis Sets for H to Rn. J. Comput. Chem. 2008, 29, 167, DOI: 10.1002/jcc.20702
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104
Hartree-Fock exchange fitting basis sets for H to Rn
Weigend Florian
Journal of computational chemistry (2008), 29 (2), 167-75 ISSN:0192-8651.
For elements H to Rn (except Lanthanides), a series of auxiliary basis sets fitting exchange and also Coulomb potentials in Hartree-Fock treatments (RI-JK-HF) is presented. A large set of small molecules representing nearly each element in all its common oxidation states was used to assess the quality of these auxiliary bases. For orbital basis sets of triple zeta valence and quadruple zeta valence quality, errors in total energies arising from the RI-JK approximation are below approximately 1 meV per atom in molecular compounds. Accuracy of RI-JK-approximated HF wave functions is sufficient for being used for post-HF treatments like Moller-Plesset perturbation theory, MP2. Compared to nonapproximated treatments, RI-JK-HF leads to large computational savings for quadruple zeta valence orbital bases and, in case of small to midsize systems, to significant savings for triple zeta valence bases.
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105
Krack, M.; Köster, A. M. An adaptive numerical integrator for molecular integrals. J. Chem. Phys. 1998, 108, 3226, DOI: 10.1063/1.475719
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105
An adaptive numerical integrator for molecular integrals
Krack, Matthias; Koster, Andreas M.
Journal of Chemical Physics (1998), 108 (8), 3226-3234CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
We present a new numerical integrator for mol. integrals that generates automatically an adaptive mol. grid. The tolerance of the numerical integration is the only input parameter of the integrator besides the at. coordinates and the at. nos. The adaptive numerical integrator was successfully implemented in our new d.-functional theory method (DFT method) ALLCHEM using the self consistent field (SCF) procedure. The accuracy of the numerical integration is superior to pruned fixed grids for a given no. of grid points. The adaptive grid generator allows a very efficient optimization of the grid for an individual mol. system. It is shown that the grid accuracy increases monotonically, if the given tolerance of the numerical integration is decreased. In this way it is possible to obtain results of high numerical precision. For a given tolerance of the numerical integration the adaptive grid generator automatically adjusts the grid to the basis set and the mol. structure. This feature increases the reliability of the numerical integration considerably and the no. of expensive ref. grid calcns. can be reduced. The time for the grid generation is small compared to the total computation time for a SCF calcn.
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106
Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865, DOI: 10.1103/PhysRevLett.77.3865
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106
Generalized gradient approximation made simple
Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
Physical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.
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107
Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic-behavior. Phys. Rev. A 1988, 38, 3098, DOI: 10.1103/PhysRevA.38.3098
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107
Density-functional exchange-energy approximation with correct asymptotic behavior
Becke, A. D.
Physical Review A: Atomic, Molecular, and Optical Physics (1988), 38 (6), 3098-100CODEN: PLRAAN; ISSN:0556-2791.
Current gradient-cor. d.-functional approxns. for the exchange energies of at. and mol. systems fail to reproduce the correct 1/r asymptotic behavior of the exchange-energy d. A gradient-cor. exchange-energy functional is given with the proper asymptotic limit. This functional, contg. only one parameter, fits the exact Hartree-Fock exchange energies of a wide variety of at. systems with remarkable accuracy, surpassing the performance of previous functionals contg. two parameters or more.
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108
Lee, C.; Yang, W.; Parr, R. G. Development of the Colle–Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B 1988, 37, 785, DOI: 10.1103/PhysRevB.37.785
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108
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
Lee, Chengteh; Yang, Weitao; Parr, Robert G.
Physical Review B: Condensed Matter and Materials Physics (1988), 37 (2), 785-9CODEN: PRBMDO; ISSN:0163-1829.
A correlation-energy formula due to R. Colle and D. Salvetti (1975), in which the correlation energy d. is expressed in terms of the electron d. and a Laplacian of the 2nd-order Hartree-Fock d. matrix, is restated as a formula involving the d. and local kinetic-energy d. On insertion of gradient expansions for the local kinetic-energy d., d.-functional formulas for the correlation energy and correlation potential are then obtained. Through numerical calcns. on a no. of atoms, pos. ions, and mols., of both open- and closed-shell type, it is demonstrated that these formulas, like the original Colle-Salvetti formulas, give correlation energies within a few percent.
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109
Perdew, J. P. Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys. Rev. B 1986, 33, 8822, DOI: 10.1103/PhysRevB.33.8822
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109
Density-functional approximation for the correlation energy of the inhomogeneous electron gas
Perdew
Physical review. B, Condensed matter (1986), 33 (12), 8822-8824 ISSN:0163-1829.
There is no expanded citation for this reference.
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110
Becke, A. D. Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals. J. Chem. Phys. 1997, 107, 8554, DOI: 10.1063/1.475007
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110
Density-functional thermochemistry. V. Systematic optimization of exchange-correlation functionals
Becke, Axel D.
Journal of Chemical Physics (1997), 107 (20), 8554-8560CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A systematic procedure for refining gradient corrections in Kohn-Sham exchange-correlation functionals is presented. The procedure is based on least-squares fitting to accurate thermochem. data. In this first application of the method, we use the G2 test set of Pople and co-workers to generate what we believe to be an optimum GGA/exact-exchange d.-functional theory (i.e., generalized gradient approxn. with mixing of exactly computed exchange).
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111
Lehtola, S.; Steigemann, C.; Oliveira, M. J. T.; Marques, M. A. L. Recent developments in Libxc – A comprehensive library of functionals for density functional theory. SoftwareX 2018, 7, 1, DOI: 10.1016/j.softx.2017.11.002
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There is no corresponding record for this reference.
112
https://www.tddft.org/programs/libxc/ (accessed May 1, 2023).
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There is no corresponding record for this reference.
113
Kozuch, S.; Martin, J. M. L. DSD-PBEP86: in search of the best double-hybrid DFT with spin-component scaled MP2 and dispersion corrections. Phys. Chem. Chem. Phys. 2011, 13, 20104, DOI: 10.1039/c1cp22592h
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113
DSD-PBEP86: in search of the best double-hybrid DFT with spin-component scaled MP2 and dispersion corrections
Kozuch, Sebastian; Martin, Jan M. L.
Physical Chemistry Chemical Physics (2011), 13 (45), 20104-20107CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
Spin-component scaled double hybrids including dispersion correction were optimized for many exchange and correlation functionals. Even DSD-LDA performs surprisingly well. DSD-PBEP86 emerged as a very accurate and robust method, approaching the accuracy of composite ab initio methods at a fraction of their computational cost.
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114
Chai, J.-D.; Mao, S.-P. Seeking for reliable double-hybrid density functionals without fitting parameters: The PBE0-2 functional. Chem. Phys. Lett. 2012, 538, 121, DOI: 10.1016/j.cplett.2012.04.045
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114
Seeking for reliable double-hybrid density functionals without fitting parameters: The PBE0-2 functional
Chai, Jeng-Da; Mao, Shan-Ping
Chemical Physics Letters (2012), 538 (), 121-125CODEN: CHPLBC; ISSN:0009-2614. (Elsevier B.V.)
Without the use of any empirical fitting to exptl. or high-level ab initio data, we present a double-hybrid d. functional approxn. for the exchange-correlation energy, combining the exact Hartree-Fock exchange and second-order Moller-Plesset (MP2) correlation with the Perdew-Burke-Ernzerhof (PBE) functional. This functional, denoted as PBE0-2, is shown to be accurate for a wide range of applications, when compared with other functionals and the ab initio MP2 method. The qual. failures of conventional d. functional approxns., such as self-interaction error and noncovalent interaction error, are significantly reduced by PBE0-2.
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115
Alipour, M. On the opposite-spin to same-spin ratio of absolute and interaction MP2 correlation energy in parameter-free spin-opposite-scaled double hybrids. Chem. Phys. Lett. 2017, 684, 423, DOI: 10.1016/j.cplett.2017.07.023
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115
On the opposite-spin to same-spin ratio of absolute and interaction MP2 correlation energy in parameter-free spin-opposite-scaled double hybrids
Alipour, Mojtaba
Chemical Physics Letters (2017), 684 (), 423-426CODEN: CHPLBC; ISSN:0009-2614. (Elsevier B.V.)
The applicability of the two types of opposite-spin to same-spin ratio of second-order Moller-Plesset correlation energy, namely the ratio of opposite-spin to same-spin of the abs. correlation energy and the most recently proposed ratio of opposite-spin to same-spin of the interaction correlation energy, in spin-opposite-scaled parameter-free double-hybrid d. functionals has been evaluated. Considering the interaction energies and hydrogen transfer barrier heights benchmark sets and comparing various functionals, it is shown that using the ratio related to the abs. correlation energy in double-hybrid calcns. provides lower deviations than that of the same ratio for the interaction correlation energy.
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Brémond, É.; Sancho-García, J. C.; Pérez-Jiménez, Á. J.; Adamo, C. Double-hybrid functionals from adiabatic-connection: The QIDH model. J. Chem. Phys. 2014, 141, 031101, DOI: 10.1063/1.4890314
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116
Communication: Double-hybrid functionals from adiabatic-connection: The QIDH model
Bremond, Eric; Sancho-Garcia, Juan Carlos; Perez-Jimenez, Angel Jose; Adamo, Carlo
Journal of Chemical Physics (2014), 141 (3), 031101/1-031101/4CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A new approach stemming from the adiabatic-connection (AC) formalism is proposed to derive parameter-free double-hybrid (DH) exchange-correlation functionals. It is based on a quadratic form that models the integrand of the coupling parameter, whose components are chosen to satisfy several well-known limiting conditions. Its integration leads to DHs contg. a single parameter controlling the amt. of exact exchange, which is detd. by requiring it to depend on the wt. of the MP2 correlation contribution. Two new parameter-free DHs functionals are derived in this way, by incorporating the non-empirical PBE and TPSS functionals in the underlying expression. Their extensive testing using the GMTKN30 benchmark indicates that they are in competition with state-of-the-art DHs, yet providing much better self-interaction errors and opening a new avenue towards the design of accurate double-hybrid exchange-correlation functionals departing from the AC integrand. (c) 2014 American Institute of Physics.
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117
Karton, A.; Tarnopolsky, A.; Lamère, J.-F.; Schatz, G. C.; Martin, J. M. L. Highly Accurate First-Principles Benchmark Data Sets for the Parametrization and Validation of Density Functional and Other Approximate Methods. Derivation of a Robust, Generally Applicable, Double-Hybrid Functional for Thermochemistry and Thermochemical Kinetics. J. Phys. Chem. A 2008, 112, 12868, DOI: 10.1021/jp801805p
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117
Highly Accurate First-Principles Benchmark Data Sets for the Parametrization and Validation of Density Functional and Other Approximate Methods. Derivation of a Robust, Generally Applicable, Double-Hybrid Functional for Thermochemistry and Thermochemical Kinetics
Karton, Amir; Tarnopolsky, Alex; Lamere, Jean-Francois; Schatz, George C.; Martin, Jan M. L.
Journal of Physical Chemistry A (2008), 112 (50), 12868-12886CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
We present a no. of near-exact, nonrelativistic, Born-Oppenheimer ref. data sets for the parametrization of more approx. methods (such as DFT functionals). The data were obtained by means of the W4 ab initio computational thermochem. protocol, which has a 95% confidence interval well below 1 kJ/mol. Our data sets include W4-08, which are total atomization energies of over 100 small mols. that cover varying degrees of non-dynamical correlations, and DBH24-W4, which are W4 theory values for Truhlar's set of 24 representative barrier heights. The usual procedure of comparing calcd. DFT values with exptl. atomization energies is hampered by comparatively large exptl. uncertainties in many exptl. values and compds. errors due to deficiencies in the DFT functional with those resulting from neglect of relativity and finite nuclear mass. Comparison with accurate, explicitly nonrelativistic, ab initio data avoids these issues. We then proceed to explore the performance of B2x-PLYP-type double hybrid functionals for atomization energies and barrier heights. The optimum hybrids for hydrogen-transfer reactions, heavy-atoms transfers, nucleophilic substitutions, and unimol. and recombination reactions are quite different from one another: out of these subsets, the heavy-atom transfer reactions are by far the most sensitive to the percentages of Hartree-Fock-type exchange y and MP2-type correlation x in an (x,y) double hybrid. The (42,72) hybrid B2K-PLYP, as reported in a preliminary communication, represents the best compromise between thermochem. and hydrogen-transfer barriers, while also yielding excellent performance for nucleophilic substitutions. By optimizing for best overall performance on both thermochem. and the DBH24-W4 data set, however, we find a new (36,65) hybrid which we term B2GP-PLYP. At a slight expense in performance for hydrogen-transfer barrier heights and nucleophilic substitutions, we obtain substantially better performance for the other reaction types. Although both B2K-PLYP and B2GP-PLYP are capable of 2 kcal/mol quality thermochem., B2GP-PLYP appears to be the more robust toward non-dynamical correlation and strongly polar character. We addnl. find that double-hybrid functionals display excellent performance for such problems as hydrogen bonding, prototype late transition metal reactions, pericyclic reactions, prototype cumulene-polyacetylene system, and weak interactions.
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118
Chai, J.-D.; Head-Gordon, M. Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615, DOI: 10.1039/b810189b
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118
Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections
Chai, Jeng-Da; Head-Gordon, Martin
Physical Chemistry Chemical Physics (2008), 10 (44), 6615-6620CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
We report re-optimization of a recently proposed long-range cor. (LC) hybrid d. functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom-atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochem., kinetics, and non-covalent interactions. Tests show that for non-covalent systems, ωB97X-D shows slight improvement over other empirical dispersion-cor. d. functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.
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119
Yanai, T.; Tew, D. P.; Handy, N. C. A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP). Chem. Phys. Lett. 2004, 393, 51, DOI: 10.1016/j.cplett.2004.06.011
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119
A new hybrid exchange-correlation functional using the Coulomb-attenuating method (CAM-B3LYP)
Yanai, Takeshi; Tew, David P.; Handy, Nicholas C.
Chemical Physics Letters (2004), 393 (1-3), 51-57CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
A new hybrid exchange-correlation functional named CAM-B3LYP is proposed. It combines the hybrid qualities of B3LYP and the long-range correction presented by Tawada et al. [J. Chem. Phys., in press]. We demonstrate that CAM-B3LYP yields atomization energies of similar quality to those from B3LYP, while also performing well for charge transfer excitations in a dipeptide model, which B3LYP underestimates enormously. The CAM-B3LYP functional comprises of 0.19 Hartree-Fock (HF) plus 0.81 Becke 1988 (B88) exchange interaction at short-range, and 0.65 HF plus 0.35 B88 at long-range. The intermediate region is smoothly described through the std. error function with parameter 0.33.
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120
Perdew, J. P.; Ernzerhof, M.; Burke, K. Rationale for mixing exact exchange with density functional approximations. J. Chem. Phys. 1996, 105, 9982, DOI: 10.1063/1.472933
Google Scholar
120
Rationale for mixing exact exchange with density functional approximations
Perdew, John P.; Ernzerhof, Matthias; Burke, Kieron
Journal of Chemical Physics (1996), 105 (22), 9982-9985CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
D. functional approxns. for the exchange-correlation energy ExcDFA of an electronic system are often improved by admixing some exact exchange Ex: Exc ≈ ExcDFA + (1/n)(Ex - ExDFA). This procedure is justified when the error in ExcDFA arises from the λ = 0 or exchange end of the coupling-const. integral ∫01dλ Exc,λDFA. We argue that the optimum integer n is approx. the lowest order of Goerling-Levy perturbation theory which provides a realistic description of the coupling-const. dependence Exc,λ in the range 0 ≤ λ ≤ 1, whence n ≈ 4 for atomization energies of typical mols. We also propose a continuous generalization of n as an index of correlation strength, and a possible mixing of second-order perturbation theory with the generalized gradient approxn.
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121
Liang, J.; Feng, X.; Hait, D.; Head-Gordon, M. Revisiting the Performance of Time-Dependent Density Functional Theory for Electronic Excitations: Assessment of 43 Popular and Recently Developed Functionals from Rungs One to Four. J. Chem. Theory Comput. 2022, 18, 3460, DOI: 10.1021/acs.jctc.2c00160
Google Scholar
121
Revisiting the Performance of Time-Dependent Density Functional Theory for Electronic Excitations: Assessment of 43 Popular and Recently Developed Functionals from Rungs One to Four
Liang, Jiashu; Feng, Xintian; Hait, Diptarka; Head-Gordon, Martin
Journal of Chemical Theory and Computation (2022), 18 (6), 3460-3473CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
In this paper, the performance of more than 40 popular or recently developed d. functionals is assessed for the calcn. of 463 vertical excitation energies against the large and accurate QuestDB benchmark set. For this purpose, the Tamm-Dancoff approxn. offers a good balance between computational efficiency and accuracy. The functionals ωB97X-D and BMK are found to offer the best performance overall with a root-mean square error (RMSE) of around 0.27 eV, better than the computationally more demanding CIS(D) wave function method with a RMSE of 0.36 eV. The results also suggest that Jacob's ladder still holds for time-dependent d. functional theory excitation energies, though hybrid meta generalized-gradient approxns. (meta-GGAs) are not generally better than hybrid GGAs. Effects of basis set convergence, gauge invariance correction to meta-GGAs, and nonlocal correlation (VV10) are also studied, and practical basis set recommendations are provided.
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122
Richard, R. M.; Marshall, M. S.; Dolgounitcheva, O.; Ortiz, J. V.; Brédas, J.-L.; Marom, N.; Sherrill, C. D. Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules I. Reference Data at the CCSD(T) Complete Basis Set Limit. J. Chem. Theory Comput. 2016, 12, 595, DOI: 10.1021/acs.jctc.5b00875
Google Scholar
122
Accurate Ionization Potentials and Electron Affinities of Acceptor Molecules I. Reference Data at the CCSD(T) Complete Basis Set Limit
Richard, Ryan M.; Marshall, Michael S.; Dolgounitcheva, O.; Ortiz, J. V.; Bredas, Jean-Luc; Marom, Noa; Sherrill, C. David
Journal of Chemical Theory and Computation (2016), 12 (2), 595-604CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
In designing org. materials for electronics applications, particularly for org. photovoltaics (OPV), the ionization potential (IP) of the donor and the electron affinity (EA) of the acceptor play key roles. This makes OPV design an appealing application for computational chem. since IPs and EAs are readily calculable from most electronic structure methods. Unfortunately reliable, high-accuracy wave function methods, such as coupled cluster theory with single, double, and perturbative triples [CCSD(T)] in the complete basis set (CBS) limit are too expensive for routine applications to this problem for any but the smallest of systems. One soln. is to calibrate approx., less computationally expensive methods against a database of high-accuracy IP/EA values; however, to our knowledge, no such database exists for systems related to OPV design. The present work is the first of a multipart study whose overarching goal is to det. which computational methods can be used to reliably compute IPs and EAs of electron acceptors. This part introduces a database of 24 known org. electron acceptors and provides high-accuracy vertical IP and EA values expected to be within ±0.03 eV of the true non-relativistic, vertical CCSD(T)/CBS limit. Convergence of IP and EA values toward the CBS limit is studied systematically for the Hartree-Fock, MP2 correlation, and beyond-MP2 coupled cluster contributions to the focal point ests.
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123
Ranasinghe, D. S.; Margraf, J. T.; Perera, A.; Bartlett, R. J. Vertical valence ionization potential benchmarks from equation-of-motion coupled cluster theory and QTP functionals. J. Chem. Phys. 2019, 150, 074108, DOI: 10.1063/1.5084728
Google Scholar
123
Vertical valence ionization potential benchmarks from equation-of-motion coupled cluster theory and QTP functionals
Ranasinghe, Duminda S.; Margraf, Johannes T.; Perera, Ajith; Bartlett, Rodney J.
Journal of Chemical Physics (2019), 150 (7), 074108/1-074108/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The ionization potential (IP) of a mol. quantifies the energy required to remove an electron from the system. As such, it is a fundamental quantity in the context of redox chem., charge transfer, and mol. electronics. The accurate theor. prediction of this property is therefore highly desirable for virtual materials design. Furthermore, vertical IPs are of interest in the development of many-body Green's function methods like the GW formalism, as well as d. functionals and semiempirical methods. In this contribution, we report over 1468 vertical valence IPs calcd. with the IP variant of equation-of-motion coupled cluster theory with singles and doubles (IP-EOM-CCSD) covering 155 mols. The purpose of this is two-fold: First, the quality of the predicted IPs is compared with respect to expts. and higher-order coupled cluster theory. This confirms the overall high accuracy and robustness of this method, with some outliers which are discussed in detail. Second, a large set of consistent theor. ref. values for vertical valence IPs are generated. This addresses a lack of reliable ref. data for lower-lying valence IPs, where exptl. data are often unavailable or of dubious quality. The benchmark set is then used to assess the quality of the eigenvalues predicted by different d. functional approxns. (via Bartlett's IP-eigenvalue theorem) and the extended Koopmans' theorem approach. The QTP family of functionals are found to be remarkably accurate, low-cost alternatives to IP-EOM-CCSD. (c) 2019 American Institute of Physics.
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124
Alag, A. S.; Jelenfi, D. P.; Tajti, A.; Szalay, P. G. Accurate Prediction of Vertical Ionization Potentials and Electron Affinities from Spin-Component Scaled CC2 and ADC(2) Models. J. Chem. Theory Comput. 2022, 18, 6794, DOI: 10.1021/acs.jctc.2c00624
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125
Śmiga, S.; Siecińska, S.; Grabowski, I. From simple molecules to nanotubes. Reliable predictions of ionization potentials from the ΔMP2-SCS methods. New J. Phys. 2020, 22, 083084, DOI: 10.1088/1367-2630/abaa00
Google Scholar
125
From simple molecules to nanotubes. Reliable predictions of ionization potentials from the ΔMP2-SCS methods
Smiga, Szymon; Siecinska, Sylwia; Grabowski, Ireneusz
New Journal of Physics (2020), 22 (Aug.), 083084CODEN: NJOPFM; ISSN:1367-2630. (IOP Publishing Ltd.)
The vertical ionization potentials for systems of various sizes, ranging from simple mols., DNA/RNA bases, donor and acceptor org. mol. systems as well as nanotubes are calcd. using the ΔMP2-SCS family of methods. We have shown that for all investigated cases, the ΔMP2-SCS methods, being almost cost free single-step post-Hartree-Fock calcn., provide very accurate vertical ionization potentials comparable in quality with state-of-art outer valence Green's function methods. Moreover, we show that a combination of the ΔMP2-SCS methods with the resoln. of identity technique is effective and reliable an alternative to the semi-empirical d. functional theory methods and Green's function-based calcns. of ionization potentials for large mol. systems such as silicon-based or org.-based solar cells, for which the IP-EOM-CCSD calcns. are too expensive for routine calcns.
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Antoine Marie, Pierre-François Loos. Reference Energies for Valence Ionizations and Satellite Transitions. Journal of Chemical Theory and Computation 2024, 20 (11) , 4751-4777. https://doi.org/10.1021/acs.jctc.4c00216
Chao Zheng, Junyuan Deng, Yuanyuan Qi, Chengxi Sun, Dongyue Cui, Cailin Chen, Chenxi Zhu, Shuang Wang, Jie Yuan, Gaozhan Xie, Ping Li, Runfeng Chen. Rational Design of Bipolar Host and Thermally Activated Delayed Fluorescence Materials in Donor–Acceptor Molecular Architecture: A Theoretical Study. The Journal of Physical Chemistry Letters 2024, 15 (2) , 525-531. https://doi.org/10.1021/acs.jpclett.3c03068

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Abstract
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Figure 1
Figure 1. Error measures for the VIPs of the acceptor test set (122) using the aug-cc-pVDZ basis set with the corresponding auxiliary bases. The MAEs (SDs) are visualized by colored (black) bars, while MAXs are presented by dots. For the sake of clarity, some outliers are omitted. The wave function (first group), ADC(2)-based DH (second group), CIS(D)-based DH (third group), and hybrid methods (fourth group) are presented in gray, blue, red, and orange, respectively. The CCSD values were taken from ref (124).
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Figure 2
Figure 2. Error measures for the VEAs of the acceptor test set (122) using the aug-cc-pVDZ basis set with the corresponding auxiliary bases. See the caption of Figure 1 for further details.
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Figure 3
Figure 3. Error measures for the VIPs of the BO test set (47,123) using the cc-pVTZ basis set with the corresponding auxiliary bases. See the caption of Figure 1 for further details.
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Figure 4
Figure 4. Error measures for the VIPs of the nucleobases (124,125) using the cc-pVDZ basis set with the corresponding auxiliary bases. See the caption of Figure 1 for further details.
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Figure 5
Figure 5. Error measures for the VEAs of the nucleobases (124,125) using the cc-pVDZ basis set with the corresponding auxiliary bases. See the caption of Figure 1 for further details.
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Figure 6
Figure 6. Mean errors for the VIPs of the nucleobases using the aug-cc-pVDZ basis sets with the corresponding auxiliary bases. Errors calculated from the orbital energies (final DH results) are visualized by the darker (lighter) bars. The wave function (first group), ADC(2)-based DH (second group), and CIS(D)-based DH (third group) methods are presented in gray, blue, and red, respectively.
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References
This article references 125 other publications.
1. 1
  Yeh, N.; Yeh, P. Organic solar cells: Their developments and potentials. Renew. Sust. Energy Rev. 2013, 21, 421, DOI: 10.1016/j.rser.2012.12.046
  1
  Organic solar cells: Their developments and potentials
  Yeh, Naichia; Yeh, Pulin
  Renewable & Sustainable Energy Reviews (2013), 21 (), 421-431CODEN: RSERFH; ISSN:1364-0321. (Elsevier Ltd.)
  This paper aims to review the developments and the potentials of org. photovoltaic, which has caught the attention of researchers of optoelectronics. The paper briefly introduces the physics underlying org. photovoltaic devices of donor-acceptor interfaces. It examines a variety of materials and architectures that benefit the performance of the org. photovoltaic cell; along with the important photogeneration factors including the exciton diffusion length as well as charge transport, sepn., and collection. The authors have reviewed the recent understanding of the mechanisms that govern these photocurrent generation steps and sketched out the search for alternative materials and device architectures. The review also discusses areas where active researches should be directed for cell efficiency improvement and outlines the issues to be resolved in order to speed up the commercialization.
  >> More from SciFinder ^®
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3sXksFags78%253D&md5=5b1dad002a9c806cbc670b98ce8a8ccf
2. 2
  Poelking, C.; Benduhn, J.; Spoltore, D.; Schwarze, M.; Roland, S.; Piersimoni, F.; Neher, D.; Leo, K.; Vandewal, K.; Andrienko, D. Open-circuit voltage of organic solar cells: interfacial roughness makes the difference. Commun. Phys. 2022, 5, 307, DOI: 10.1038/s42005-022-01084-x
  2
  Open-circuit voltage of organic solar cells: interfacial roughness makes the difference
  Poelking, Carl; Benduhn, Johannes; Spoltore, Donato; Schwarze, Martin; Roland, Steffen; Piersimoni, Fortunato; Neher, Dieter; Leo, Karl; Vandewal, Koen; Andrienko, Denis
  Communications Physics (2022), 5 (1), 307CODEN: CPOHDJ; ISSN:2399-3650. (Nature Portfolio)
  Org. photovoltaics (PV) is an energy-harvesting technol. that offers many advantages, such as flexibility, low wt. and cost, as well as environmentally benign materials and manufg. techniques. Despite growth of power conversion efficiencies to around 19% in the last years, org. PVs still lag behind inorg. PV technologies, mainly due to high losses in open-circuit voltage. Understanding and improving open circuit voltage in org. solar cells is challenging, as it is controlled by the properties of a donor-acceptor interface where the optical excitations are sepd. into charge carriers. Here, we provide an electrostatic model of a rough donor-acceptor interface and test it exptl. on small mol. PV materials systems. The model provides concise relationships between the open-circuit voltage, photovoltaic gap, charge-transfer state energy, and interfacial morphol. In particular, we show that the electrostatic bias generated across the interface reduces the photovoltaic gap. This neg. influence on open-circuit voltage can, however, be circumvented by adjusting the morphol. of the donor-acceptor interface.
  >> More from SciFinder ^®
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XjtVWhtrzJ&md5=25621b124d3ad3c461ba6f824ddd9d05
3. 3
  Delgado, J. L.; Bouit, P.-A.; Filippone, S.; Herranz, M. A. Á.; Martín, N. Organic photovoltaics: a chemical approach. Chem. Commun. 2010, 46, 4853, DOI: 10.1039/c003088k
  3
  Organic photovoltaics: a chemical approach
  Delgado, Juan Luis; Bouit, Pierre-Antoine; Filippone, Salvatore; Herranz, Ma. Angeles; Martin, Nazario
  Chemical Communications (Cambridge, United Kingdom) (2010), 46 (27), 4853-4865CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
  A review. The fundamental contribution of chem. to the multidisciplinary field of org. photovoltaics is presented in a systematic way through the wide variety of org. compds. synthesized to be successfully used in photovoltaic devices. Basic processes in org. solar cells, bulk heterojunction plastic solar cells based on semiconducting π-conjugated polymers and fullerenes, mol. bulk heterojunction solar cells based on π-conjugated oligomers or dyes and fullerenes, and org. solar cells with innovative carbon nanostructures are discussed.
  >> More from SciFinder ^®
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXotFensL8%253D&md5=429cc61efe0178bd3a61bdc0fb03eb63
4. 4
  Alizadeh, E.; Sanche, L. Precursors of Solvated Electrons in Radiobiological Physics and Chemistry. Chem. Rev. 2012, 112, 5578, DOI: 10.1021/cr300063r
  4
  Precursors of Solvated Electrons in Radiobiological Physics and Chemistry
  Alizadeh, Elahe; Sanche, Leon
  Chemical Reviews (Washington, DC, United States) (2012), 112 (11), 5578-5602CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  A review. The following topics are discussed: Secondary electrons in water; low-energy electrons (LEEs) and damage to cellular constituents (DNA, protein subunits, amino acids, peptides); LEEs in Radiobiol. and radiation therapy; Prehydrated electrons interacting with biomols.
  >> More from SciFinder ^®
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5. 5
  Alizadeh, E.; Orlando, T. M.; Sanche, L. Biomolecular Damage Induced by Ionizing Radiation: The Direct and Indirect Effects of Low-Energy Electrons on DNA. Annu. Rev. Phys. Chem. 2015, 66, 379, DOI: 10.1146/annurev-physchem-040513-103605
  5
  Biomolecular damage induced by ionizing radiation: the direct and indirect effects of low-energy electrons on DNA
  Alizadeh, Elahe; Orlando, Thomas M.; Sanche, Leon
  Annual Review of Physical Chemistry (2015), 66 (), 379-398CODEN: ARPLAP; ISSN:0066-426X. (Annual Reviews)
  Many exptl. and theor. advances have recently allowed the study of direct and indirect effects of low-energy electrons (LEEs) on DNA damage. In an effort to explain how LEEs damage the human genome, researchers have focused efforts on LEE interactions with bacterial plasmids, DNA bases, sugar analogs, phosphate groups, and longer DNA moieties. Here, we summarize the current understanding of the fundamental mechanisms involved in LEE-induced damage of DNA and complex biomol. films. Results obtained by several labs. on films prepd. and analyzed by different methods and irradiated with different electron-beam current densities and fluencies are presented. Despite varied conditions (e.g., film thicknesses and morphologies, intrinsic water content, substrate interactions, and extrinsic atm. compns.), comparisons show a striking resemblance in the types of damage produced and their yield functions. The potential of controlling this damage using mol. and nanoparticle targets with high LEE yields in targeted radiation-based cancer therapies is also discussed.
  >> More from SciFinder ^®
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6. 6
  Kumar, A.; Becker, D.; Adhikary, A.; Sevilla, M. D. Reaction of Electrons with DNA: Radiation Damage to Radiosensitization. Int. J. Mol. Sci. 2019, 20, 3998, DOI: 10.3390/ijms20163998
  6
  Reaction of electrons with DNA: radiation damage to radiosensitization
  Kumar, Anil; Becker, David; Adhikary, Amitava; Sevilla, Michael D.
  International Journal of Molecular Sciences (2019), 20 (16), 3998CODEN: IJMCFK; ISSN:1422-0067. (MDPI AG)
  This review article provides a concise overview of electron involvement in DNA radiation damage. The review begins with the various states of radiation-produced electrons: Secondary electrons (SE), low energy electrons (LEE), electrons at near zero kinetic energy in water (quasi-free electrons, (e-qf)) electrons in the process of solvation in water (presolvated electrons, e-pre), and fully solvated electrons (e-aq). a current summary of the structure of e-aq, and its reactions with DNA-model systems is presented. Theor. works on redn. potentials of DNA-bases were found to be in agreement with expts. This review points out the proposed role of LEE-induced frank DNA-strand breaks in ion-beam irradiated DNA. The final section presents radiation-produced electron-mediated site-specific formation of oxidative neutral aminyl radicals from azidonucleosides and the evidence of radiosensitization provided by these aminyl radicals in azidonucleoside-incorporated breast cancer cells.
  >> More from SciFinder ^®
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsVCksb8%253D&md5=bfe7563709da52fb29a011eda5ff0dbd
7. 7
  Zheng, Y.; Cloutier, P.; Hunting, D. J.; Sanche, L.; Wagner, J. R. Chemical Basis of DNA Sugar–Phosphate Cleavage by Low-Energy Electrons. J. Am. Chem. Soc. 2005, 127, 16592, DOI: 10.1021/ja054129q
  7
  Chemical basis of DNA sugar-phosphate cleavage by low-energy electrons
  Zheng, Yi; Cloutier, Pierre; Hunting, Darel J.; Sanche, Leon; Wagner, J. Richard
  Journal of the American Chemical Society (2005), 127 (47), 16592-16598CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  DNA damage by low-energy electrons (LEE) was examd. using a novel system in which thin solid films of oligonucleotide tetramers (CGTA and GCAT) were irradiated with monoenergetic electrons (10 eV) under ultrahigh vacuum. The products of irradn. were examd. by HPLC. These analyses permitted the quantitation of 16 nonmodified nucleobase, nucleoside, and nucleotide fragments of each tetramer resulting from the cleavage of phosphodiester and N-glycosidic bonds. The distribution of nonmodified products suggests a mechanism of damage involving initial electron attachment to nucleobase moieties, followed by electron transfer to the sugar-phosphate backbone, and subsequent dissocn. of the phosphodiester bond. Moreover, virtually all the nonmodified fragments contained a terminal phosphate group at the site of cleavage. These results demonstrate that the phosphodiester bond breaks by a distinct pathway in which the neg. charge localizes on the phosphodiester bond giving rise to nonmodified fragments with an intact phosphate group. Conversely, the radical must localize on the sugar moiety to give as yet unidentified modifications. In summary, the reaction of LEE with simple tetramers involved dissociative electron attachment leading to phosphodiester bond cleavage and the formation of nonmodified fragments.
  >> More from SciFinder ^®
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8. 8
  Dong, Y.; Gao, Y.; Liu, W.; Gao, T.; Zheng, Y.; Sanche, L. Clustered DNA Damage Induced by 2–20 eV Electrons and Transient Anions: General Mechanism and Correlation to Cell Death. J. Phys. Chem. Lett. 2019, 10, 2985, DOI: 10.1021/acs.jpclett.9b01063
  8
  Clustered DNA Damage Induced by 2-20 eV Electrons and Transient Anions: General Mechanism and Correlation to Cell Death
  Dong, Yanfang; Gao, Yingxia; Liu, Wenhui; Gao, Ting; Zheng, Yi; Sanche, Leon
  Journal of Physical Chemistry Letters (2019), 10 (11), 2985-2990CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  The mechanisms of action of low-energy electrons (LEEs) generated in large quantities by ionizing radiation constitute an essential element of our understanding of early events in radiolysis and radiobiol. We present the 2-20 eV electron energy dependence of the yields of base damage (BD), BD-related crosslinks (CLs), and non-double-strand break (NDSB) clustered damage induced in DNA. These new yield functions are generated by the impact of LEEs on plasmid DNA films. The damage is analyzed by gel electrophoresis with and without enzyme treatment. Maxima at 5 and 10 eV in BDs and BD-related CLs yield functions, and two others, at 6 and 10 eV, in those of NDSB clustered damage are ascribed to core-excited transient anions that decay into bond-breaking channels. The mechanism causing all types of DNA damages can be attributed to the capture of a single electron by a base followed by multiple different electron transfer pathways.
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9. 9
  Mukherjee, M.; Tripathi, D.; Brehm, M.; Riplinger, C.; Dutta, A. K. Efficient EOM-CC-based Protocol for the Calculation of Electron Affinity of Solvated Nucleobases: Uracil as a Case Study. J. Chem. Theory Comput. 2021, 17, 105, DOI: 10.1021/acs.jctc.0c00655
  9
  Efficient EOM-CC-based Protocol for the Calculation of Electron Affinity of Solvated Nucleobases: Uracil as a Case Study
  Mukherjee, Madhubani; Tripathi, Divya; Brehm, Martin; Riplinger, Christoph; Dutta, Achintya Kumar
  Journal of Chemical Theory and Computation (2021), 17 (1), 105-116CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  We present an explicit solvation protocol for the calcn. of electron affinity values of the solvated nucleobases. The protocol uses a quantum mechanics/mol. mechanics (QM/MM) approach based on the newly implemented domain-based pair natural orbital EOM-CCSD (equation-of-motion coupled-cluster single-double) method. The stability of the solvated nucleobase anion is sensitive to the local distribution of the water mols. around the nucleobase, and the calcd. electron affinity values converge slowly with respect to the no. of snapshots and the size of the water box. The use of nonpolarizable water mols. leads to an overestimation of the electron affinity and makes the result sensitive to the size of the QM region in the QM/MM calcn. The electron affinity values, although sensitive to the size of the basis set, lead to an almost const. blue shift of the electron affinity upon the increase in the basis set. The present protocol allows for a controllable description of the various parameters affecting the electron affinity value, and the calcd. adiabatic electron affinity values are in excellent agreement with exptl. results.
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10. 10
  Verma, P.; Ghosh, D.; Dutta, A. K. Electron Attachment to Cytosine: The Role of Water. J. Phys. Chem. A 2021, 125, 4683, DOI: 10.1021/acs.jpca.0c10199
  10
  Electron Attachment to Cytosine: The Role of Water
  Verma, Pooja; Ghosh, Debashree; Dutta, Achintya Kumar
  Journal of Physical Chemistry A (2021), 125 (22), 4683-4694CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  We present an EOM-CCSD-based quantum mech./mol. mech. (QM/MM) study on the electron attachment process to solvated cytosine. The electron attachment in the bulk solvated cytosine occurs through a doorway mechanism, where the initial electron is localized on water. The electron is subsequently transferred to cytosine by the mixing of electronic and nuclear degrees of freedom, which occurs on an ultrafast time scale. The bulk water environment stabilizes the cytosine-bound anion by an extensive hydrogen-bond network and drastically enhances the electron transfer rate from that obsd. in the gas phase. Microhydration studies cannot reproduce the effect of the bulk water environment on the electron attachment process, and one needs to include a large no. of water mols. in the calcn. to obtain converged results. The predicted adiabatic electron affinity and electron transfer rate obtained from our QM/MM calcns. are consistent with the available exptl. results.
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11. 11
  Kohn, W.; Sham, L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 1965, 140, A1133, DOI: 10.1103/PhysRev.140.A1133
  There is no corresponding record for this reference.
12. 12
  Zhan, C.-G.; Nichols, J. A.; Dixon, D. A. Ionization Potential, Electron Affinity, Electronegativity, Hardness, and Electron Excitation Energy: Molecular Properties from Density Functional Theory Orbital Energies. J. Phys. Chem. A 2003, 107, 4184, DOI: 10.1021/jp0225774
  12
  Ionization Potential, Electron Affinity, Electronegativity, Hardness, and Electron Excitation Energy: Molecular Properties from Density Functional Theory Orbital Energies
  Zhan, Chang-Guo; Nichols, Jeffrey A.; Dixon, David A.
  Journal of Physical Chemistry A (2003), 107 (20), 4184-4195CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  Representative at. and mol. systems, including various inorg. and org. mols. with covalent and ionic bonds, have been studied by using d. functional theory. The calcns. were done with the commonly used exchange-correlation functional B3LYP followed by a comprehensive anal. of the calcd. highest-occupied and lowest-unoccupied Kohn-Sham orbital (HOMO and LUMO) energies. The basis set dependence of the DFT results shows that the economical 6-31+G* basis set is generally sufficient for calcg. the HOMO and LUMO energies (if the calcd. LUMO energies are neg.) for use in correlating with mol. properties. The directly calcd. ionization potential (IP), electron affinity (EA), electronegativity (χ), hardness (η), and first electron excitation energy (τ) are all in good agreement with the available exptl. data. A generally applicable linear correlation relationship exists between the calcd. HOMO energies and the exptl./calcd. IPs. We have also found satisfactory linear correlation relationships between the calcd. LUMO energies and exptl./calcd. EAs (for the bound anionic states), between the calcd. av. HOMO/LUMO energies and χ values, between the calcd. HOMO-LUMO energy gaps and η values, and between the calcd. HOMO-LUMO energy gaps and exptl./calcd. first excitation energies. By using these linear correlation relationships, the calcd. HOMO and LUMO energies can be employed to semiquant. est. ionization potential, electron affinity, electronegativity, hardness, and first excitation energy.
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13. 13
  Perdew, J. P.; Levy, M. Comment on “Significance of the highest occupied Kohn–Sham eigenvalue. Phys. Rev. B 1997, 56, 16021, DOI: 10.1103/PhysRevB.56.16021
  13
  Comment on "Significance of the highest occupied Kohn-Sham eigenvalue"
  Perdew, John P.; Levy, Mel
  Physical Review B: Condensed Matter (1997), 56 (24), 16021-16028CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  With more explanation than usual and without appeal to Janak's theorem, we discuss the statement and proof of the ionization potential theorems for the exact Kohn-Sham d.-functional theory of a many-electron system: (1) For any av. electron no. N between the integers Z - 1 and Z, and thus for N → Z from below, the highest occupied or partly occupied Kohn-Sham orbital energy is minus the ionization energy of the Z-electron system. (2) For Z - 1 < N < Z, the exact Kohn-Sham effective potential vs(r) tends to zero as |r| → ∞. We then argue that an objection to these theorems [L. Kleinman, Phys. Rev. B 56, 12042 (1997)] overlooks a crucial step in the proof of theorem (2): The asymptotic exponential decay of the exact electron d. of the Z-electron system is controlled by the exact ionization energy, but the decay of an approx. d. is not controlled by the approx. ionization energy. We discuss relevant evidence from the numerical construction of the exact Kohn-Sham potential. In particular, we point out a model two-electron problem for which the ionization potential theorems are exactly confirmed. Finally, we comment on related issues: the self-interaction correction, the discontinuity of the exact Kohn-Sham potential as N passes through the integer Z, and the generalized sum rule on the exchange-correlation hole.
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14. 14
  Levy, M.; Perdew, J. P.; Sahni, V. Exact differential equation for the density and ionization energy of a many-particle system. Phys. Rev. A 1984, 30, 2745, DOI: 10.1103/PhysRevA.30.2745
  There is no corresponding record for this reference.
15. 15
  Zhang, G.; Musgrave, C. B. Comparison of DFT Methods for Molecular Orbital Eigenvalue Calculations. J. Phys. Chem. A 2007, 111, 1554, DOI: 10.1021/jp061633o
  15
  Comparison of DFT Methods for Molecular Orbital Eigenvalue Calculations
  Zhang, Gang; Musgrave, Charles B.
  Journal of Physical Chemistry A (2007), 111 (8), 1554-1561CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  We report how closely the Kohn-Sham HOMO and LUMO eigenvalues of 11 d. functional theory (DFT) functionals, resp., correspond to the neg. ionization potentials (-IPs) and electron affinities (EAs) of a test set of mols. We also report how accurately the HOMO-LUMO gaps of these methods predict the lowest excitation energies using both time-independent and time-dependent DFT (TD-DFT). The 11 DFT functionals include the local spin d. approxn. (LSDA), five generalized gradient approxn. (GGA) functionals, three hybrid GGA functionals, one hybrid functional, and one hybrid meta GGA functional. We find that the HOMO eigenvalues predicted by KMLYP, BH and HLYP, B3LYP, PW91, PBE, and BLYP predict the -IPs with av. abs. errors of 0.73, 1.48, 3.10, 4.27, 4.33, and 4.41 eV, resp. The LUMOs of all functionals fail to accurately predict the EAs. Although the GGA functionals inaccurately predict both the HOMO and LUMO eigenvalues, they predict the HOMO-LUMO gap relatively accurately (∼0.73 eV). On the other hand, the LUMO eigenvalues of the hybrid functionals fail to predict the EA to the extent that they include HF exchange, although increasing HF exchange improves the correspondence between the HOMO eigenvalue and -IP so that the HOMO-LUMO gaps are inaccurately predicted by hybrid DFT functionals. We find that TD-DFT with all functionals accurately predicts the HOMO-LUMO gaps. A linear correlation between the calcd. HOMO eigenvalue and the exptl. -IP and calcd. HOMO-LUMO gap and exptl. lowest excitation energy enables us to derive a simple correction formula.
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16. 16
  Grimme, S. Semiempirical hybrid density functional with perturbative second-order correlation. J. Chem. Phys. 2006, 124, 034108, DOI: 10.1063/1.2148954
  16
  Semiempirical hybrid density functional with perturbative second-order correlation
  Grimme, Stefan
  Journal of Chemical Physics (2006), 124 (3), 034108/1-034108/16CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A new hybrid d. functional for general chem. applications is proposed. It is based on a mixing of std. generalized gradient approxns. (GGAs) for exchange by Becke (B) and for correlation by Lee, Yang, and Parr (LYP) with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional contains only two global parameters that describe the mixt. of HF and GGA exchange (ax) and of the PT2 and GGA correlation (c), resp. The parameters are obtained in a least-squares-fit procedure to the G2/97 set of heat of formations. Opposed to conventional hybrid functionals, the optimum ax is found to be quite large (53% with c = 27%) which at least in part explains the success for many problematic mol. systems compared to conventional approaches. The performance of the new functional termed B2-PLYP is assessed by the G2/97 std. benchmark set, a second test suite of atoms, mols., and reactions that are considered as electronically very difficult (including transition-metal compds., weakly bonded complexes, and reaction barriers) and comparisons with other hybrid functionals of GGA and meta-GGA types. According to many realistic tests, B2-PLYP can be regarded as the best general purpose d. functional for mols. (e.g., a mean abs. deviation for the two test sets of only 1.8 and 3.2 kcal/mol compared to about 3 and 5 kcal/mol, resp., for the best other d. functionals). Very importantly, also the max. and minium errors (outliers) are strongly reduced (by about 10-20 kcal/mol). Furthermore, very good results are obtained for transition state barriers but unlike previous attempts at such a good description, this definitely comes not at the expense of equil. properties. Preliminary calcns. of the equil. bond lengths and harmonic vibrational frequencies for diat. mols. and transition-metal complexes also show very promising results. The uniformity with which B2-PLYP improves for a wide range of chem. systems emphasizes the need of (virtual) orbital-dependent terms that describe nonlocal electron correlation in accurate exchange-correlation functionals. From a practical point of view, the new functional seems to be very robust and it is thus suggested as an efficient quantum chem. method of general purpose.
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17. 17
  Goerigk, L.; Grimme, S. Double-hybrid density functionals. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2014, 4, 576, DOI: 10.1002/wcms.1193
  17
  Double-hybrid density functionals
  Goerigk, Lars; Grimme, Stefan
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2014), 4 (6), 576-600CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  Double-hybrid d. functionals (DHDFs) are reviewed in this study. In DHDFs parts of conventional d. functional theory (DFT) exchange and correlation are replaced by contributions from nonlocal Fock-exchange and second-order perturbative correlation. The latter portion is based on the well-known MP2 wave-function approach in which, however, Kohn-Sham orbitals are used to calc. its contribution. First, related methods preceding this idea are reviewed, followed by a thorough discussion of the first modern double-hybrid B2-PLYP. Parallels and differences between B2-PLYP and its various successors are then outlined. This discussion is rounded off with representative thermochem. examples demonstrating that DHDFs belong to the most robust and accurate DFT approaches currently available. This anal. also presents hitherto unpublished results for recently developed DHDFs. Finally, how double-hybrids can be combined with linear-response time-dependent DFT is also outlined and the value of this approach for electronically excited states is shown. WIREs Comput Mol Sci 2014, 4:576-600. doi: 10.1002/wcms.1193 For further resources related to this article, please visit the . Conflict of interest: The authors have declared no conflicts of interest for this article.
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18. 18
  Brémond, É.; Ciofini, I.; Sancho-García, J. C.; Adamo, C. Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists. Acc. Chem. Res. 2016, 49, 1503, DOI: 10.1021/acs.accounts.6b00232
  18
  Nonempirical Double-Hybrid Functionals: An Effective Tool for Chemists
  Bremond, Eric; Ciofini, Ilaria; Sancho-Garcia, Juan Carlos; Adamo, Carlo
  Accounts of Chemical Research (2016), 49 (8), 1503-1513CODEN: ACHRE4; ISSN:0001-4842. (American Chemical Society)
  A review. D. functional theory (DFT) emerged in the last two decades as the most reliable tool for the description and prediction of properties of mol. systems and extended materials, coupling in an unprecedented way high accuracy and reasonable computational cost. This success rests also on the development of more and more performing d. functional approxns. (DFAs). Indeed, the Achilles' heel of DFT is represented by the exchange-correlation contribution to the total energy, which, being unknown, must be approximated. Since the beginning of the 1990s, global hybrids (GH) functionals, where an explicit dependence of the exchange-correlation energy on occupied Kohn-Sham orbitals is introduced thanks to a fraction of Hartree-Fock-like exchange, imposed themselves as the most reliable DFAs for chem. applications. However, if these functionals normally provide results of sufficient accuracy for most of the cases analyzed, some properties, such as thermochem. or dispersive interactions, can still be significantly improved. A possible way out is represented by the inclusion, into the exchange-correlation functional, of an explicit dependence on virtual Kohn-Sham orbitals via perturbation theory. This leads to a new class of functionals, called double-hybrids (DHs). In this Account, we describe our nonempirical approach to DHs, which, following the line traced by the Perdew-Burke-Ernzerhof approach, allows for the definition of a GH (PBE0) and a DH (QIDH) model. In such a way, a whole family of nonempirical functionals, spanning on the highest rungs of the Perdew's quality scale, is now available and competitive with other-more empirical-DFAs. Discussion of selected cases, ranging from thermochem. and reactions to weak interactions and excitation energies, not only show the large range of applicability of nonempirical DFAs, but also underline how increasing the no. of theor. constraints parallels with an improvement of the DFA's numerical performances. This fact further consolidates the strong theor. framework of nonempirical DFAs.Finally, even if nonempirical DH approaches are still computationally expensive, relying on the fact that they can benefit of all tech. enhancements developed for speeding up post-Hartree-Fock methods, there is substantial hope for their near future routine application to the description and prediction of complex chem. systems and reactions.
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19. 19
  Martin, J. M. L.; Santra, G. Empirical Double-Hybrid Density Functional Theory: A ‘Third Way’ in Between WFT and DFT. Isr. J. Chem. 2020, 60, 787, DOI: 10.1002/ijch.201900114
  19
  Empirical Double-Hybrid Density Functional Theory: A 'Third Way' in Between WFT and DFT
  Martin, Jan M. L.; Santra, Golokesh
  Israel Journal of Chemistry (2020), 60 (8-9), 787-804CODEN: ISJCAT; ISSN:0021-2148. (Wiley-VCH Verlag GmbH & Co. KGaA)
  A review. Double hybrid d. functional theory arguably sits on the seamline between wavefunction methods and DFT: it represents a special case of Rung 5 on the "Jacob's Ladder" of John P. Perdew. For large and chem. diverse benchmarks such as GMTKN55, empirical double hybrid functionals with dispersion corrections can achieve accuracies approaching wavefunction methods at a cost not greatly dissimilar to hybrid DFT approaches, provided RI-MP2 and/or another MP2 acceleration techniques are available in the electronic structure code. Only a half-dozen or fewer empirical parameters are required. For vibrational frequencies, accuracies intermediate between CCSD and CCSD(T) can be achieved, and performance for other properties is encouraging as well. Organometallic reactions can likewise be treated well, provided static correlation is not too strong. Further prospects are discussed, including range-sepd. and RPA-based approaches.
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20. 20
  Su, N. Q.; Xu, X. The XYG3 Type of Doubly Hybrid Density Functionals. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2016, 6, 721, DOI: 10.1002/wcms.1274
  20
  The XYG3 type of doubly hybrid density functionals
  Su, Neil Qiang; Xu, Xin
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2016), 6 (6), 721-747CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  Doubly hybrid (DH) functionals have emerged as a new class of d. functional approxns. (DFAs), which not only have a nonlocal orbital-dependent component in the exchange part, but also incorporate the information of unoccupied orbitals in the correlation part, being at the top rung of Perdew's view of Jacob's ladder in DFAs. This review article focuses on the XYG3 type of DH (xDH) functionals, which use a low rung functional to perform the self-consistent-field calcn. to generate orbitals and densities, with which a top rung DH functional is used for final energy evaluation. We will discuss the theor. background of the xDH functionals, briefly reviewing the adiabatic connection formalism, coordinate scaling relations, and Goerling-Levy perturbation theory. General performance of the xDH functionals will be presented for both energies and structures. In particular, we will present the fractional charge behaviors of the xDH functionals, examg. the self-interaction errors, the delocalization errors and the deviation from the linearity condition, as well as their effects on the predicted ionization potentials, electron affinities and fundamental gaps. This provides a theor. rationale for the obsd. good performance of the xDH functionals. WIREs Comput Mol Sci 2016, 6:721-747. doi: 10.1002/wcms.1274 For further resources related to this article, please visit the .
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21. 21
  Sancho-García, J. C.; Adamo, C. Double-hybrid density functionals: Merging wavefunction and density approaches to get the best of both worlds. Phys. Chem. Chem. Phys. 2013, 15, 14581, DOI: 10.1039/c3cp50907a
  21
  Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds
  Sancho-Garcia, J. C.; Adamo, C.
  Physical Chemistry Chemical Physics (2013), 15 (35), 14581-14594CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  A review. We review why and how double-hybrid d. functionals have become new leading actors in the field of computational chem., thanks to the combination of an unprecedented accuracy together with large robustness and reliability. Similar to their predecessors, the widely employed hybrid d. functionals, they are rooted in the Adiabatic Connection Method from which they emerge in a natural way. We present recent achievements concerning applications to chem. systems of the most interest, and current extensions to deal with challenging issues such as non-covalent interactions and excitation energies. These promising methods, despite a slightly higher computational cost than other typical d.-based models, are called to play a key role in the near future and can thus pave the way towards new discoveries or advances.
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22. 22
  Geertsen, J.; Rittby, M.; Bartlett, R. J. The equation-of-motion coupled-cluster method: Excitation energies of Be and CO. Chem. Phys. Lett. 1989, 164, 57, DOI: 10.1016/0009-2614(89)85202-9
  22
  The equation-of-motion coupled-cluster method: excitation energies of beryllium and carbon monoxide
  Geertsen, Jan; Rittby, Magnus; Bartlett, Rodney J.
  Chemical Physics Letters (1989), 164 (1), 57-62CODEN: CHPLBC; ISSN:0009-2614.
  The equation-of-motion coupled-cluster (EOM-CC) method for the calcn. of excitation energies is presented. The procedure is based upon representing an excited state as an excitation from a coupled-cluster ground state and the excitation energies are obtained by solving a non-Hermitian eigenvalue problem. Numerical applications are reported for Be and CO, and the compared to full CI, Fock space multi-ref. coupled-cluster, multi-ref. MBPT, and propagator results.
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23. 23
  Stanton, J. F.; Bartlett, R. J. The equation of motion coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties. J. Chem. Phys. 1993, 98, 7029, DOI: 10.1063/1.464746
  23
  The equation-of-motion, coupled-cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited-state properties
  Stanton, John F.; Bartlett, Rodney J.
  Journal of Chemical Physics (1993), 98 (9), 7029-39CODEN: JCPSA6; ISSN:0021-9606.
  A comprehensive overview of the equation of motion coupled-cluster (EOM-CC) method and its application to mol. systems is presented. By exploiting the biorthogonal nature of the theory, it is shown that excited-state properties and transition strengths can be evaluated via a generalized expectation-value approach that incorporates both the bra and ket state wave functions. Reduced d. matrixes defined by this procedure are given by closed form expressions. For the root of the EOM-CC effective Hamiltonian that corresponds to the ground state, the resulting equations are equiv. to the usual expressions for normal single-ref. CC d. matrixes. Thus, the method described in this paper provides a universal definition of coupled-cluster d. matrixes, providing a link between EOM-CC and traditional ground state CC theory. Excitation energy, oscillator strength, and property calcns. are illustrated by means of several numerical examples, including comparisons with full CI calcns. and a detailed study of the 10 lowest electronically excited states of the cyclic isomer of C4.
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24. 24
  Watts, J. D.; Bartlett, R. J. The inclusion of connected triple excitations in the equation-of-motion coupled-cluster method. J. Chem. Phys. 1994, 101, 3073, DOI: 10.1063/1.467620
  24
  The inclusion of connected triple excitations in the equation-of-motion coupled-cluster method
  Watts, John D.; Bartlett, Rodney
  Journal of Chemical Physics (1994), 101 (4), 3073-8CODEN: JCPSA6; ISSN:0021-9606.
  The implementation of connected triple excitations in the equation-of-motion (EOM) coupled-cluster (CC) method for excitation energies is reported for the first time. The ref. state is described by the complete CC singles, doubles, and triples (CCSDT) method. Excited states are generated from the ref. state wave function by the action of a linear excitation operator including single, double, and triple excitations. The excited state wave functions and energies are obtained by diagonalizing the effective Hamiltonian e-THeT, where T is the cluster operator for the ref. state, in the space of singly, doubly, and triply excited determinants. Comparison is made with full CI excitation energies for several examples (CH+, Be, SiH2, and CH2). These show that EOM-CCSDT is able to describe states which are doubly excited relative to the ref. state, as well as singly excited states. Calcns. of several excitation energies of BH using an extended basis set are also reported, and show good agreement with expt.
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25. 25
  Bartlett, R. J. Coupled-cluster theory and its equation-of-motion extensions. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 126, DOI: 10.1002/wcms.76
  25
  Coupled-cluster theory and its equation-of-motion extensions
  Bartlett, Rodney J.
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (1), 126-138CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  A review. Coupled-cluster theory offers today's ref. quantum chem. method for most of the problems encountered in electronic structure theory. It has been instrumental in establishing the now well-known paradigm of converging, many-body methods, MBPT2 < CCD < CCSD < MBPT4 < CCSD(T) < CCSDT-n < CCSDT < CCSDT(Q) < CCSDTQ-n < CCSDTQ < fullCI. Many-body perturbation theory (MBPT) for second, MBPT2, and fourth-order MBPT4; and coupled-cluster (CC) theory for different categories of excitations, singles, doubles, triples, quadruples (SDTQ). Although built on the same basic concept as CI (CI), many-body methods fundamentally improve upon CI approxns. by introducing the property of size extensivity, meaning that contrary to any truncated CI all terms properly scale with the no. of electrons in the problem. This fundamental aspect of many-electron methods leads to the exceptional performance of CC theory and its finite-order MBPT approxns. plus its equation-of-motion extensions for excited, ionized, and electron attached states. This brief overview will describe formal aspects of the theory which should be understood by perspective users of CC methods. We will also comment on some current developments that are improving the theory's accuracy or applicability.
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26. 26
  Sneskov, K.; Christiansen, O. Excited state coupled cluster methods. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 566, DOI: 10.1002/wcms.99
  26
  Excited state coupled cluster methods
  Sneskov, Kristian; Christiansen, Ove
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (4), 566-584CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  We review coupled cluster (CC) theory for electronically excited states. We outline the basics of a CC response theory framework that allows the transfer of the attractive accuracy and convergence properties assocd. with CC methods over to the calcn. of electronic excitation energies and properties. Key factors affecting the accuracy of CC excitation energy calcns. are discussed as are some of the key CC models in this field. To aid both the practitioner as well as the developer of CC excited state methods, we also briefly discuss the key computational steps in a working CC response implementation. Approaches aimed at extending the application range of CC excited state methods either in terms of mol. size and phenomena or in terms of environment (soln. and proteins) are also discussed.
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27. 27
  Nooijen, M.; Bartlett, R. J. Similarity transformed equation-of-motion coupled-cluster theory: Details, examples, and comparisons. J. Chem. Phys. 1997, 107, 6812, DOI: 10.1063/1.474922
  27
  Similarity transformed equation-of-motion coupled-cluster theory: Details, examples, and comparisons
  Nooijen, Marcel; Bartlett, Rodney J.
  Journal of Chemical Physics (1997), 107 (17), 6812-6830CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The similarity transformed equation-of-motion coupled-cluster (STEOM-CC) method is presented in full detail. Comparisons are made with the Fock space coupled-cluster (FSCC) method and the equation-of-motion coupled-cluster (EOM-CC) scheme. The role of implicit triple excitations and, relatedly, charge transfer separability in STEOM is discussed. The dependence on the choice of active space in STEOM is addressed and criteria for the selection of the active space are given. The evaluation of properties within STEOM is outlined and a large no. of illustrative examples of STEOM is presented.
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28. 28
  Stanton, J. F.; Gauss, J. Perturbative treatment of the similarity transformed Hamiltonian in equation-of-motion coupled-cluster approximations. J. Chem. Phys. 1995, 103, 1064, DOI: 10.1063/1.469817
  28
  Perturbative treatment of the similarity transformed Hamiltonian in equation-of-motion coupled-cluster approximations
  Stanton, John F.; Gauss, Juergen
  Journal of Chemical Physics (1995), 103 (3), 1064-76CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A series of size-consistent approxns. to the equation-of-motion coupled cluster method in the singles and doubles approxn. (EOM-CCSD) are developed by subjecting the similarity transformed Hamiltonian ‾H = exp(-T)H exp(T) to a perturbation expansion. Attention is directed to N and N - 1 electron final state realizations of the method defined by truncation of ‾H at second order. Explicit spin-orbital equations for the energy and its first deriv. are documented for both approaches [EOMEE-CCSD(2) and EOMIP-CCSD(2), resp.], and have been implemented in a large-scale quantum chem. program. Vertical ionization potentials calcd. by EOMIP-CCSD(2) are shown to be equiv. to those of an approach presented recently by Nooijen and Snijders [J. Chem. Phys. 102, 1681,(1995)]. Applications of both EOMIP-CCSD(2) and EOMEE-CCSD(2) provide results for final state properties that compare favorably with those obtained in full EOM-CCSD calcns. Anal. of the computational aspects of the approx. and full EOM-CCSD methods shows that the cost of EOMIP-CCSD(2) energy and gradient calcns. scales in proportion to the fifth power of the basis set size, a significant savings over the sixth power dependence of EOMIP-CCSD. This feature is of great practical importance, as it shows that this N - 1 electron final state approach has a large domain of applicability and is therefore likely to become a valuable tool for application calcns. On the other hand, the same cannot be said for EOMEE-CCSD(2) since its asymptotic computational dependence and storage requirements are the same as the full EOMEE-CCSD method.
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29. 29
  Stanton, J. F.; Gauss, J. Analytic energy derivatives for ionized states described by the equation-of-motion coupled cluster method. J. Chem. Phys. 1994, 101, 8938, DOI: 10.1063/1.468022
  29
  Analytical energy derivatives for ionized states described by the equation-of-motion coupled cluster method
  Stanton, John F.; Gauss, Juergen
  Journal of Chemical Physics (1994), 101 (10), 8938-44CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The theory for analytic energy derivs. of excited electronic states described by the equation-of-motion coupled cluster (EOM-CC) method has been generalized to treat cases in which ref. and final states differ in the no. of electrons. While this work specializes to the sector of Fock space that corresponds to ionization of the ref., the approach can be trivially modified for electron attached final states. Unlike traditional coupled cluster methods that are based on single determinant ref. functions, several electronic configurations are treated in a balanced way by EOM-CC. Therefore, this quantum chem. approach is appropriate for problems that involve important nondynamic electron correlation effects. Furthermore, a fully spin adapted treatment of doublet electronic states is guaranteed when a spin restricted closed shell ref. state is used-a desirable feature that is not easily achieved in std. coupled cluster approaches. The efficient implementation of analytic gradients reported here allows this variant of EOM-CC theory to be routinely applied to multidimensional potential energy surfaces for the first time. Use of the method is illustrated by an investigation of the formyloxyl radical (HCOO), which suffers from notorious symmetry breaking effects.
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30. 30
  Pieniazek, P. A.; Bradforth, S. E.; Krylov, A. I. Charge localization and Jahn–Teller distortions in the benzene dimer cation. J. Chem. Phys. 2008, 129, 074104, DOI: 10.1063/1.2969107
  30
  Charge localization and Jahn-Teller distortions in the benzene dimer cation
  Pieniazek, Piotr A.; Bradforth, Stephen E.; Krylov, Anna I.
  Journal of Chemical Physics (2008), 129 (7), 074104/1-074104/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Jahn-Teller (JT) distortions and charge localization in the benzene dimer cation are analyzed using the equation-of-motion coupled cluster with single and double substitutions for ionization potential (EOM-IP-CCSD) method. Ionization of the dimer changes the bonding from noncovalent to covalent and induces significant geometrical distortions, e.g., shorter interfragment distance and JT displacements. Relaxation along interfragment coordinates lowers the energy of the t-shaped and displaced sandwich isomers by 0.07 and 0.23 eV, resp., whereas JT displacements result in addnl. 0.18 and 0.23 eV. Energetically, the effect of JT distortion on the dimer is similar to the monomer where JT relaxation lowers the energy by 0.18 eV. While the change in the interfragment distance has dramatic spectroscopic consequences, the JT distortion causes only a small perturbation in the electronic spectra. The two geometrical relaxations in the t-shaped isomer lead to opposing effects on hole localization. Intermol. relaxation leads to an increased delocalization, whereas JT ring distortion localizes the charge. In the sandwich isomers, breaking the symmetry by ring rotation does not induce considerable charge localization. The optimization and property calcns. were performed using a new implementation of EOM-IP-CCSD energies and gradients in the Q-CHEM electronic structure package. (c) 2008 American Institute of Physics.
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31. 31
  Musiał, M.; Kucharski, S. A.; Bartlett, R. J. Equation-of-motion coupled cluster method with full inclusion of the connected triple excitations for ionized states: IP-EOM-CCSDT. J. Chem. Phys. 2003, 118, 1128, DOI: 10.1063/1.1527013
  31
  Equation-of-motion coupled cluster method with full inclusion of the connected triple excitations for ionized states: IP-EOM-CCSDT
  Musial, Monika; Kucharski, Stanislaw A.; Bartlett, Rodney J.
  Journal of Chemical Physics (2003), 118 (3), 1128-1136CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The equation-of-motion (EOM) coupled cluster (CC) method with full inclusion of the connected triple excitations for ionization energies has been formulated and implemented. Using proper factorization of the three- and four-body parts of the effective Hamiltonian, an efficient computational procedure has been proposed for IP-EOM-CCSDT which at the EOM level requires no-higher-than nocc3nvir4 scaling. The method is calibrated by the evaluation of the valence vertical ionization potentials for CO, N2, and F2 mols. for several basis sets up to 160 basis functions. At the basis set limit, errors vary from 0.0 to 0.2 eV, compared to "exptl." vertical ionization potentials.
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32. 32
  Nooijen, M.; Bartlett, R. J. Equation of motion coupled cluster method for electron attachment. J. Chem. Phys. 1995, 102, 3629, DOI: 10.1063/1.468592
  32
  Equation of motion coupled cluster method for electron attachment
  Nooijen, Marcel; Bartlett, Rodney J.
  Journal of Chemical Physics (1995), 102 (9), 3629-47CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The electron attachment equation of motion coupled cluster (EA-EOMCC) method is derived which enables detn. of the various bound states of an (N+1)-electron system and the corresponding energy eigenvalues relative to the energy of an N-electron CCSD ref. state. Detailed working equations for the EA-EOMCC method are derived using diagrammatic techniques for both closed-shell and open-shell CCSD ref. states based upon a single determinant. The EA-EOMCC method is applied to a variety of different problems, the main purpose being to establish its prospects and limitations. The results from EA-EOMCC calcns. are compared to other EOMCC approaches, starting from different ref. states, as well as other theor. methods and exptl. values, where available. We have investigated electron affinities for a wide selection of both closed-shell and open-shell systems. Excitation spectra of atoms and mols. with an odd no. of electrons are obtained, taking the closed-shell ground state of the ion as a ref. in the EA-EOMCC calcn. Finally we consider excitation spectra of some closed-shell systems, and find in particular that the electron attachment approach is capable of yielding accurate triplet excitation energies in an efficient way.
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33. 33
  Musiał, M.; Bartlett, R. J. Equation-of-motion coupled cluster method with full inclusion of connected triple excitations for electron-attached states: EA-EOM-CCSDT. J. Chem. Phys. 2003, 119, 1901, DOI: 10.1063/1.1584657
  33
  Equation-of-motion coupled cluster method with full inclusion of connected triple excitations for electron-attached states: EA-EOM-CCSDT
  Musial, Monika; Bartlett, Rodney J.
  Journal of Chemical Physics (2003), 119 (4), 1901-1908CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  We extend the full triples equation-of-motion (EOM) coupled cluster (CC) method to electron attached states. Proper factorization of the three- and four-body parts of the effective Hamiltonian makes it possible to achieve for the EA-EOM part a scaling no higher than nocc2nvir5. The method is calibrated by the evaluation of the valence vertical electron affinities for the C2 and O3 mols. for several basis sets up to 160 basis functions. For C2, EA-EOM-CCSDT gives 3.24 eV at the extrapolated basis limit, while the exptl. adiabatic EA is equal to 3.27 ± 0.008 eV. For O3 the agreement is ∼1.9 eV compared to an adiabatic value of 2.1 eV.
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34. 34
  Schirmer, J. Beyond the random-phase approximation: A new approximation scheme for the polarization propagator. Phys. Rev. A 1982, 26, 2395, DOI: 10.1103/PhysRevA.26.2395
  34
  Beyond the random-phase approximation: A new approximation scheme for the polarization propagator
  Schirmer, Jochen
  Physical Review A: Atomic, Molecular, and Optical Physics (1982), 26 (5), 2395-416CODEN: PLRAAN; ISSN:0556-2791.
  Within the framework of the many-body Green's-function method, a new approach is given to the polarization propagator for finite Fermi systems. This approach makes explicit use of the diagrammatic perturbation expansion for the polarization propagator, and reformulates the exact summation in terms of a simple algebraic scheme, referred to as the algebraic diagrammatic construction (ADC). The ADC defines in a natural way a set of approxn. schemes (nth-order ADC schemes) which represent infinite partial summations exact up to nth order of perturbation theory. In contrast to the random-phase-approxn. (RPA)-like schemes, the corresponding math. procedures are essentially Hermitian eigenvalue problems in limited configuration spaces of unperturbed excited configurations. Explicit equations for the 1st- and 2nd-order ADC schemes are derived. These schemes are thoroughly discussed and compared with the Tamm-Dancoff approxn. and RPA schemes.
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35. 35
  Schirmer, J.; Cederbaum, L. S.; Walter, O. New approach to the one-particle Green’s function for finite Fermi systems. Phys. Rev. A 1983, 28, 1237, DOI: 10.1103/PhysRevA.28.1237
  35
  New approach to the one-particle Green's function for finite Fermi systems
  Schirmer, J.; Cederbaum, L. S.; Walter, O.
  Physical Review A: Atomic, Molecular, and Optical Physics (1983), 28 (3), 1237-59CODEN: PLRAAN; ISSN:0556-2791.
  A new approach to the one-particle Green's functions G for finite electronic systems is presented. This approach is based on the diagrammatic perturbation expansions of the Green's function and of the dynamic self-energy part M related to G via the Dyson equation. The exact summation of the latter expansion is reformulated in terms of a simple algebraic form referred to as algebraic diagrammatic construction (ADC). The ADC defines in a systematic way a set of approxn. schemes (nth-order ADC schemes) that represent infinite partial summations for M and (via the Dyson equation) for G being complete through nth order of perturbation theory. The corresponding math. procedures are essentially Hermitian eigenvalue problems in restricted configuration spaces of unperturbed ionic configurations. Explicit equations for the second-, third-, and fourth-order ADC schemes are derived and analyzed.
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36. 36
  Schirmer, J.; Trofimov, A. B.; Stelter, G. A non-Dyson third-order approximation scheme for the electron propagator. J. Chem. Phys. 1998, 109, 4734, DOI: 10.1063/1.477085
  36
  A non-Dyson third-order approximation scheme for the electron propagator
  Schirmer, J.; Trofimov, A. B.; Stelter, G.
  Journal of Chemical Physics (1998), 109 (12), 4734-4744CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  An efficient third-order propagator method to compute ionization potentials and electron affinities of atoms and mols. is presented. The development is based on the algebraic diagrammatic construction (ADC) representing a specific reformulation of the diagrammatic perturbation series of the electron propagator G(ω). In contrast with previous approxn. schemes, relying on the Dyson equation and approxns. for the self-energy part, the ADC procedure here is applied directly to the (N.-+.1)-electron parts G-(ω) and G+(ω), resp., of the electron propagator. This leads to decoupled secular equations for the ionization energies ((N-1)-electron part) and electron affinities ((N+1)-electron part), resp. In comparison with the Dyson-type approach, there is a substantial redn. of the secular matrix dimension opposed by a small addnl. expense in computing some second- and third-order contributions to the secular matrix elements. The relationship of the non-Dyson ADC(3) method to coupled cluster methods is outlined.
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37. 37
  Trofimov, A. B.; Schirmer, J. Molecular ionization energies and ground- and ionic-state properties using a non-Dyson electron propagator approach. J. Chem. Phys. 2005, 123, 144115, DOI: 10.1063/1.2047550
  37
  Molecular ionization energies and ground- and ionic-state properties using a non-Dyson electron propagator approach
  Trofimov, A. B.; Schirmer, J.
  Journal of Chemical Physics (2005), 123 (14), 144115/1-144115/15CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  An earlier proposed propagator method for the treatment of mol. ionization is tested in first applications. The method referred to as the non-Dyson third-order algebraic-diagrammatic construction [nD-ADC(3)] approxn. for the electron propagator represents a computationally promising alternative to the existing Dyson ADC(3) method. The advantage of the nD-ADC(3) scheme is that the (N±1)-electronic parts of the one-particle Green's function are decoupled from each other and the corresponding equations can be solved sep. For a test of the method the nD-ADC(3) results for the vertical ionization transitions in C2H4, CO, CS, F2, H2CO, H2O, HF, N2, and Ne are compared with available exptl. and theor. data including results of full CI (FCI) and coupled cluster computations. The mean error of the nD-ADC(3) ionization energies relative to the exptl. and FCI results is about 0.2 eV. The nD-ADC(3) method, scaling as n5 with the no. of orbitals, requires the soln. of a relatively simple Hermitian eigenvalue problem. The method renders access to ground-state properties such as dipole moments. Moreover, also one-electron properties of (N±1) electron states can now be studied as a consequence of a specific intermediate-state representation (ISR) formulation of the nD-ADC approach. Corresponding second-order ISR equations are presented.
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38. 38
  Dempwolff, A. L.; Schneider, M.; Hodecker, M.; Dreuw, A. Efficient implementation of the non-Dyson third-order algebraic diagrammatic construction approximation for the electron propagator for closed- and open-shell molecules. J. Chem. Phys. 2019, 150, 064108, DOI: 10.1063/1.5081674
  38
  Efficient implementation of the non-Dyson third-order algebraic diagrammatic construction approximation for the electron propagator for closed- and open-shell molecules
  Dempwolff, Adrian L.; Schneider, Matthias; Hodecker, Manuel; Dreuw, Andreas
  Journal of Chemical Physics (2019), 150 (6), 064108/1-064108/10CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A novel efficient implementation of the non-Dyson algebraic diagrammatic construction (ADC) scheme of the (N - 1)-part of the electron propagator up to third order of perturbation theory is presented. Due to the underlying spin-orbital formulation, for the first time, the computation of ionization potentials of open-shell radicals is thus possible via non-Dyson ADC schemes. Thorough evaluation of the accuracy, applicability, and capabilities of the new method reveals a mean error of 0.15 eV for closed- as well as open-shell atoms and mols. (c) 2019 American Institute of Physics.
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39. 39
  Banerjee, S.; Sokolov, A. Y. Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green’s function implementation. J. Chem. Phys. 2019, 151, 224112, DOI: 10.1063/1.5131771
  39
  Third-order algebraic diagrammatic construction theory for electron attachment and ionization energies: Conventional and Green's function implementation
  Banerjee, Samragni; Sokolov, Alexander Yu.
  Journal of Chemical Physics (2019), 151 (22), 224112/1-224112/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  We present implementation of second- and third-order algebraic diagrammatic construction (ADC) theory for efficient and accurate computations of mol. electron affinities (EA), ionization potentials (IP), and densities of states [EA-/IP-ADC(n), n = 2, 3]. Our work utilizes the non-Dyson formulation of ADC for the single-particle propagator and reports working equations and benchmark results for the EA-ADC(2) and EA-ADC(3) approxns. We describe two algorithms for solving EA-/IP-ADC equations: (i) conventional algorithm that uses iterative diagonalization techniques to compute low-energy EA, IP, and d. of states and (ii) Green's function algorithm (GF-ADC) that solves a system of linear equations to compute d. of states directly for a specified spectral region. To assess the accuracy of EA-ADC(2) and EA-ADC(3), we benchmark their performance for a set of atoms, small mols., and five DNA/RNA nucleobases. As our next step, we demonstrate the efficiency of our GF-ADC implementation by computing core-level K-, L-, and M-shell ionization energies of a zinc atom without introducing the core-valence sepn. approxn. Finally, we use EA- and IP-ADC methods to compute the bandgaps of equally spaced hydrogen chains Hn with n up to 150, providing their ests. near thermodn. limit. Our results demonstrate that EA-/IP-ADC(n) (n = 2, 3) methods are efficient and accurate alternatives to widely used electronic structure methods for simulations of electron attachment and ionization properties. (c) 2019 American Institute of Physics.
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40. 40
  Hodecker, M.; Dempwolff, A. L.; Schirmer, J.; Dreuw, A. Theoretical analysis and comparison of unitary coupled-cluster and algebraic-diagrammatic construction methods for ionization. J. Chem. Phys. 2022, 156, 074104, DOI: 10.1063/5.0070967
  40
  Theoretical analysis and comparison of unitary coupled-cluster and algebraic-diagrammatic construction methods for ionization
  Hodecker, Manuel; Dempwolff, Adrian L.; Schirmer, Jochen; Dreuw, Andreas
  Journal of Chemical Physics (2022), 156 (7), 074104CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  This article describes a novel approach for the calcn. of ionization potentials (IPs), or, more generally, electron-detachment energies, based on a unitary coupled-cluster (UCC) parameterization of the ground-state wave function. Explicit working equations for a scheme referred to as IP-UCC3 are given, providing electron-detachment energies and spectroscopic amplitudes of electron-detached states dominated by one-hole excitations correct through third order. In the derivation, an expansion of the UCC transformed Hamiltonian involving Bernoulli nos. as expansion coeffs. is employed. Both the secular matrix and the effective transition moments are shown to be essentially equiv. to the strict third-order algebraic-diagrammatic construction scheme for the electron propagator (IP-ADC). Interestingly, due to the Bernoulli expansion, neglecting triple substitutions in the UCC expansion manifold does not affect the third-order consistency of the IP-UCC effective transition moments. Finally, the equivalence between ADC and UCC excited-state schemes is shown to not hold in fourth or higher order due to a different treatment of the correlated excited-state basis. (c) 2022 American Institute of Physics.
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41. 41
  Dempwolff, A. L.; Hodecker, M.; Dreuw, A. Vertical ionization potential benchmark for unitary coupled-cluster and algebraic-diagrammatic construction methods. J. Chem. Phys. 2022, 156, 054114, DOI: 10.1063/5.0079047
  41
  Vertical ionization potential benchmark for unitary coupled-cluster and algebraic-diagrammatic construction methods
  Dempwolff, Adrian L.; Hodecker, Manuel; Dreuw, Andreas
  Journal of Chemical Physics (2022), 156 (5), 054114CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The performance of several methods for the calcn. of vertical ionization potentials (IPs) or, more generally, electron-detachment energies based on unitary coupled-cluster (UCC) theory and the algebraic-diagrammatic construction (ADC) scheme is evaluated with respect to benchmark data computed at the level of equation-of-motion coupled-cluster theory, including single, double, and triple excitations (IP-EOM-CCSDT). Based on a statistical evaluation of about 200 electron-detached states of 41 mols., the second-order methods IP-ADC(2) and IP-UCC2 show modest accuracies with IP-EOM-CCSDT as ref., exposing a mean signed error and a std. deviation of the error of -0.54 ± 0.50 and -0.49 ± 0.54 eV, resp., accompanied by a mean abs. error (MAE) of 0.61 and 0.58 eV, resp. The strict third-order IP-ADC method demonstrates an accuracy of 0.26 ± 0.35 eV (MAE = 0.35 eV), while the IP-UCC3 method is slightly more accurate with 0.24 ± 0.26 eV (MAE = 0.29 eV). Employing the static self-energy computed using the Dyson expansion method (DEM) improves the IP-ADC(3) performance to 0.27 ± 0.28 eV, with the mean abs. error of this method being 0.32 eV. However, employing the simpler improved fourth-order scheme Σ(4+) for the static self-energy provides almost identical results as the DEM. Based on the quality of the present benchmark results, it therefore appears not necessary to use the computationally more demanding DEM. (c) 2022 American Institute of Physics.
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42. 42
  Dempwolff, A. L.; Paul, A. C.; Belogolova, A. M.; Trofimov, A. B.; Dreuw, A. Intermediate state representation approach to physical properties of molecular electron-detached states. I. Theory and implementation. J. Chem. Phys. 2020, 152, 024113, DOI: 10.1063/1.5137792
  42
  Intermediate state representation approach to physical properties of molecular electron-detached states. I. Theory and implementation
  Dempwolff, Adrian L.; Paul, Alexander C.; Belogolova, Alexandra M.; Trofimov, Alexander B.; Dreuw, Andreas
  Journal of Chemical Physics (2020), 152 (2), 024113CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The third-order non-Dyson algebraic-diagrammatic construction approach to the electron propagator [IP-ADC(3)] is extended using the intermediate state representation (ISR) formalism, allowing the wave functions and properties of mol. states with detached electron to be studied. The second-order ISR equations [ISR(2)] for the one-particle (transition) d. matrix have been derived and implemented in the Q-CHEM program. The approach is completely general and enables evaluation of arbitrary one-particle operators and interpretation of electron detachment processes in terms of d.-based quantities. The IP-ADC(3)/ISR(2) equations were implemented for Ŝz-adapted intermediate states, allowing open-shell mols. to be studied using UHF refs. As a first test for computations of ground state properties, dipole moments of various closed- and open-shell mols. have been computed by means of electron detachment from the corresponding anions. The results are in good agreement with exptl. data. The potential of IP-ADC(3)/ISR(2) for the interpretation of photoelectron spectra is demonstrated for the galvinoxyl free radical. (c) 2020 American Institute of Physics.
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43. 43
  Dempwolff, A. L.; Paul, A. C.; Belogolova, A. M.; Trofimov, A. B.; Dreuw, A. Intermediate state representation approach to physical properties of molecular electron-detached states. II. Benchmarking. J. Chem. Phys. 2020, 152, 024125, DOI: 10.1063/1.5137794
  43
  Intermediate state representation approach to physical properties of molecular electron-detached states. II. Benchmarking
  Dempwolff, Adrian L.; Paul, Alexander C.; Belogolova, Alexandra M.; Trofimov, Alexander B.; Dreuw, Andreas
  Journal of Chemical Physics (2020), 152 (2), 024125CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The third-order algebraic-diagrammatic construction method for studies of electron detachment processes within the electron propagator framework [IP-ADC(3)] was extended to treat the properties of mol. states with a detached electron using the intermediate state representation (ISR) formalism. The second-order ISR(2) equations for the one-particle (transition) d. matrix have been derived and implemented as an extension of the IP-(U)ADC(3) method available in the Q-CHEM program. As a first systematic test of the present IP-(U)ADC(3)/ISR(2) method, the dipole moments of various electronic states of closed- and open-shell mols. have been computed and compared to full CI (FCI) results. The present study employing FCI benchmarks also provides the first rigorous ests. for the accuracy of electron detachment energies obtained using the IP-ADC(3) method. (c) 2020 American Institute of Physics.
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44. 44
  Dempwolff, A. L.; Belogolova, A. M.; Trofimov, A. B.; Dreuw, A. Intermediate state representation approach to physical properties of molecular electron-attached states: Theory, implementation, and benchmarking. J. Chem. Phys. 2021, 154, 104117, DOI: 10.1063/5.0043337
  44
  Intermediate state representation approach to physical properties of molecular electron-attached states: Theory, implementation, and benchmarking
  Dempwolff, Adrian L.; Belogolova, Alexandra M.; Trofimov, Alexander B.; Dreuw, Andreas
  Journal of Chemical Physics (2021), 154 (10), 104117CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Computational schemes for comprehensive studies of mol. electron-attached states and the calcn. of electron affinities (EAs) are formulated and implemented employing the intermediate state representation (ISR) formalism and the algebraic-diagrammatic construction approxn. for the electron propagator (EA-ADC). These EA-ADC(n)/ISR(m) schemes allow for a consistent treatment of not only electron affinities and pole strengths up to third-order of perturbation theory (n = 3) but also one-electron properties of electron-attached states up to second order (m = 2). The EA-ADC/ISR equations were implemented in the Q-CHEM program for Ŝz-adapted intermediate states, allowing also open-shell systems to be studied using UHF refs. For benchmarking of the EA-(U)ADC/ISR schemes, EAs and dipole moments of various electron-attached states of small closed- and open-shell mols. were computed and compared to full CI data. As an illustrative example, EA-ADC(3)/ISR(2) has been applied to the thymine-thymine (6-4) DNA photolesion. (c) 2021 American Institute of Physics.
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45. 45
  Ortiz, J. V. Electron propagator theory: an approach to prediction and interpretation in quantum chemistry. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2013, 3, 123, DOI: 10.1002/wcms.1116
  45
  Electron propagator theory: an approach to prediction and interpretation in quantum chemistry
  Ortiz, Joseph Vincent
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2013), 3 (2), 123-142CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  A review. Electron propagator theory provides a practical means of calcg. electron binding energies, Dyson orbitals, and ground-state properties from first principles. This approach to ab initio electronic structure theory also facilitates the interpretation of its quant. predictions in terms of concepts that closely resemble those of one-electron theories. An explanation of the phys. meaning of the electron propagator's poles and residues is followed by a discussion of its couplings to more complicated propagators. These relationships are exploited in superoperator theory and lead to a compact form of the electron propagator that is derived by matrix partitioning. Expressions for ref.-state properties, relationships to the extended Koopmans's theorem technique for evaluating electron binding energies, and connections between Dyson orbitals and transition probabilities follow from this discussion. The inverse form of the Dyson equation for the electron propagator leads to a strategy for obtaining electron binding energies and Dyson orbitals that generalizes the Hartree-Fock equations through the introduction of the self-energy operator. All relaxation and correlation effects reside in this operator, which has an energy-dependent, nonlocal form that is systematically improvable. Perturbative arguments produce several, convenient (e.g. partial third order, outer valence Green's function, and second-order, transition-operator) approxns. for the evaluation of valence ionization energies, electron affinities, and core ionization energies. Renormalized approaches based on Hartree-Fock or approx. Brueckner orbitals are employed when correlation effects become qual. important. Ref.-state total energies based on contour integrals in the complex plane and gradients of electron binding energies enable exploration of final-state potential energy surfaces.
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46. 46
  Ortiz, J. V. Partial third-order quasiparticle theory: Comparisons for closed-shell ionization energies and an application to the borazine photoelectron spectrum. J. Chem. Phys. 1996, 104, 7599, DOI: 10.1063/1.471468
  46
  Partial third-order quasiparticle theory: comparisons for closed-shell ionization energies and an application to the Borazine photoelectron spectrum
  Ortiz, J. V.
  Journal of Chemical Physics (1996), 104 (19), 7599-7605CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Valence ionization energies of a set closed-shell mols. calcd. in a partial 3rd-order (P3) quasiparticle approxn. of the electron propagator have an av. abs. error of 0.19 eV. Diagonal elements of the self-energy matrix include all 2nd-order and some 3rd-order self-energy diagrams. Because of its 5th power dependence on basis set size and its independence from electron repulsion integrals with four virtual indexes, this method has considerable potential for large mols. Formal and computational comparisons with other electron propagator techniques illustrate the advantages of the P3 procedure. Addnl. applications to benzene and borazine display the efficacy of the P3 propagator in assigning photoelectron spectra. In the borazine spectrum, 2E' and 2A2' final states are responsible for an obsd. feature at 14.76 eV. Another peak at 17.47 eV is assigned to a 2E' final state.
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47. 47
  Corzo, H. H.; Galano, A.; Dolgounitcheva, O.; Zakrzewski, V. G.; Ortiz, J. V. NR2 and P3+: Accurate, Efficient Electron-Propagator Methods for Calculating Valence, Vertical Ionization Energies of Closed-Shell Molecules. J. Phys. Chem. A 2015, 119, 8813, DOI: 10.1021/acs.jpca.5b00942
  47
  NR2 and P3+: Accurate, Efficient Electron-Propagator Methods for Calculating Valence, Vertical Ionization Energies of Closed-Shell Molecules
  Corzo, H. H.; Galano, Annia; Dolgounitcheva, O.; Zakrzewski, V. G.; Ortiz, J. V.
  Journal of Physical Chemistry A (2015), 119 (33), 8813-8821CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  Two accurate and computationally efficient electron-propagator (EP) methods for calcg. the valence, vertical ionization energies (VIEs) of closed-shell mols. have been identified through comparisons with related approxns. VIEs of a representative set of closed-shell mols. were calcd. with EP methods using 10 basis sets. The most easily executed method, the diagonal, second-order (D2) EP approxn., produces results that steadily rise as basis sets are improved toward values based on extrapolated coupled-cluster singles and doubles plus perturbative triples calcns., but its mean errors remain unacceptably large. The outer valence Green function, partial third-order and renormalized partial third-order methods (P3+), which employ the diagonal self-energy approxn., produce markedly better results but have a greater tendency to overestimate VIEs with larger basis sets. The best combination of accuracy and efficiency with a diagonal self-energy matrix is the P3+ approxn., which exhibits the best trends with respect to basis-set satn. Several renormalized methods with more flexible nondiagonal self-energies also have been examd.: the two-particle, one-hole Tamm-Dancoff approxn. (2ph-TDA), the third-order algebraic diagrammatic construction or ADC(3), the renormalized third-order (3+) method, and the nondiagonal second-order renormalized (NR2) approxn. Like D2, 2ph-TDA produces steady improvements with basis set augmentation, but its av. errors are too large. Errors obtained with 3+ and ADC(3) are smaller on av. than those of 2ph-TDA. These methods also have a greater tendency to overestimate VIEs with larger basis sets. The smallest av. errors occur for the NR2 approxn.; these errors decrease steadily with basis augmentations. As basis sets approach satn., NR2 becomes the most accurate and efficient method with a nondiagonal self-energy.
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48. 48
  Ortiz, J. V. An efficient, renormalized self-energy for calculating the electron binding energies of closed-shell molecules and anions. Int. J. Quantum Chem. 2005, 105, 803, DOI: 10.1002/qua.20664
  48
  An efficient, renormalized self-energy for calculating the electron binding energies of closed-shell molecules and anions
  Ortiz, J. V.
  International Journal of Quantum Chemistry (2005), 105 (6), 803-808CODEN: IJQCB2; ISSN:0020-7608. (John Wiley & Sons, Inc.)
  The energy-dependent, nonlocal correlation potential known as the self-energy that appears in the Dyson equation has a pole and residue structure that enables renormalizations of its low-order, perturbative contributions to be estd. The partial third-order (P3) approxn. has been extensively applied to the ionization energies of closed-shell, org. mols. and is the most successful example of a low-order, self-energy method. A renormalization based on the P3 self-energy ests. higher-order contributions by scaling low-order terms that chiefly describe final-state relaxation. The resulting P3 + self-energy retains the accuracy and efficiency of the P3 approxn., but also improves the latter method's performance with respect to the calcn. of anion electron detachment energies without the introduction of adjustable parameters. An application to an anion that previously has yielded only to more intricate treatments of electron correlation demonstrates the power of this simple, new approxn.
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49. 49
  Ortiz, J. V. A nondiagonal, renormalized extension of partial third-order quasiparticle theory: Comparisons for closed-shell ionization energies. J. Chem. Phys. 1998, 108, 1008, DOI: 10.1063/1.475463
  49
  A nondiagonal, renormalized extension of partial third-order quasiparticle theory: comparisons for closed-shell ionization energies
  Ortiz, J. V.
  Journal of Chemical Physics (1998), 108 (3), 1008-1014CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Valence ionization energies of a set closed-shell mols. calcd. in a nondiagonal, renormalized approxn. of the electron propagator have an av. abs. error of 0.17 eV. This procedure extends the partial third order, quasiparticle approxn. of J. Chem. Phys. 104, 7599 (1996) that has proven successful in many applications. Elements of the self-energy matrix include all second-order and many higher-order terms. Because of its fifth power dependence on basis set size and its independence from electron repulsion integrals with four virtual orbital indexes, this method has considerable promise for large mols. Formal and computational comparisons with renormalized electron propagator techniques that are complete through third-order illustrate the advantages of this procedure.
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50. 50
  Opoku, E.; Pawłowski, F.; Ortiz, J. V. A new generation of diagonal self-energies for the calculation of electron removal energies. J. Chem. Phys. 2021, 155, 204107, DOI: 10.1063/5.0070849
  50
  A new generation of diagonal self-energies for the calculation of electron removal energies
  Opoku, Ernest; Pawlowski, Filip; Ortiz, J. V.
  Journal of Chemical Physics (2021), 155 (20), 204107CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A new generation of diagonal self-energy approxns. in ab initio electron propagator theory for the calcn. of electron removal energies of mols. and mol. ions has been derived from an intermediately normalized, Hermitized super-operator metric. These methods and widely used antecedents such as the outer valence Green's function and the approx. renormalized partial third order method are tested with respect to a dataset of vertical ionization energies generated with a valence, triple-ζ, correlation-consistent basis set and a converged series of many-body calcns. whose accuracy approaches that of full CI. Several modifications of the diagonal second-order self-energy, a version of G0W0 theory based on Tamm-Dancoff excitations and several non-diagonal self-energies are also included in the tests. All new methods employ canonical Hartree-Fock orbitals. No adjustable or empirical parameters appear. A hierarchy of methods with optimal accuracy for a given level of computational efficiency is established. Several widely used diagonal self-energy methods are rendered obsolete by the new hierarchy whose members, in order of increasing accuracy, are (1) the opposite-spin non-Dyson diagonal second-order or os-nD-D2, (2) the approx. renormalized third-order quasiparticle or Q3+ , (3) the renormalized third-order quasiparticle or RQ3, (4) the approx. renormalized linear third-order or L3+ , and (5) the renormalized linear third-order or RL3 self-energies. (c) 2021 American Institute of Physics.
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51. 51
  Opoku, E.; Pawłowski, F.; Ortiz, J. V. Electron Propagator Theory of Vertical Electron Detachment Energies of Anions: Benchmarks and Applications to Nucleotides. J. Phys. Chem. A 2023, 127, 1085, DOI: 10.1021/acs.jpca.2c08372
  51
  Electron Propagator Theory of Vertical Electron Detachment Energies of Anions: Benchmarks and Applications to Nucleotides
  Opoku, Ernest; Pawlowski, Filip; Ortiz, J. V.
  Journal of Physical Chemistry A (2023), 127 (4), 1085-1101CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  A new generation of ab initio electron-propagator self-energy approxns. that is free of adjustable parameters is tested on a benchmark set of 55 vertical electron detachment energies of closed-shell anions. Comparisons with older self-energy approxns. indicate that several new methods that make the diagonal self-energy approxn. in the canonical Hartree-Fock orbital basis provide superior accuracy and computational efficiency. These methods, their acronyms, mean abs. errors (in eV) and arithmetic bottlenecks expressed in terms of occupied (O) and virtual (V) orbitals are the opposite-spin, non-Dyson, diagonal second-order method (os-nD-D2, 0.2, OV2), the approx. renormalized quasiparticle third-order method (Q3+ , 0.15, O2V3) and the approx. renormalized, non-Dyson, linear, third-order method (nD-L3+ , 0.1, OV4). The BD-T1 (Brueckner Doubles with Triple field operators) nondiagonal electron-propagator method provides such close agreement with coupled-cluster single, double and perturbative triple replacement total energy differences that it may be used as an alternative means of obtaining std. data. The new methods with diagonal self-energy matrixes are the foundation of a composite procedure for estg. basis-set effects. This model produces accurate predictions and clear interpretations based on Dyson orbitals for the photoelectron spectra of the nucleotides found in DNA.
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52. 52
  Gilbert, A. T. B.; Besley, N. A.; Gill, P. M. W. Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM). J. Phys. Chem. A 2008, 112, 13164, DOI: 10.1021/jp801738f
  52
  Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM)
  Gilbert, Andrew T. B.; Besley, Nicholas A.; Gill, Peter M. W.
  Journal of Physical Chemistry A (2008), 112 (50), 13164-13171CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  We present a simple algorithm, which we call the max. overlap method (MOM), for finding excited-state solns. to SCF equations. Instead of using the aufbau principle, the algorithm maximizes the overlap between the occupied orbitals on successive SCF iterations. This prevents variational collapse to the ground state and guides the SCF process toward the nearest, rather than the lowest energy, soln. The resulting excited-state solns. can be treated in the same way as the ground-state soln. and, in particular, derivs. of excited-state energies can be computed using ground-state code. We assess the performance of our method by applying it to a variety of excited-state problems including the calcn. of excitation energies, charge-transfer states, and excited-state properties.
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53. 53
  Bagus, P. S. Self-Consistent-Field Wave Functions for Hole States of Some Ne-Like and Ar-Like Ions. Phys. Rev. 1965, 139, A619, DOI: 10.1103/PhysRev.139.A619
  53
  Self-consistent-field wave functions for hole states of some Ne-like and Ar-like ions
  Bagus, P. S.
  Physical Review (1965), 139 (3A), 619-34CODEN: PHRVAO; ISSN:0031-899X.
  Analytic self-consistent-field (SCF) wave functions were computed for the ground states of the closed-shell at. systems F-, Ne, and Na+ and Cl-, Ar, and K+; and for those ground and excited states of the open-shell systems which are obtained by removing a single electron from any one of the occupied shells of these closed-shell systems. Details of the calcn. of the functions are presented, with emphasis on a justification of the procedures used for the calcns. for excited states. A high accuracy is obtained; the calcns. for the closed-shell systems give the most accurate analytic SCF wave functions which have yet been reported. Ionization potentials are compared with exptl. values. Computed ionization potentials for the removal of a 2s electron from Cl-, Ar, and K+, for which no direct exptl. data are available, are estd. to be accurate to 1%. The removal of an electron from the outermost s shell increases the correlation energy, in contradiction to the predictions of a recently proposed semi- empirical scheme for estg. the correlation energy. For example, the magnitude of the correlation energy of the lowest 2S state of Ar+ is ∼4 ev. greater than the magnitude of the correlation energy of neutral Ar. The effect of the nonzero off-diagonal Lagrangian multipliers is important for the inner shell hole states.
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54. 54
  Triguero, L.; Pettersson, L. G. M.; Ågren, H. Calculations of near-edge x-ray-absorption spectra of gas-phase and chemisorbed molecules by means of density-functional and transition-potential theory. Phys. Rev. B 1998, 58, 8097, DOI: 10.1103/PhysRevB.58.8097
  54
  Calculations of near-edge x-ray-absorption spectra of gas-phase and chemisorbed molecules by means of density-functional and transition-potential theory
  Triguero, L.; Pettersson, L. G. M.; Agren, H.
  Physical Review B: Condensed Matter and Materials Physics (1998), 58 (12), 8097-8110CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  The authors explore the utility of d.-functional theory (DFT) in conjunction with the transition-potential (TP) method to simulate x-ray-absorption spectra. Calcns. on a set of small C-contg. mols. and chemisorbed species show that this provides a viable option for obtaining excitation energies and oscillator strengths close to the exptl. accuracy of core-valence transitions. Systematic variations in energy positions and intensities of the different spectra in the test series were studied, and comparison is made with respect to the static exchange-, SCF, and explicit electron-correlation methods. The choice between std. exchange-correlation functionals is of little consequence for the valence resonant, here π*, parts of the x-ray-absorption spectra, while the long-range behavior of presently available functionals is found not to be completely satisfactory for Rydberg-like transitions. Implementing a basis set augmentation technique, DFT methods still account well for most of the salient features in the near-edge x-ray-absorption spectra, save for the multielectron transitions in the near continuum, and for some loss of Rydberg structure. For clusters modeling surface adsorbates, the DFT transition potential method reproduces well the spectral compression and intensity redn. for the valence level absorption compared to the free phase, provided fairly large clusters are taken into account. While for near-edge x-ray-absorption fine-structure (NEXAFS) spectra of free mols. the DFT-TP and Hartree-Fock/static exchange methods have complementary advantages, the DFT-TP method is clearly to be preferred when using clusters to simulate NEXAFS spectra of surface adsorbates.
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55. 55
  Lee, J.; Small, D. W.; Head-Gordon, M. Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states. J. Chem. Phys. 2019, 151, 214103, DOI: 10.1063/1.5128795
  55
  Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states
  Lee, Joonho; Small, David W.; Head-Gordon, Martin
  Journal of Chemical Physics (2019), 151 (21), 214103/1-214103/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  In this work, we revisited the idea of using the coupled-cluster (CC) ground state formalism to target excited states. Our main focus was targeting doubly excited states and double core hole states. Typical equation-of-motion (EOM) approaches for obtaining these states struggle without higher-order excitations than doubles. We showed that by using a non-Aufbau determinant optimized via the max. overlap method, the CC ground state solver can target higher energy states. Furthermore, just with singles and doubles (i.e., CCSD), we demonstrated that the accuracy of ΔCCSD and ΔCCSD(T) (triples) far surpasses that of EOM-CCSD for doubly excited states. The accuracy of ΔCCSD(T) is nearly exact for doubly excited states considered in this work. For double core hole states, we used an improved ansatz for greater numerical stability by freezing core hole orbitals. The improved methods, core valence sepn. (CVS)-ΔCCSD and CVS-ΔCCSD(T), were applied to the calcn. of the double ionization potential of small mols. Even without relativistic corrections, we obsd. qual. accurate results with CVS-ΔCCSD and CVS-ΔCCSD(T). Remaining challenges in ΔCC include the description of open-shell singlet excited states with the single-ref. CC ground state formalism as well as excited states with genuine multireference character. The tools and intuition developed in this work may serve as a stepping stone toward directly targeting arbitrary excited states using ground state CC methods. (c) 2019 American Institute of Physics.
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56. 56
  Meissner, L.; Balková, A.; Bartlett, R. J. Multiple solutions of the single-reference coupled-cluster method. Chem. Phys. Lett. 1993, 212, 177, DOI: 10.1016/0009-2614(93)87127-O
  56
  Multiple solutions of the single-reference coupled-cluster method
  Meissner, Leszek; Balkova, Anna; Bartlett, Rodney J.
  Chemical Physics Letters (1993), 212 (1-2), 177-84CODEN: CHPLBC; ISSN:0009-2614.
  The nonlinear coupled-cluster (CC) equations possess several solns. They describe various excited states as long as they contain a contribution from the ref. function. The authors study the addnl. solns. of the single-ref. CC equations and demonstrate that unlike the ground state, the approx. soln. for excited states in general does not satisfy the cluster condition nor the std. proof of extensivity. For such states that makes the CC approxn. poorer than that for the analogous CI.
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57. 57
  Zheng, X.; Cheng, L. Performance of Delta-Coupled-Cluster Methods for Calculations of Core-Ionization Energies of First-Row Elements. J. Chem. Theory Comput. 2019, 15, 4945, DOI: 10.1021/acs.jctc.9b00568
  57
  Performance of Delta-Coupled-Cluster Methods for Calculations of Core-Ionization Energies of First-Row Elements
  Zheng, Xuechen; Cheng, Lan
  Journal of Chemical Theory and Computation (2019), 15 (9), 4945-4955CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  A thorough study of the performance of delta-coupled-cluster (ΔCC) methods for calcns. of core-ionization energies for elements of the first long row of the periodic table is reported. Inspired by the core-valence sepn. (CVS) scheme in response theories, a simple CVS scheme of excluding the vacant core orbital from the CC treatment has been adopted to solve the convergence problem of the CC equations for core-ionized states. Dynamic correlation effects have been shown to make important contributions to the computed core-ionization energies, esp. to chem. shifts of these quantities. The max. abs. error (MaxAE) and std. deviation (SD) of delta-Hartree-Fock results for chem. shifts of core-ionization energies with respect to the corresponding exptl. values amt. to more than 1.7 and 0.6 eV, resp. In contrast, the inclusion of electron correlation in ΔCC singles and doubles augmented with a noniterative triples correction [ΔCCSD(T)] method significantly reduces the corresponding deviations to around 0.3 and 0.1 eV. With the consideration of basis set effects and the corrections to the CVS approxn., ΔCCSD(T) has been shown to provide highly accurate results for abs. values of core-ionization energies, with a MaxAE of 0.22 eV and SD of 0.13 eV. To further demonstrate the usefulness of ΔCCSD(T), calcns. of carbon K-edge ionization energies of Et trifluoroacetate, a mol. of significant interest to the study of X-ray spectroscopy and dynamics, are reported.
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58. 58
  Hirata, S.; Hermes, M. R.; Simons, J.; Ortiz, J. V. General-Order Many-Body Green’s Function Method. J. Chem. Theory Comput. 2015, 11, 1595, DOI: 10.1021/acs.jctc.5b00005
  58
  General-Order Many-Body Green's Function Method
  Hirata, So; Hermes, Matthew R.; Simons, Jack; Ortiz, J. V.
  Journal of Chemical Theory and Computation (2015), 11 (4), 1595-1606CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Electron binding energies are evaluated as differences in total energy between the N- and (N ± 1)-electron systems calcd. by the nth-order Moller-Plesset perturbation (MPn) theory using the same set of orbitals. The MPn energies up to n = 30 are, in turn, obtained by the determinant-based method of Knowles et al. (Chem. Phys. Lett.1985, 113, 8-12). The zeroth- through third-order electron binding energies thus detd. agree with those obtained by solving the Dyson equation in the diagonal and frequency-independent approxns. of the self-energy. However, as n → ∞, they converge at the exact basis-set solns. from the Dyson equation with the exact self-energy, which is nondiagonal and frequency-dependent. This suggests that the MPn energy differences define an alternative diagrammatic expansion of Koopmans-like electron binding energies, which takes into account the perturbation corrections from the off-diagonal elements and frequency dependence of the irreducible self-energy. Our anal. shows that these corrections are included as semireducible and linked-disconnected diagrams, resp., which are also found in a perturbation expansion of the electron binding energies of the equation-of-motion coupled-cluster methods. The rate of convergence of the electron binding energies with respect to n and its acceleration by Pade approximants are also discussed.
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59. 59
  Hirata, S.; Doran, A. E.; Knowles, P. J.; Ortiz, J. V. One-particle many-body Green’s function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms. J. Chem. Phys. 2017, 147, 044108, DOI: 10.1063/1.4994837
  59
  One-particle many-body Green's function theory: Algebraic recursive definitions, linked-diagram theorem, irreducible-diagram theorem, and general-order algorithms
  Hirata, So; Doran, Alexander E.; Knowles, Peter J.; Ortiz, J. V.
  Journal of Chemical Physics (2017), 147 (4), 044108/1-044108/31CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A thorough anal. and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equiv. algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approxns. at 1 ≤ n ≤ 3 but converges at the full-configuration-interaction (FCI) limit at n = ∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approxn. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified math. using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approxns. at 1 ≤ n ≤ 3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams. (c) 2017 American Institute of Physics.
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60. 60
  Goerigk, L.; Hansen, A.; Bauer, C.; Ehrlich, S.; Najibi, A.; Grimme, S. A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions. Phys. Chem. Chem. Phys. 2017, 19, 32184, DOI: 10.1039/C7CP04913G
  60
  A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions
  Goerigk, Lars; Hansen, Andreas; Bauer, Christoph; Ehrlich, Stephan; Najibi, Asim; Grimme, Stefan
  Physical Chemistry Chemical Physics (2017), 19 (48), 32184-32215CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  We present the GMTKN55 benchmark database for general main group thermochem., kinetics and noncovalent interactions. Compared to its popular predecessor GMTKN30, it allows assessment across a larger variety of chem. problems - with 13 new benchmark sets being presented for the first time - and it also provides ref. values of significantly higher quality for most sets. GMTKN55 comprises 1505 relative energies based on 2462 single-point calcns. and it is accessible to the user community via a dedicated website. Herein, we demonstrate the importance of better ref. values, and we re-emphasize the need for London-dispersion corrections in d. functional theory (DFT) treatments of thermochem. problems, including Minnesota methods. We assessed 217 variations of dispersion-cor. and -uncorrected d. functional approxns., and carried out a detailed anal. of 83 of them to identify robust and reliable approaches. Double-hybrid functionals are the most reliable approaches for thermochem. and noncovalent interactions, and they should be used whenever tech. feasible. These are, in particular, DSD-BLYP-D3(BJ), DSD-PBEP86-D3(BJ), and B2GPPLYP-D3(BJ). The best hybrids are ωB97X-V, M052X-D3(0), and ωB97X-D3, but we also recommend PW6B95-D3(BJ) as the best conventional global hybrid. At the meta-generalized-gradient (meta-GGA) level, the SCAN-D3(BJ) method can be recommended. Other meta-GGAs are outperformed by the GGA functionals revPBE-D3(BJ), B97-D3(BJ), and OLYP-D3(BJ). We note that many popular methods, such as B3LYP, are not part of our recommendations. In fact, with our results we hope to inspire a change in the user community's perception of common DFT methods. We also encourage method developers to use GMTKN55 for cross-validation studies of new methodologies.
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61. 61
  Goerigk, L.; Grimme, S. A general database for main group thermochemistry, kinetics, and noncovalent interactions – Assessment of common and reparameterized (meta-)GGA density functionals. J. Chem. Theory Comput. 2010, 6, 107, DOI: 10.1021/ct900489g
  61
  A General Database for Main Group Thermochemistry, Kinetics, and Noncovalent Interactions - Assessment of Common and Reparameterized (meta-)GGA Density Functionals
  Goerigk, Lars; Grimme, Stefan
  Journal of Chemical Theory and Computation (2010), 6 (1), 107-126CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  We present a quantum chem. benchmark database for general main group thermochem., kinetics, and noncovalent interactions (GMTKN24). It is an unprecedented compilation of 24 different, chem. relevant subsets that either are taken from already existing databases or are presented here for the first time. The complete set involves a total of 1.049 at. and mol. single point calcns. and comprises 731 data points (relative chem. energies) based on accurate theor. or exptl. ref. values. The usefulness of the GMTKN24 database is shown by applying common d. functionals on the (meta-)generalized gradient approxn. (GGA), hybrid-GGA, and double-hybrid-GGA levels to it, including an empirical London dispersion correction. Furthermore, we refitted the functional parameters of four (meta-)GGA functionals based on a fit set contg. 143 systems, comprising seven chem. different problems. Validation against the GMTKN24 and the mol. structure (bond lengths) databases shows that the reparameterization does not change bond lengths much, whereas the description of energetic properties is more prone to the parameters' values. The empirical dispersion correction also often improves for conventional thermodn. problems and makes a functional's performance more uniform over the entire database. The refitted functionals typically have a lower mean abs. deviation for the majority of subsets in the proposed GMTKN24 set. This, however, is also often accompanied at the expense of poor performance for a few other important subsets. Thus, creating a broadly applicable (and overall better) functional by just reparameterizing existing ones seems to be difficult. Nevertheless, this benchmark study reveals that a reoptimized (i.e., empirical) version of the TPSS-D functional (oTPSS-D) performs well for a variety of problems and may meet the stds. of an improved functional. We propose validation against this new compilation of benchmark sets as a definitive way to evaluate a new quantum chem. method's true performance.
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62. 62
  Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. Gaussian-2 theory for molecular energies of first-and second-row compounds. J. Chem. Phys. 1991, 94, 7221, DOI: 10.1063/1.460205
  62
  Gaussian-2 theory for molecular energies of first- and second-row compounds
  Curtiss, Larry A.; Raghavachari, Krishnan; Trucks, Gary W.; Pople, John A.
  Journal of Chemical Physics (1991), 94 (11), 7221-30CODEN: JCPSA6; ISSN:0021-9606.
  The Gaussian-2 theor. procedure (G2 theory), based on ab-initio MO theory, for calcn. of mol. energies (atomization energies, ionization potentials, electron affinities, and proton affinities) of compds. contg. first- (Li-F) and second-row atoms (Na-Cl) is presented. This new theor. procedure adds three features to G1 theory (P., et al., 1989; C., et al., 1990), including a correction for nonadditivity of diffuse-sp and 2df basis-set extensions, a basis-set extension contg. a third d-function on nonhydrogen atoms and a second p-function on hydrogen atoms, and a modification of the higher level correction. G2 theory is a significant improvement over G1 theory, because it eliminates a no. of deficiencies present in G1 theory. Of particular importance is the improvement in atomization energies of ionic mols. such as LiF and hydrides such as C2H6,NH3, N2H4, H2O2, and CH3SH. The av. abs. deviation from expt. of atomization energies of 39 first-row compds. is reduced from 1.42 to 0.92 kcal/mol. In addn., G2 theory gives improved performance for hypervalent species and electron affinities of second-row species (the av. deviation from expt. of electron affinities of second-row species is reduced from 1.94 to 1.08 kcal/mol). Finally, G2 atomization energies for another 43 mols., not previously studied with G1 theory, many of which have uncertain exptl. data, are presented and differences with expt. are assessed.
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63. 63
  Śmiga, S.; Franck, O.; Mussard, B.; Buksztel, A.; Grabowski, I.; Luppi, E.; Toulouse, J. Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method. J. Chem. Phys. 2016, 145, 144102, DOI: 10.1063/1.4964319
  63
  Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method
  Smiga, Szymon; Franck, Odile; Mussard, Bastien; Buksztel, Adam; Grabowski, Ireneusz; Luppi, Eleonora; Toulouse, Julien
  Journal of Chemical Physics (2016), 145 (14), 144102/1-144102/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  We introduce an orbital-optimized double-hybrid (DH) scheme using the optimized-effective-potential (OEP) method. The orbitals are optimized using a local potential corresponding to the complete exchange-correlation energy expression including the second-order Moller-Plesset correlation contribution. We have implemented a one-parameter version of this OEP-based self-consistent DH scheme using the BLYP d.-functional approxn. and compared it to the corresponding non-self-consistent DH scheme for calcns. on a few closed-shell atoms and mols. While the OEP-based self-consistency does not provide any improvement for the calcns. of ground-state total energies and ionization potentials, it does improve the accuracy of electron affinities and restores the meaning of the LUMO orbital energy as being connected to a neutral excitation energy. Moreover, the OEP-based self-consistent DH scheme provides reasonably accurate exchange-correlation potentials and correlated densities. (c) 2016 American Institute of Physics.
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64. 64
  Śmiga, S.; Grabowski, I.; Witkowski, M.; Mussard, B.; Toulouse, J. Self-Consistent Range-Separated Density-Functional Theory with Second-Order Perturbative Correction via the Optimized-Effective-Potential Method. J. Chem. Theory Comput. 2020, 16, 211, DOI: 10.1021/acs.jctc.9b00807
  64
  Self-Consistent Range-Separated Density-Functional Theory with Second-Order Perturbative Correction via the Optimized-Effective-Potential Method
  Smiga Szymon; Grabowski Ireneusz; Witkowski Mateusz; Mussard Bastien; Toulouse Julien
  Journal of chemical theory and computation (2020), 16 (1), 211-223 ISSN:.
  We extend the range-separated double-hybrid RSH+MP2 method (Angyan, J. G.; et al. Phys. Rev. A2005, 72, 012510), combining long-range HF exchange and MP2 correlation with a short-range density functional to a fully self-consistent version using the optimized-effective-potential technique in which the orbitals are obtained from a local potential including the long-range HF and MP2 contributions. We test this approach, that we name RS-OEP2, on a set of small closed-shell atoms and molecules. For the commonly used value of the range-separation parameter μ = 0.5 bohr(-1), we find that self-consistency does not seem to bring any improvement for total energies, ionization potentials, and electronic affinities. However, contrary to the non-self-consistent RSH+MP2 method, the present RS-OEP2 method gives a LUMO energy which physically corresponds to a neutral excitation energy and gives local exchange-correlation potentials which are reasonably good approximations to the corresponding Kohn-Sham quantities. At a finer scale, we find that RS-OEP2 gives largely inaccurate correlation potentials and correlated densities, which points to the need of further improvement of this type of range-separated double hybrids.
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65. 65
  Cohen, A. J.; Mori-Sánchez, P.; Yang, W. Second-Order Perturbation Theory with Fractional Charges and Fractional Spins. J. Chem. Theory Comput. 2009, 5, 786, DOI: 10.1021/ct8005419
  65
  Second-Order Perturbation Theory with Fractional Charges and Fractional Spins
  Cohen, Aron J.; Mori-Sanchez, Paula; Yang, Weitao
  Journal of Chemical Theory and Computation (2009), 5 (4), 786-792CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  The behavior of MP2 for fractional occupations is investigated. The consideration of fractional charge behavior gives a simple derivation of an expression for the chem. potential (or the deriv. of energy with respect to the no. of electrons) of MP2. A generalized optimized effective potential formalism (OEP) has been developed in which the OEP is a nonlocal potential, which can be applied to explicit functionals of the orbitals and eigenvalues and also facilitates the evaluation of the chem. potential. The MP2 deriv. improves upon the corresponding Koopmans' theorem in Hartree-Fock theory for the ionization energy and also gives a good est. of the electron affinity. In strongly correlated systems with degeneracies and fractional spins, MP2 diverges, and another cor. second-order perturbative method ameliorates this failure for the energy but still does not recapture the correct behavior for the energy derivs. that yield the gap. Overall we present a view of wave function based methods and their behavior for fractional charges and spins that offers insight into the application of these methods to challenging chem. problems.
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66. 66
  Su, N. Q.; Yang, W.; Mori-Sánchez, P.; Xu, X. Fractional Charge Behavior and Band Gap Predictions with the XYG3 Type of Doubly Hybrid Density Functionals. J. Phys. Chem. A 2014, 118, 9201, DOI: 10.1021/jp5029992
  66
  Fractional Charge Behavior and Band Gap Predictions with the XYG3 Type of Doubly Hybrid Density Functionals
  Su, Neil Qiang; Yang, Weitao; Mori-Sanchez, Paula; Xu, Xin
  Journal of Physical Chemistry A (2014), 118 (39), 9201-9211CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  In this work, we examine the fractional charge behaviors of doubly hybrid (DH) functionals. By plotting the ground-state energies E and energy derivs. for atoms and mols. with fractional electron nos. N, we directly quantify the delocalization errors of some representative DH functionals such as B2PLYP, XYG3, and XYGJ-OS. Numerical assessments on ionization potentials (IPs), electron affinities (EAs), and fundamental gaps, from either integer no. calcns. or energy deriv. calcns., are provided. It is shown that the XYG3 type of DH functionals gives good agreement between their energy derivs. and the exptl. IPs, EAs, and gaps, as expected from their nearly straight line fractional charge behaviors.
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67. 67
  Mussard, B.; Toulouse, J. Fractional-charge and fractional-spin errors in range-separated density-functional theory. Mol. Phys. 2017, 115, 161, DOI: 10.1080/00268976.2016.1213910
  67
  Fractional-charge and fractional-spin errors in range-separated density-functional theory
  Mussard, Bastien; Toulouse, Julien
  Molecular Physics (2017), 115 (1-2), 161-173CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)
  We investigate fractional-charge and fractional-spin errors in range-sepd. d.-functional theory (DFT). Specifically, we consider the range-sepd. hybrid (RSH) method which combines long-range Hartree-Fock (HF) exchange with a short-range semilocal exchange-correlation d. functional, and the RSH+MP2 method which adds long-range, second-order Moller-Plesset (MP2) correlation. Results on atoms and mols. show that the fractional-charge errors obtained in RSH are much smaller than in the std. Kohn-Sham (KS) scheme applied with semilocal or hybrid approxns., and also generally smaller than in the std. HF method. The RSH+MP2 method tends to have smaller fractional-charge errors than std. MP2 for the most diffuse systems, but larger fractional-charge errors for the more compact systems. Even though the individual contributions to the fractional-spin errors in the H atom coming from the short-range exchange and correlation d.-functional approxns. are smaller than the corresponding contributions for the full-range exchange and correlation d.-functional approxns., RSH gives fractional-spin errors that are larger than in the std. KS scheme and only slightly smaller than in std. HF. Adding long-range MP2 correlation only leads to infinite fractional-spin errors. This work clarifies the successes and limitations of range-sepd. DFT approaches for eliminating self-interaction and static-correlation errors.
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68. 68
  Su, N. Q.; Xu, X. Insights into Direct Methods for Predictions of Ionization Potential and Electron Affinity in Density Functional Theory. J. Phys. Chem. Lett. 2019, 10, 2692, DOI: 10.1021/acs.jpclett.9b01052
  68
  Insights into Direct Methods for Predictions of Ionization Potential and Electron Affinity in Density Functional Theory
  Su, Neil Qiang; Xu, Xin
  Journal of Physical Chemistry Letters (2019), 10 (11), 2692-2699CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  Vertical ionization potential (IP) and electron affinity (EA) are fundamental mol. properties, while the Δ method and the direct method are the widely used approaches to compute these properties. The Δ method is calcd. by taking the total energy difference of the initial and final states, whose reliability is seriously affected by the issue assocd. with the imbalanced treatment of these two states. The direct method based on the derivs. involving only one single-state calcn. can yield a quasiparticle spectrum whose accuracy, on the other hand, is mostly affected by the levels of approx. mol. structure theories. Because of the aforementioned issues, EA prediction can be particularly problematic. Here we present, for the first time, an analytic theory on the derivation and realization of generalized Kohn-Sham (KS) eigenvalues of doubly hybrid (DH) functionals that depend on both occupied and unoccupied orbitals. The method based on the KS eigenvalues of neutral systems, termed the NKS method, is found to suffer little from the imbalance issue, while it is only the NKS method that can offer accurate EA prediction from a good functional approxn., such as the XYG3 type of DH functionals. Being less sensitive to the size of basis sets, the NKS method is of great significance for its application to large systems. The insights gained in this work are useful for the calcn. of properties assocd. with small energy differences while emphasizing the importance of the development of generalized functionals that rely on both occupied and unoccupied orbitals.
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69. 69
  Beste, A.; Vázquez-Mayagoitia, Á.; Ortiz, J. V. Direct ΔMBPT(2) method for ionization potentials, electron affinities, and excitation energies using fractional occupation numbers. J. Chem. Phys. 2013, 138, 074101, DOI: 10.1063/1.4790626
  69
  Direct ΔMBPT(2) method for ionization potentials, electron affinities, and excitation energies using fractional occupation numbers
  Beste, Ariana; Vazquez-Mayagoitia, Alvaro; Ortiz, J. V.
  Journal of Chemical Physics (2013), 138 (7), 074101/1-074101/13CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A direct method (D-ΔMBPT(2)) to calc. 2nd-order ionization potentials (IPs), electron affinities (EAs), and excitation energies is developed. The ΔMBPT(2) method is defined as the correlated extension of the ΔHF method. Energy differences are obtained by integrating the energy deriv. with respect to occupation nos. over the appropriate parameter range. This is made possible by writing the 2nd-order energy as a function of the occupation nos. Relaxation effects are fully included at the SCF level. This is in contrast to linear response theory, which makes the D-ΔMBPT(2) applicable not only to single excited but also higher excited states. We show the relationship of the D-ΔMBPT(2) method for IPs and EAs to a 2nd-order approxn. of the effective Fock-space coupled-cluster Hamiltonian and a 2nd-order electron propagator method. We also discuss the connection between the D-ΔMBPT(2) method for excitation energies and the CIS-MP2 method. Finally, as a proof of principle, we apply our method to calc. ionization potentials and excitation energies of some small mols. For IPs, the ΔMBPT(2) results compare well to the 2nd-order soln. of the Dyson equation. For excitation energies, the deviation from equation of motion coupled cluster singles and doubles increases when correlation becomes more important. When using the numerical integration technique, we encounter difficulties that prevented us from reaching the ΔMBPT(2) values. Most importantly, relaxation beyond the Hartree-Fock level is significant and needs to be included in future research. (c) 2013 American Institute of Physics.
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70. 70
  Gu, Y.; Xu, X. Extended Koopmans’ theorem in the adiabatic connection formalism: Applied to doubly hybrid density functionals. J. Chem. Phys. 2020, 153, 044109, DOI: 10.1063/5.0010743
  70
  Extended Koopmans' theorem in the adiabatic connection formalism: Applied to doubly hybrid density functionals
  Gu, Yonghao; Xu, Xin
  Journal of Chemical Physics (2020), 153 (4), 044109CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A rigorous framework that combines the extended Koopmans' theorem (EKT) with the adiabatic connection (AC) formalism of d. functional theory is developed here, namely, EKT-AC, to calc. the vertical ionization potentials (IPs) of mol. systems. When applied to the doubly hybrid d. functional approxns. (DH-DFAs), the EKT-DH approach is established for the B2PLYP-type DHs with one-parameter and two-parameters, as well as the XYG3-type DHs. Based on EKT-DH, an approxn. of the KT type is introduced, leading to the KT-DH approach. The IP-condition that the calcd. vertical IPs with EKT-DH or KT-DH are to reproduce the exptl. IPs closely is applied to investigate the commonly used DH-DFAs for such a purpose and is utilized as a principle for DH-DFA developments. Considering the systematic improvements, as well as its numeric stability, we recommend the KT-B2GPPLYP approach as a pragmatic way for vertical IP calcns. (c) 2020 American Institute of Physics.
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71. 71
  Grimme, S.; Neese, F. Double-hybrid density functional theory for excited electronic states of molecules. J. Chem. Phys. 2007, 127, 154116, DOI: 10.1063/1.2772854
  71
  Double-hybrid density functional theory for excited electronic states of molecules
  Grimme, Stefan; Neese, Frank
  Journal of Chemical Physics (2007), 127 (15), 154116/1-154116/18CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Double-hybrid d. functionals are based on a mixing of std. generalized gradient approxns. (GGAs) for exchange and correlation with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional (dubbed B2PLYP) contains only two empirical parameters that describe the mixt. of HF and GGA exchange (ax) and of the PT2 and GGA correlation (ac), resp. Extensive testing has recently demonstrated the outstanding accuracy of this approach for various ground state problems in general chem. applications. The method is extended here without any further empirical adjustments to electronically excited states in the framework of time-dependent d. functional theory (TD-DFT) or the closely related Tamm-Dancoff approxn. (TDA-DFT). In complete analogy to the ground state treatment, a scaled second-order perturbation correction to CI with singles (CIS(D)) wave functions developed some years ago by Head-Gordon et al. is computed on the basis of d. functional data and added to the TD(A)-DFT/GGA excitation energy. The method is implemented by applying the resoln. of the identity approxn. and the efficiency of the code is discussed. Extensive tests for a wide variety of mols. and excited states (of singlet, triplet, and doublet multiplicities) including electronic spectra are presented. In general, rather accurate excitation energies (deviations from ref. data typically <0.2 eV) are obtained that are mostly better than those from std. functionals. Still, systematic errors are obtained for Rydberg (too low on av. by about 0.3 eV) and charge-transfer transitions but due to the relatively large ax parameter (0.53), B2PLYP outperforms most other functionals in this respect. Compared to conventional HF-based CIS(D), the method is more robust in electronically complex situations due to the implicit account of static correlation effects by the GGA parts. The (D) correction often works in the right direction and compensates for the overestimation of the transition energy at the TD level due to the elevated fraction of HF exchange in the hybrid GGA part. Finally, the limitations of the method are discussed for challenging systems such as transition metal complexes, cyanine dyes, and multireference cases.
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72. 72
  Hirata, S.; Head-Gordon, M. Time-dependent density functional theory within the Tamm–Dancoff approximation. Chem. Phys. Lett. 1999, 314, 291, DOI: 10.1016/S0009-2614(99)01149-5
  72
  Time-dependent density functional theory within the Tamm-Dancoff approximation
  Hirata, S.; Head-Gordon, M.
  Chemical Physics Letters (1999), 314 (3,4), 291-299CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)
  A computationally simple method for mol. excited states, namely, the Tamm-Dancoff approxn. to time-dependent d. functional theory, is proposed and implemented. This method yields excitation energies for several closed- and open-shell mols. that are essentially of the same quality as those obtained from time-dependent d. functional theory itself, when the same exchange-correlation functional is used.
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73. 73
  Foresman, J. B.; Head-Gordon, M.; Pople, J. A.; Frisch, M. J. Toward a systematic molecular orbital theory for excited states. J. Phys. Chem. 1992, 96, 135, DOI: 10.1021/j100180a030
  73
  Toward a systematic molecular orbital theory for excited states
  Foresman, James B.; Head-Gordon, Martin; Pople, John A.; Frisch, Michael J.
  Journal of Physical Chemistry (1992), 96 (1), 135-49CODEN: JPCHAX; ISSN:0022-3654.
  The methodol. and computational considerations necessary for the detn. of the ab initio energy, wave function, and gradient of a mol. in an electronically excited state using MO theory are discussed. A fundamental level of theory is reexamd. which was employed several years ago for the interpretation of the electronic spectra of simple org. mols.: CI (CI) among all singly substituted determinants using a Hartree-Fock ref. state. Several new enhancements to this general theory are given. First, it is shown how the "CI-singles" wave function can be used to compute efficiently the analytic first deriv. of the energy in order to obtain accurate properties and optimized geometries for a wide range of mols. in their excited states. Secondly, a computer program is described which allows these computations to be done in a "direct" fashion, with no disk storage required for the two-electron repulsion integrals. This allows investigations of systems with large nos. of atoms (or large nos. of basis functions). Thirdly it is shown how the CI-singles approxn. can be cor. via second-order Moeller-Plesset perturbation theory to produce a level of theory for excited states which further includes some effects of electronic correlation. The relative success of the model as a function of basis set indicates that a judicious choice of basis set is needed in order to evaluate its performance adequately. Application of the method to the excited states of formaldehyde, ethylene, pyridine, and porphin demonstrates the utility of CI-singles theory.
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74. 74
  Head-Gordon, M.; Rico, R. J.; Oumi, M.; Lee, T. J. A doubles correction to electronic excited states from configuration interaction in the space of single substitutions. Chem. Phys. Lett. 1994, 219, 21, DOI: 10.1016/0009-2614(94)00070-0
  74
  A doubles correction to electronic excited states from configuration interaction in the space of single substitutions
  Head-Gordon, Martin; Rico, Rudolph J.; Oumi, Manabu; Lee, Timothy J.
  Chemical Physics Letters (1994), 219 (1-2), 21-9CODEN: CHPLBC; ISSN:0009-2614.
  A perturbative correction to the method of CI with single substitutions (CIS) is presented. This CIS(D) correction approx. introduces the effect of double substitutions which are absent in CIS excited states. CIS(D) is a second-order perturbation expansion of the coupled-cluster excited state method, restricted to single and double substitutions, in a series in which CIS is zeroth order, and the first-order correction vanishes. CIS(D) excitation energies are size consistent and the calculational complexity scales with the fifth power of mol. size, akin to second-order Moeller-Plesset theory for the ground state. Calcns. on singlet excited states of ethylene,

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Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional LevelClick to copy article linkArticle link copied!

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Abstract

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1. Introduction

2. Theoretical Overview

2.1. Double-Hybrid Density Functional Theory for Excitations

2.2. VIP and VEA Calculations for CIS(D)

2.3. VIP and VEA Calculations for ADC(2)

3. Computational Details

3.1. Calculation of the Numerical Results

3.2. The Benchmark Sets

4. Results and Discussion

4.1. The Acceptor Test Set

Figure 1

Figure 2

4.2. The Bartlett/Ortiz Test Set

Figure 3

4.3. Nucleobases

Figure 4

Figure 5

Figure 6

4.4. Overall Performance

5. Conclusions

Supporting Information

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Vertical Ionization Potentials and Electron Affinities at the Double-Hybrid Density Functional Level
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