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Quantum Electronic StructureOctober 21, 2023

Role of Spin Polarization and Dynamic Correlation in Singlet–Triplet Gap Inversion of Heptazine Derivatives
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Daria Drwal
Daria Drwal
Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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Mikulas Matousek
Mikulas Matousek
J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
Faculty of Mathematics and Physics, Charles University, 12116 Prague, Czech Republic
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Pavlo Golub
Pavlo Golub
J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
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Aleksandra Tucholska
Aleksandra Tucholska
Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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https://orcid.org/0000-0003-2691-5463
Michał Hapka
Michał Hapka
Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
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https://orcid.org/0000-0001-7423-3198
Jiri Brabec
Jiri Brabec
J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
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Libor Veis*
Libor Veis
J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
*Email: [email protected]
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https://orcid.org/0000-0002-4229-6335
Katarzyna Pernal*
Katarzyna Pernal
Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
*Email: [email protected]
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https://orcid.org/0000-0003-1261-9065

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Journal of Chemical Theory and Computation

Cite this: J. Chem. Theory Comput. 2023, 19, 21, 7606–7616

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https://doi.org/10.1021/acs.jctc.3c00781

Published October 21, 2023

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Abstract

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The new generation of proposed light-emitting molecules for organic light-emitting diodes (OLEDs) has raised considerable research interest due to its exceptional feature─a negative singlet–triplet (ST) gap violating Hund’s multiplicity rule in the excited S₁ and T₁ states. We investigate the role of spin polarization in the mechanism of ST gap inversion. Spin polarization is associated with doubly excited determinants of certain types, whose presence in the wave function expansion favors the energy of the singlet state more than that of the triplet. Using a perturbation theory-based model for spin polarization, we propose a simple descriptor for prescreening of candidate molecules with negative ST gaps and prove its usefulness for heptazine-type molecules. Numerical results show that the quantitative effect of spin polarization decreases linearly with the increasing highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO–LUMO) exchange integral. Comparison of single- and multireference coupled-cluster predictions of ST gaps shows that the former methods provide good accuracy by correctly balancing the effects of doubly excited determinants and dynamic correlation. We also show that accurate ST gaps may be obtained using a complete active space model supplemented with dynamic correlation from multireference adiabatic connection theory.

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Subjects

Introduction

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Detecting candidates for organic light-emitting diodes (OLEDs) through the screening of potential chromophores remains a challenge for quantum chemistry methods. OLED molecules may rely on different light-emitting mechanisms, ranging from pure fluorescence or phosphorescence (first- and second-generation emitters) to more complex processes aimed at harvesting nonfluorescent triplet excitons (third and fourth generations). (1,2) Typically, organic molecules obey Hund’s multiplicity rule (3) and the triplet state T₁ is lower than the first excited singlet state S₁. Hence, only a minor part of the excitons is available for photon emission through the radiative recombination of singlets. This restricts the internal quantum efficiency (IQE) to 25% when the distribution of excitons between S₁ and T₁ states is most favorable. (4) For molecules characterized by small singlet–triplet gaps, it is possible to thermally induce reverse intersystem crossing (RISC), i.e., the transition from lower-lying T₁ (dark state) to higher S₁ (bright state). This process, known as thermally activated delayed fluorescence (TADF), results in higher-rate fluorescent emission from the singlet state. (5−9)

Recent attention has been focused on systems with inverted singlet–triplet gap (INVEST) molecules. In INVEST emitters, the S₁ state lies below T₁, so that the relaxation from T₁ takes place with no need for thermal induction and 100% IQE of luminescence could, in principle, be achieved. (10−13) It is worth mentioning that aromatic chromophores with negative S₁–T₁ energy difference (ST gap) are of interest in another area of active research, namely, in water-splitting photocatalysis. It has been shown that derivatives of heptazine may act as efficient photocatalysts. Thanks to the negative ST energy gap, the S₁ state is exceptionally long-lived, as it does not suffer from quenching through intersystem crossing (ISC) to T₁. (14)

The first calculations proving the possibility of ST gap inversion were carried out independently in 2019 by de Silva for cycl[3.3.3]azine (10) and Sobolewski, Domcke, and co-workers for heptazine. (15) Ref (15) also presented the first indirect experimental proof for the gap inversion and indicated that this phenomenon could explain the high efficiency of OLEDs observed already in 2013 (16) and 2014 (17,18) by Adachi and co-workers. A subsequent theoretical study by Sobolewski and Domcke (11) confirmed this hypothesis. The works of Sancho-Garcia and co-workers (19,20) demonstrated the ST gap inversion across N- and B-doped triangulenes of different sizes. In 2022, Aizawa and co-workers (21) proposed a prescreening approach for INVEST candidates. Based on the elimination process, two heptazine analogues were chosen for further experimental evaluation, which confirmed the gap inversion.

The magnitude of the S₁–T₁ energy gap is directly related to the exchange integral involving the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). (22−24) A vanishing overlap between frontier orbitals is a prerequisite for ST inversion but is not sufficient. Several studies have demonstrated that accounting for electron correlation via the inclusion of double excitations is essential to stabilize the singlet state with respect to triplet and obtain negative ST gaps of chromophore molecules. (10,12,24) Results from single-reference response methods suggest that double excitations contribute at a relatively low level to the S₁ state, estimated at ca. 10% by de Silva. (10) Time-dependent density functional theory (TD-DFT) approaches are incapable of capturing double excitations and do not predict negative gaps, as corroborated by a range of investigations. (10,15,19,20,,26)

In pursuit of efficient strategies in designing novel INVEST materials, Pollice et al. (23) investigated all possible permutations of cyclazine and heptazine derivatives with C–H replaced by a set of electron-donating and electron-withdrawing substituents and described them at the EOM-CCSD and TD-DFT levels of theory. Aizawa and co-workers (21) expanded on this work by introducing 186 new substituents and finding almost 35,000 potential candidates for INVEST molecules. Their further TD-DFT screening resulted in a significant limitation of this set. Still, TD-DFT-based screening is inherently limited, as the method cannot distinguish INVEST molecules from cases in which the ST gap is small but not negative. Having studied the relationship between the structure and properties of selected INVEST molecules, Olivier and co-workers (13) formulated a set of design rules in which the C_2v point group of the triangulene core was identified as a prerequisite for the gap inversion.

Advances in designing novel INVEST systems are hindered by two factors: a limited understanding of the mechanism behind gap reversal at the electronic structure level and the lack of efficient descriptors that could account for the main effects lowering S₁ below T₁. In one of the first theoretical works devoted to the violation of Hund’s rule in closed-shell molecules, Kollmar and Staemmler (22) introduced a concept of dynamic spin polarization (sp), which associates the ST gap inversion to the energetic effect exerted by a small subset of doubly excited configurations involving frontier orbitals. Numerical investigations on conjugated hydrocarbons carried out by Koseki et al. (27) showed that spin polarization may indeed lead to gap inversion in some molecules. Spin polarization has been also indirectly identified as a key effect in ST gap inversion of the heptazine molecule, without, however, providing its quantitative measure. (15)

The main objective of our study is to elucidate the role of both spin polarization and dynamic correlation energy in the mechanism of ST gap inversion in heptazine-based molecules. Based on the spin polarization model, we propose a simple descriptor for the prescreening of molecules with a negative ST gap. We also demonstrate the efficacy of selected multireference methods in accurately predicting the magnitudes of ST gaps in organic INVEST emitters. We compare multireference adiabatic connection methods (28−34) and the second-order n-electron valence state perturbation theory (NEVPT2) (35) against Mukherjee’s multireference coupled-cluster with noniterative triple excitations [Mk-MRCCSD(T)]. (36)

Computational Details

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Our analysis is focused on six heptazine-based systems (see Figure 1). Geometries were optimized at the MP2 level using the Molpro (37) program. All results were obtained using the def2-TZVP (38) basis set.

Figure 1. Structures of the studied molecules. The color codes are as follows: N (blue), C (brown), and H (white).

Complete active space self-consistent field (CASSCF) and NEVPT2 results were obtained with the Molpro (37) program. We used the same software for restricted Hartree–Fock (HF), CASSCF, and Kohn–Sham DFT calculations to obtain electron integrals and one- and two-electron-reduced density matrices needed for spin polarization models and adiabatic connection, AC0 and ACn, calculations. The latter were performed with the GammCor program. (39) Multireference coupled-cluster Mk-MRCCSD(T) (36) energies for the S₁ and T₁ states computed using the CASSCF(2,2) natural orbitals were obtained with the NWChem program (40) and set as benchmark. CC2 results in def2-TZVP were taken from ref (24), while EOM-CCSD ST gaps were calculated with the Orca code. (41)

The ground state geometry of each molecule was used for both the S₁ and T₁ states. Except for system 4, calculations were performed by employing the C_2v point group symmetry, which allowed for state-specific CASSCF calculations for the S₁ and T₁ states. System 4 is in a lower, C_s, point group symmetry, so that a two-state state-average CASSCF calculation is required to access the S₁ state.

Additional calculations were performed on an extended test set including heptazine derivatives obtained by substituting C–H groups with N atoms in all possible ways. Geometries of all molecules from the extended set were optimized at the B3LYP/cc-pVDZ level with no symmetry constraints using Orca code. (41)

Inverting S₁–T₁ Energy Gaps by Including Dynamic Spin Polarization

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Throughout the text, ΔE_ST will denote the singlet–triplet energy gap defined as a difference of T₁ energy subtracted from the energy of the S₁ state, namely

Δ E_{ST} = E (S_{1}) - E (T_{1})

(1)

Gap inversion would be equivalent to obtaining a negatively valued ΔE_ST energy difference.

In the first approximation, the S₁ and T₁ states of the considered systems can be described by singly excited determinants, where one electron from the HOMO (H) orbital is excited to the orbital LUMO (L)

Ψ_{S}^{0} = \frac{1}{\sqrt{2}} (| \bar{H} L | - | H \bar{L} |)

(2)

Ψ_{T}^{0} = \frac{1}{\sqrt{2}} (| \bar{H} L | + | H \bar{L} |)

(3)

A notation |H̅L| stands for an N-electron Slater determinant comprising N/2 – 1 doubly occupied orbitals and H, L singly occupied orbitals. H̅, L̅ and H, L indicate orbitals with α and β spin components, respectively. In addition, we use {pq} and {pqrs} symbols to indicate which orbitals in open-shell determinants are singly occupied without explicitly specifying their spin components. For example, both determinants | H̅L| and |H L̅| would be denoted as {HL}.

As it is well-known, the ST energy gap corresponding to a wave function including only {HL} singly excited determinants (eqs 2 and 3)

Δ E_{ST}^{0} = ⟨ Ψ_{S}^{0} | \hat{H} | Ψ_{S}^{0} ⟩ - ⟨ Ψ_{T}^{0} | \hat{H} | Ψ_{T}^{0} ⟩ = 2 ⟨ HL | LH ⟩ \geq 0

(4)

is determined by the magnitude of the HOMO–LUMO (HL) exchange integral (throughout the text, two-electron integrals are written in the ⟨12|12⟩ convention) and is non-negative. eq 4 is a manifestation of Hund’s rule satisfied by wave functions Ψ_S⁰ and Ψ_T⁰.

In Hund’s picture, the ST gap is determined by the coupling of H and L electrons in the target spin state of the total wave function. This approach ignores the interaction of the unpaired α and β electrons with the core electrons. However, Kollmar and Staemmler (22) showed that including these interactions is not merely a quantitative refinement, but may explain the ST gap inversion in some systems. Their approach is based on extending the first-order wave function with double excited determinants {iaHL}, where core orbitals i relax by excitations to an arbitrary virtual orbital a. Including such determinants is referred to as “dynamic” spin polarization to distinguish from the conventional “static” spin polarization. While static spin polarization leads to unequal spin components of electron density, dynamic spin polarization does not lead to nonzero spin density. Our goal is to quantify the effect of dynamic spin polarization for heptazine-type molecules and investigate if this mechanism is responsible for changing the sign of ΔE_ST⁰ gaps. We also investigate if the sp-based gap inversion model of Kollmar and Staemmler can be employed for prescreening molecules likely to act as INVEST systems.

We begin by following ref (22) and construct singlet functions by applying i → a excitations to determinants in the Ψ_S⁰ function, which leads to two functions

Ψ_{S}^{1} = \frac{1}{\sqrt{12}} (2 | \bar{i} \bar{a} HL | + 2 | ia \bar{H} \bar{L} | - | \bar{i} a \bar{H} L | - | \bar{i} aH \bar{L} | - | i \bar{a} \bar{H} L | - | i \bar{a} H \bar{L} |)

(5)

Ψ_{S}^{1'} = \frac{1}{2} (| i \bar{a} H \bar{L} | - | i \bar{a} \bar{H} L | - | \bar{i} aH \bar{L} | + | \bar{i} a \bar{H} L |)

(6)

Analogously, three triplet M_S = 0 functions can be generated from Ψ_T⁰ by considering i → a excitations and they read

Ψ_{T}^{1} = - \frac{1}{2} (| \bar{i} a \bar{H} L | - | \bar{i} aH \bar{L} | + | i \bar{a} \bar{H} L | - | i \bar{a} H \bar{L} |)

(7)

Ψ_{T}^{2} = - \frac{1}{\sqrt{2}} (| \bar{i} \bar{a} HL | - | ia \bar{H} \bar{L} |)

(8)

Ψ_{T}^{1'} = - \frac{1}{2} (| \bar{i} a \bar{H} L | + | \bar{i} aH \bar{L} | - | i \bar{a} \bar{H} L | - | i \bar{a} H \bar{L} |)

(9)

Recall that from the Epstein–Nesbet perturbation theory (PT), the drop in the unperturbed energy, E⁰ = ⟨Ψ⁰|Ĥ|Ψ⁰⟩, that results from including in the wave function a configuration Ψ′ and corresponds to the second-order correction, is given by |⟨Ψ⁰|Ĥ|Ψ′⟩|²/(E⁰ – E′), where E′ = ⟨Ψ′|Ĥ|Ψ′⟩. After evaluating PT terms for functions given in eqs 5–9 (see Supporting Information for explicit expressions of Hamiltonian elements and energy differences in terms of two-electron integrals) and subtracting triplet contributions from the singlet ones, the following spin-free expression is obtained

Δ E_{i, a}^{sp} = \frac{3}{2} \frac{{(⟨ iH | Ha ⟩ - ⟨ iL | La ⟩)}^{2}}{E_{S}^{0} - E_{S}^{1}} - \frac{1}{2} \frac{{(⟨ iH | Ha ⟩ - ⟨ iL | La ⟩)}^{2}}{E_{T}^{0} - E_{T}^{1}} - \frac{{(⟨ iH | Ha ⟩ + ⟨ iL | La ⟩)}^{2}}{E_{T}^{0} - E_{T}^{2}}

(10)

in agreement with ref (22) (notice that contributions to ΔE_i,a^sp from states Ψ_S^1′ and Ψ_T^1′, not considered in ref (22), cancel each other). ΔE_i,a^sp represents a contribution to the ST gap from spin polarization of two electrons occupying orbital i by allowing their excitation to orbital a. To ease its interpretation, the expression in eq 10 can be approximated by assuming a common denominator given as Hartree–Fock orbital energy difference ε_i – ε_a for all three terms, leading to

Δ E_{i, a}^{sp} \approx 4 \frac{⟨ iH | Ha ⟩ ⟨ iL | La ⟩}{ε_{a} - ε_{i}}

(11)

It is now clear that spin polarization energy, ΔE_i,a^sp, pertaining to a pair of orbitals (i, a), where i < H and a > L, stabilizes the singlet state with respect to triplet if orbitals i and a overlap significantly with both H and L orbitals and, taking into account that ϵ_a – ϵ_i > 0, exchange integrals ⟨iH|Ha⟩ and ⟨iL|La⟩ are of the opposite sign. The magnitude of the ΔE_i,a^sp energy is dependent on the closeness of the i and a orbital energy levels.

For the studied systems, the (H – 1, H – 2) and (L + 1, L + 2) pairs of orbitals are degenerate, so the simplest model for the ST gap accounting for major spin polarization would include two pairs of orbitals, and the ST energy gap expression of such a “12” model would read

Δ E_{ST}^{s p_{12}} = Δ E_{ST}^{0} + Δ E_{H - 1, L + 1}^{sp} + Δ E_{H - 2, L + 2}^{sp}

(12)

For system 4, the model also included the contributions from the other two combinations of orbitals ΔE_H–1,L+2^sp + ΔE_H–2,L+1^sp, which are negligible in the other systems due to point group symmetry. To fully account for spin polarization, considered pairs of orbitals (i < H, a > L) must fulfill conditions leading to ST gap reversal, formulated below eq 11: (i) orbitals within each pair should strongly overlap with H and L orbitals, (ii) the exchange integrals ⟨iH|Ha⟩ and ⟨iL|La⟩ are of the opposite signs. For heptazine derivatives, the π orbitals satisfy these requirements and the all-π sp-inclusive ST energy gap reads

Δ E_{ST}^{s p_{π}} = Δ E_{ST}^{0} + \sum_{i < H} \sum_{a > L} Δ E_{i, a}^{sp}

(13)

(orbitals i and a are of the π-type).

We consider two sets of orbitals in further analysis. The first set is given by canonical HF orbitals. The second one corresponds to a ground state CASSCF(14,14) wave function with the active space containing all the π electrons and orbitals (2p_z orbitals on carbon and nitrogen atoms plus one virtual orbital of the “double-shell” 3p_z character (24)). The CASSCF(14,14) natural occupation numbers for systems 2 and 4, used as illustrative cases, are given in Table 1. Notice that orbitals H and L pertain to (N/2)th and (N/2 + 1)th orbitals, respectively, of occupation numbers close to 0.5. These orbitals are depicted in Figure 2 (see also Figures 1–12 in Supporting Information) together with four other most strongly correlated, i.e., of the occupancies deviating most from 0 and 1, orbitals.

Figure 2. Natural orbitals of system 2 corresponding to state-averaged CASSCF(14,14) calculations with one singlet and one triplet states.

Table 1. Natural Occupation Numbers for Systems 2 and 4 from State-Averaged CASSCF(14,14) Calculations, for System 2 Corresponding to the Natural Orbitals Presented in Figure 2

	sys 2		sys 4
orbital	S₁	T₁	S₁	T₁
H – 6	0.995	0.993	0.990	0.989
H – 5	0.969	0.970	0.971	0.971
H – 4	0.967	0.968	0.970	0.971
H – 3	0.967	0.968	0.969	0.971
H – 2	0.928	0.933	0.936	0.939
H – 1	0.929	0.933	0.933	0.936
H	0.513	0.504	0.639	0.509
L	0.485	0.492	0.359	0.486
L + 1	0.074	0.073	0.070	0.071
L + 2	0.074	0.073	0.069	0.070
L + 3	0.036	0.035	0.033	0.031
L + 4	0.036	0.035	0.032	0.031
L + 5	0.026	0.023	0.024	0.022
L + 6	0.001	0.001	0.004	0.004
CI Coefficients
{HL}	68.6%	69.3%	67.3%	71.3%
{(H – p) (L + p) H L}_p=1,2	8.2%	7.8%	7.2%	0.3%
{i a H L}_i,a∈π	15.0%	14.6%	13.4%	5.6%

The results for ST gaps obtained without spin polarization, ΔE_ST⁰, with partial and full spin polarization, ΔE_ST^sp₁₂ and ΔE_ST^sp_π models, respectively, are presented in Table 2. First, it can be seen that ΔE_ST⁰ gaps are positive and small, which indicates that for all considered systems the H and L orbitals overlap marginally at both the HF and CASSCF(14,14) levels of theory. Accounting for dynamic spin polarization from only two pairs of orbitals (H – 1, L + 1) and (H – 2, L + 2) (see eq 12) significantly reduces ST gaps. Using canonical HF orbitals leads to negative ST gaps for systems 1 and 2, while with CASSCF(14,14) natural orbitals, all ST gaps turn negative. Considering all (i < H, a > L) pairs of π orbitals (eq 13) removes another 0.2–0.3 eV from the ST gap, regardless of the employed orbitals. We conclude that the PT-based model for dynamic spin polarization substantially lowers the S₁ state energy with respect to T₁, possibly leading to a sign reversal of the ST gap. The combined sp effect of two pairs of orbitals, (H – 1, L + 1) and (H – 2, L + 2), accounts for more than half of the ST gap reduction.

Table 2. S₁–T₁ Energy Gaps Obtained without Spin Polarization, ΔE_ST⁰, with Spin Polarization Computed from Two Pairs of π Orbitals, ΔE_ST^sp₁₂, from All Occupied-Virtual Pairs of π Orbitals, ΔE_ST^sp_π, and from CI with {HL}, {H – 1 L + 1 H L}, and {H – 2 L + 2 H L} Determinants, ΔE_ST^CI₁₂^a

orbitals	ST gap	1	2	3	4	5	6
HF	ΔE_ST⁰	0.25	0.25	0.49	0.67	0.68	0.61
	ΔE_ST^sp₁₂	–0.16	–0.18	0.09	0.29	0.33	0.22
	ΔE_ST^sp_π	–0.37	–0.45	–0.11	0.09	0.07	0.00
	ΔE_ST^CI₁₂	–0.21	–0.25	0.10	0.27	0.10	0.08
CASSCF	ΔE_ST⁰	0.19	0.19	0.25	0.32	0.25	0.28
	ΔE_ST^sp₁₂	–0.33	–0.40	–0.28	–0.19	–0.31	–0.27
	ΔE_ST^sp_π	–0.60	–0.73	–0.54	–0.46	–0.61	–0.55
	ΔE_ST^CI₁₂	–0.29	–0.36	–0.25	–0.14	–0.28	–0.24

^{^a}

HF canonical and CASSCF(14,14) orbitals were used. The latter followed state-averaged CASSCF calculations with one singlet state and one triplet state. All values are in eV.

Spin polarization in the wave function picture is manifested by the presence of doubly excited determinants. To check if the simple PT-based model for sp yields qualitatively correct predictions, we have performed CI calculations constructing the S₁ and T₁ wave functions from {HL}, {H – 1 L + 1 H L}, and {H – 2 L + 2 H L} singly excited and doubly excited determinants, employing either HF or CASSCF(14,14) orbitals. The CI results, denoted as ΔE_ST^CI₁₂ in Table 2, are in close agreement with those of the ΔE_ST^sp₁₂ model. This suggests that the PT-based approach can be used as a cost-saving alternative to CI calculations in the prescreening for molecules with inverted gaps.

ST gaps obtained from ΔE_ST^sp₁₂ and ΔE_ST^sp_π should be considered as basic approximations due to the fact that there are only {HL} and {iaHL} determinants in the wave functions. Thus, the model gaps cannot be quantitatively correct. A comparison with Mk-MRCCSD(T) results, shown in the last column of Table 3, reveals that ST gaps predicted by sp₁₂ and sp_π models employed with HF orbitals (cf. Table 2) deviate on average by 0.26 and 0.15 eV from the Mk-MRCCSD(T) benchmarks, respectively. With CASSCF(14,14) orbitals, the respective mean absolute errors amount to 0.14 and 0.43 eV. Such inaccuracies result from the lack of dynamic electron correlation in the considered models. This problem is addressed in the next section.

Table 3. S₁–T₁ Energy Gaps in eV Obtained from CASSCF, AC₀, AC_n, and NEVPT2 Methods for Small, Intermediate, and All-π Models for Active Spaces Compared against CC2 and Mk-MRCCSD(T) Values

system	active space	CAS	AC₀	AC_n	NEVPT2	CC2 (24)	Mk-MRCCSD(T)
1	(2,2)	1.76	0.70	0.00	–0.37	–0.13	–0.18
	(6,6)	–0.18	0.16	0.01	–0.08
	(14,14)	–0.47	–0.10	–0.21	0.07
2	(2,2)	0.31	–0.78	–0.28	–1.04	–0.24	–0.28
	(6,6)	–0.31	–0.02	–0.14	1.01
	(14,14)	–0.62	–0.21	–0.34	–0.06
3	(2,2)	0.44	–0.28	0.02	–0.59	–0.11	–0.15
	(6,6)	–0.17	0.08	–0.01	–0.04
	(14,14)	–0.45	–0.05	–0.19	0.09
4	(2,2)	0.79	–0.45	–0.22	–0.92	–0.08	–0.04
	(6,6)	0.18	–0.32	–0.01	–0.59
	(14,14)	–0.31	–0.04	–0.12	–0.07^a
5	(2,2)	0.70	–0.64	–0.06	–0.94	–0.14	–0.15
	(6,6)	–0.12	0.04	–0.33	–0.25
	(14,14)	–0.50	–0.06	–0.20	0.09
6	(2,2)	0.72	–0.67	–0.06	–0.98	–0.12	–0.14
	(6,6)	–0.22	0.08	–0.08	0.05
	(14,14)	–0.50	–0.01	–0.15	0.11

^{^a}

Due to problems with the convergence of NEVPT2, the active space has been reduced to (14,13).

To further explore if the sp effect is decisive in inverting the ST gap and if the model presented in eq 13 would be useful in screening for INVEST candidates, we have applied it to an extended test set of molecules including heptazine-derived systems obtained by the substitution of C–H with N in all possible ways, similar as in ref (23). The ST gaps were computed using eqs 10 and 13. Initial tests on systems 1–6 have shown (see Table 2) that CASSCF(14,14) orbitals satisfy conditions required to invert the ST gaps via the sp mechanism to a greater extent than HF orbitals, and unlike the latter, they have led to obtaining negative gaps for all molecules. This suggests that correlated orbitals are a better choice for INVEST screening. Guided by this finding, we have used KS-DFT orbitals from ground state BLYP (42−44) calculations for tests on our extended set of molecules. In Figure 3, we present ST energy gaps obtained without spin polarization (see eq 4) and with spin polarization fully accounted for (eq 13) compared with the EOM-CCSD values. Evidently, employing only the HOMO–LUMO exchange integral for INVEST prescreening does a poor job as hardly any correlation between ΔE_ST⁰ and EOM-CCSD ST gap values can be seen. Shifting the ΔE_ST⁰ values by −0.30 eV and keeping only molecules with resulting negative gaps would leave us with a too large set: it would include not only molecules with EOM-CCSD-predicted negative gaps but also most of those with positive gaps (see the left panel in Figure 3). Thus, a criterion based on ΔE_ST⁰ values is not sufficiently selective in screening for INVEST systems. A satisfactory correlation is obtained by employing the full sp_π model with KS-DFT orbitals and shifting the ΔE_ST^sp_π energies by +0.2 eV. This value is recommended in future INVEST prescreening calculations, as it results in a good overlap between the subsets of molecules with positive and negative gaps obtained from the sp model and EOM-CCSD, as shown in Figure 3, right panel. Notice that the correlation is worse with HF orbitals (see the right panel of Figure 13 in Supporting Information).

Figure 3. Left panel: ST energy gaps without spin polarization (eq 4). Right panel: ST energy gaps with spin polarization from all occupied-virtual π orbital pairs (eqs 13 and 10). Results obtained with BLYP ground state orbitals vs EOM-CCSD values for the extended test set of molecules.

Another observation following from calculations on the extended set of molecules is that the magnitude of the sp effect decreases linearly with the increasing HL exchange interaction (see Figure 4). Therefore, larger HL integrals correspond to lower spin polarization, both effects being detrimental to obtaining negative ST gaps. Apparently, sp for the considered isoelectronic molecules is as sensitive as HL exchange integrals to the composition and distribution of carbon and nitrogen atoms in heptazine derivatives.

Figure 4. Left panel: Contributions from spin polarization to ST energy gaps (second term on the right-hand side of eq 13) vs ST energy gaps without spin polarization (eq 4). Right panel: Molecules corresponding to the lowest and highest HL exchange interaction. Results obtained with BLYP ground state orbitals.

In ref (13), low HL exchange interaction has been associated with high symmetry point groups D/C_3h, C_3v, C_2v. In particular, the existence of the σ_v plane was identified as critical in minimizing the HL overlap. Since, as we have shown, minimization of the latter is accompanied by maximization of the sp effect, in general, it seems to be a good strategy to account for symmetry while designing INVEST molecules. However, symmetry cannot be used as the only criterion in high-throughput screening. Recall that system 4 does not possess σ_v plane as a symmetry element (Figure 1), but the corresponding ST gap is negative. In contrast, the molecule with the largest HL exchange integral and most positive ΔE_ST^sp_π gap (Figure 4) belongs to the C_2v point group.

Results obtained on the extended set show that a simple spin polarization model considered in this section, used with KS-DFT orbitals, can serve as a computationally inexpensive predictor of INVEST molecules. Notice that for systems 1–6 a common-denominator approximation adopted in eq 11 yields energy gaps in good agreement with those obtained if sp from all π orbital pairs is included as in eq 10 (see Table 1 in Supporting Information). Thus, further simplification of the model is achievable if eq 11 is used instead of eq 10. Compared to predictors used in ref (23), based on a double-hybrid DFT functional, the proposed model is computationally more efficient (it requires performing a ground state calculation with a semilocal functional) and above all physically meaningful, as it explicitly includes the sp effect responsible for the gap inversion.

Effect of Dynamic Correlation Energy

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CAS wave functions should effectively capture the sp effect. One expects that expanding the active space from (2,2), two electrons on H and L orbitals, via (6,6), six electrons on H, L, and two pairs of degenerate orbitals H – 1, H – 2 and L + 1, L + 2, up to (14,14), all π electrons on all π orbitals, would lead to ST energy gaps that reflect the ΔE_ST⁰ > ΔE_ST^sp₁₂ > ΔE_ST^sp_π relation observed for PT-based models, namely

Δ E_{ST}^{CASSCF (2, 2)} > Δ E_{ST}^{CASSCF (6, 6)} > Δ E_{ST}^{CASSCF (14, 14)}

(14)

Indeed, CASSCF energy gaps presented in Table 3 agree with the predicted inequality relations (eq 14) for each system (see the column denoted as CAS). Going from CAS(2,2) to CAS(6,6) lowers the gap by as much as 0.6–1.9 eV. Including all π orbitals as active, in the CASSCF(14,14) model, reduces the gaps by another 0.3–0.5 eV. The ΔE_ST^{CASSCF(14,14)} values are all negative and correspond well with the ΔE_ST^sp_π results obtained using CASSCF(14,14) orbitals (cf. Table 2). We conclude that doubly excited determinants {iaHL}, where i < H and a > L are π orbitals, are the main contributors to the wave function, after the leading singly excited {HL} determinant. In Table 1, we report sums of squares of pertinent CI coefficients for systems 2 and 4. The contribution of the aforementioned double excitations is up to 15%. This is far less than a contribution from {HL} determinants amounting to ca. 70%, but it determines the ST gap inversion. It also stresses the importance of having a small value of the HOMO–LUMO exchange integral to achieve gap inversion.

A comparison between CASSCF(14,14) and Mk-MRCCSD(T) reference values (cf. Table 3) reveals that CASSCF gaps are too negative with the mean unsigned deviation exceeding 0.3 eV (see also Figure 5). To correct CASSCF for the missing dynamic correlation energy, we use the multireference adiabatic connection (AC) approach, (32,33,45−49) which recently has been successfully applied to predicting singlet–triplet gaps of biradicals. (34) Two AC variants are employed in this work: AC0 and ACn. The first one is based on linearizing the adiabatic connection integrand. (32,49) ACn is free of such an approximation and is expected to yield more accurate predictions. (34) It is worth mentioning that the computational cost of both AC0 and ACn scales with the fifth power of the system size, AC0 being more efficient than ACn due to a smaller prefactor. AC methods rely only on 1- and 2-electron reduced density matrices (1- and 2-RDMs, respectively), which makes them computationally more efficient in treating large active spaces compared with canonical multireference perturbation theory methods. (48)

Figure 5. S₁–T₁ energy gaps for systems 1–6, panel (a). Mean unsigned deviations of the gaps with respect to Mk-MRCCSD(T) values, panel (b). CASSCF, AC0, ACn, and NEVPT2 results correspond to the (14,14) active space.

AC0 (ACn) ST gaps are computed by adding dynamic correlation correction to the CASSCF gap according to

Δ E_{ST}^{AC} = Δ E_{ST}^{CASSCF} + E^{AC} (S_{1}) - E^{AC} (T_{1})

(15)

where E^AC(S₁) and E^AC(T₁) are AC0 (ACn) adiabatic connection correlation energies computed from CASSCF 1,2-RDMs for the S₁ and T₁ states, respectively. Inspection of the AC0 and ACn energy gaps in Table 3 shows that accounting for dynamic correlation energy counteracts the spin polarization effect. While spin polarization lowers the singlet state energy more than the triplet, leading to a negatively valued ST gap, dynamic correlation shifts the S₁ energy upward relative to T₁. In the case of AC0, this effect is overestimated, leading to too small gaps. AC0 gaps computed for CASSCF(6,6) change the sign back to positive for systems 1, 3, 5, and 6. Combining AC0 with CASSCF(14,14) retains the negative sign of the gaps, but their magnitudes are underestimated compared with Mk-MRCCSD(T) values (see also Figure 5). The best accuracy is obtained if ACn is applied together with a CASSCF(14,14) model: the resulting gap values agree up to 0.04 eV with the Mk-MRCCSD(T) reference. AC correlation energy computed for CASSCF(2,2) models yields poor results. This is expected since the CASSCF(2,2) does not contain doubly excited determinants, which AC approximations cannot amend. Ideally, the CASSCF model should include all of the spin polarization, leaving only dynamic correlation energy for adiabatic connection. ACn combined with CASSCF(14,14) proves that this strategy leads to accurate predictions.

In addition to AC, in Table 3, we present the results of NEVPT2 calculations. (35) Although our previous studies show that NEVPT2 is typically as accurate as AC methods, in particular AC0, (32,45) for heptazine-based systems the performance of NEVPT2 is inferior. The NEVPT2 energy gap values do not show a systematic improvement when the CAS(n,n) model is extended. Quite contrary, the behavior is erratic and the gaps are of the wrong sign, except for systems 2 and 4, even if the CAS(14,14) model is employed (cf. Table 3). NEVPT2 gaps deviate on average by 0.2 eV from the reference values (see Figure 5).

The presented results show that two factors are equally important for the accurate prediction of ST gap inversion: accounting for a modest contribution of double excitations and proper treatment of the dynamic correlation. Apparently, single-reference methods such as CC2 or ADC(2) (10,24) are capable of predicting ST gaps as accurately as multireference approaches. The CC2 energy gaps taken from ref (24) (see Table 3 and Figure 5) stay in good agreement with the multireference CCSD(T) results deviating from the latter by only 0.03 eV. Since the contribution from double excitations in the wave function is substantial, amounting to 15% (see Table 1), single-reference CC methods may owe their good performance in gap prediction to error cancellation. Finally, we notice that the energy gaps predicted by both single- and multireference methods are quite insensitive to the basis set used (compare the results from Table 3 and Table 2 in Supporting Information).

Summary and Conclusions

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We have investigated the sources of S₁–T₁ energy gap inversion in heptazine-based molecules, focusing on the effect of dynamic spin polarization. (22) We have found that spin polarization, which is equivalent to including doubly excited determinants involving HOMO, LUMO, and any two of the other π orbitals in the wave function expansion, drives the gap inversion. Our findings are summarized in Figure 6. While ignoring spin polarization leads to positive ST gaps (green bars in Figure 6), accounting for this effect alone results in gaps that are too negative (red and blue bars in Figure 6). For a quantitative ST gap prediction, it is essential to consider both spin polarization and accurately treat dynamic correlation energy. Dynamic correlation closes the gap, exerting an effect opposite to that of sp (see pink bars in Figure 6). Comparing several multiconfigurational wave function approaches that account for dynamic correlation, we recommend AC-based methods as having the best accuracy/cost ratio. Among them, the ACn method combined with CASSCF(14,14) was able to reproduce accurate ST gaps for all studied heptazine derivatives.

Figure 6. S₁–T₁ energy gaps for systems 1–6. 0: no spin polarization (eq 4); sp_π: PT-based model accounting for spin polarization (eq 13); CASSCF: spin polarization from CASSCF(14,14); ACn: spin polarization at the CAS(14,14) level and dynamic correlation via adiabatic connection (eq 15).

In the investigated systems, the contribution of double excitations in wave functions varies from 6 to 15%. The effect of double excitations on the relative energies of the S₁ and T₁ states can be apparently captured with single-reference coupled-cluster methods. Indeed, we reported a good agreement between CC2 and multireference approaches [ACn and Mk-MRCCSD(T)] in predicting the ST gaps. The agreement may result from error cancellation, as single-reference methods do not fully account for both double-excitation and dynamic correlation effects. As we have shown, including only double excitations in wave functions results in too negative ST gaps. This effect is compensated by accounting for dynamic correlation. Improving a low-order method by increasing the level of the dynamic correlation energy, which is not accompanied by an increased inclusion of double excitations, will erroneously decrease the magnitude of the ST gap, or even change its sign to positive. The latter has been recently reported by Dreuw et al. (50)

We have proposed a simple model for selecting INVEST systems that accounts for two critical factors that favor negative gaps: vanishing HL exchange integral and spin polarization. In this approach, the ST gap is approximated via a PT-based expression involving orbital energies and exchange integrals. When KS-DFT orbitals are employed, the model is capable of efficient and accurate prescreening for INVEST candidates, as we demonstrated on a test set of ∼100 heptazine derivatives. We have found a previously unknown linear correlation between the sp contribution to the ST gap and the magnitude of the HOMO–LUMO (HL) exchange integral. It implies that the quantitative contribution to the gap from the effect of spin polarization is negligible if the HL exchange interaction is relatively large. Our future work will include further validation of the proposed spin-polarization-based model for a broader set of INVEST molecules, going beyond heptazine-based systems. Having the advantage of being low-cost to compute, the model can be used in high-throughput screening for INVEST systems. It can also be used for the prediction of ST gap inversion by machine-learning algorithms.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.3c00781.

Expressions: Hamiltonian matrix elements of doubly excited states, energy differences of doubly excited states. Tables: ST energy gaps from sp models, ST energy gaps in cc-pVDZ and cc-pVQZ basis sets, singlet- and triplet-state energies for systems 1–6, energy characteristics for all heptazine-derived systems from the extended set. Figures: CASSCF(14,14) orbitals for the S₁ and T₁ states, ST energy gaps from sp models with HF orbitals vs EOM-CCSD for an extended set of molecules. Geometries of systems 1–6 (PDF)
Geometries_xyz_extended_set (ZIP)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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Corresponding Authors
- Libor Veis - J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic; https://orcid.org/0000-0002-4229-6335; Email: [email protected]
- Katarzyna Pernal - Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland; https://orcid.org/0000-0003-1261-9065; Email: [email protected]
Authors
- Daria Drwal - Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
- Mikulas Matousek - J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic; Faculty of Mathematics and Physics, Charles University, 12116 Prague, Czech Republic
- Pavlo Golub - J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
- Aleksandra Tucholska - Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland; https://orcid.org/0000-0003-2691-5463
- Michał Hapka - Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland; https://orcid.org/0000-0001-7423-3198
- Jiri Brabec - J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, 18223 Prague 8, Czech Republic
Author Contributions
D.D. and M.M. contributed equally.
Notes
The authors declare no competing financial interest.

Acknowledgments

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This work was supported by the Czech Science Foundation (Grant No. 23-04302L); the National Science Center of Poland (Grant No. 2019/35/B/ST4/01310); Lodz University of Technology (Internal Grant FU2N─Fundusz Udoskonalania Umiejȩtności Młodych Naukowców from Excellence Initiative─Research University); the Charles University Grant Agency (Grant No. 218222); the Center for Scalable and Predictive methods for Excitation and Correlated phenomena (SPEC), which is funded by the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, the Division of Chemical Sciences, Geosciences, and Biosciences. This paper was completed while the first author was a Doctoral Candidate in the Interdisciplinary Doctoral School at the Lodz University of Technology, Poland. This work was also supported by the Ministry of Education, Youth and Sports of the Czech Republic through the e-INFRA CZ (ID:90254) and the European Centre of Excellence in Exascale Computing TREX - Targeting Real Chemical Accuracy at the Exascale. This project has received funding from the European Union’s Horizon 2020 - Research and Innovation Program under grant agreement no. 952165.

References

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This article references 50 other publications.

1
Tyan, Y.-S. Organic light-emitting-diode lighting overview. J. Photonics Energy 2011, 1, 011009, DOI: 10.1117/1.3529412
Google Scholar
There is no corresponding record for this reference.
2
Hong, G.; Gan, X.; Leonhardt, C.; Zhang, Z.; Seibert, J.; Busch, J. M.; Bräse, S. A Brief History of OLEDs─Emitter Development and Industry Milestones. Adv. Mater. 2021, 33, 2005630 DOI: 10.1002/adma.202005630
Google Scholar
2
A Brief History of OLEDs-Emitter Development and Industry Milestones
Hong, Gloria; Gan, Xuemin; Leonhardt, Celine; Zhang, Zhen; Seibert, Jasmin; Busch, Jasmin M.; Braese, Stefan
Advanced Materials (Weinheim, Germany) (2021), 33 (9), 2005630CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
Org. light-emitting diodes (OLEDs) have come a long way ever since their first introduction in 1987 at Eastman Kodak. Today, OLEDs are esp. valued in the display and lighting industry for their promising features. As one of the research fields that equally inspires and drives development in academia and industry, OLED device technol. has continuously evolved over more than 30 years. OLED devices have come forward based on three generations of emitter materials relying on fluorescence (first generation), phosphorescence (second generation), and thermally activated delayed fluorescence (third generation). Furthermore, research in academia and industry toward the fourth generation of OLEDs is in progress. Excerpts from the history of green, orange-red, and blue OLED emitter development on the side of academia and milestones achieved by key players in the industry are included in this report.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhsl2ksLo%253D&md5=c7c3fb2f400d493fb80cfd8019d5372c
3
Hund, F. Zur Deutung verwickelter Spektren, insbesondere der Elemente Scandium bis Nickel. Z. Phys. 1925, 33, 345– 371, DOI: 10.1007/BF01328319
Google Scholar
3
The interpretation of complicated spectra
Hund, F.
Zeitschrift fuer Physik (1925), 33 (), 345-71CODEN: ZEPYAA; ISSN:0044-3328.
On the basis of the suggestions of Russel and Saunders, Pauli and Heisenberg on the interaction of electrons in emitting light, the spectral terms of some elements have been correlated to definite quantum nos. which specify the arrangements of the electrons in the atoms. For Sc it is found that the first electron to be added to the Sc+++ ion goes into a 33 orbit giving a doublet 2D term as the normal state of Sc++. The next electron enters a 41 orbit and gives a 3D term for the normal state for the Sc+. The last electron enters a 41 orbit and gives a 2D term for the normal state. The predicted terms for the normal states agree with the exptly. obsd. terms. It is noted that for terms of the same quantum nos. (i. c. the azimuthal quantum nos. of the electrons which do not form a closed shell) that term which has the highest multiplicity lies lowest. Making use of this rule it has been possible to give the type of term (S, P, D, F, G, etc.) and its multiplicity for the normal states of the second short series of the periodic table and for the elements from Sc to Zn. The predicted term agrees with expt. for all cases in which the spectra are known with the exception of Cr. In this case the term for four electrons in the 33 shell and two in the 41 shell was predicted and expt. agrees with five electrons in the 32 shell and one in the 41 shell. The spectra of O, Ne, Sn and Pb are discussed and found to agree with theory. The singly ionized atoms from Ca to Fe inclusive are also considered and excellent agreement between calcn. and expt. is secured.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaB28XhsFw%253D&md5=2810d62b22282eb6ebda7657affd0b9d
4
Li, Z.; Li, Z. R.; Meng, H. Organic Light-Emitting Materials and Devices; CRC Press, 2006.
Google Scholar
There is no corresponding record for this reference.
5
Endo, A.; Sato, K.; Yoshimura, K.; Kai, T.; Kawada, A.; Miyazaki, H.; Adachi, C. Efficient up-conversion of triplet excitons into a singlet state and its application for organic light emitting diodes. Appl. Phys. Lett. 2011, 98, 083302 DOI: 10.1063/1.3558906
Google Scholar
5
Efficient up-conversion of triplet excitons into a singlet state and its application for organic light emitting diodes
Endo, Ayataka; Sato, Keigo; Yoshimura, Kazuaki; Kai, Takahiro; Kawada, Atsushi; Miyazaki, Hiroshi; Adachi, Chihaya
Applied Physics Letters (2011), 98 (8), 083302/1-083302/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
A material possessing a small energy gap between its singlet and triplet excited states, ΔE1-3, which allows efficient up-conversion of triplet excitons into a singlet state and leads to efficient thermally activated delayed fluorescence (TADF), is reported. The compd., 2-biphenyl-4,6-bis(12-phenylindolo[2,3-a]carbazol-11-yl)-1,3,5-triazine, breaks the restriction of a large energy gap, with a ΔE1-3 of just 0.11 eV, while maintaining a high fluorescent radiative decay rate (kr ∼ 107). The intense TADF provides a pathway for highly efficient electroluminescence. (c) 2011 American Institute of Physics.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXisVagtr4%253D&md5=2dc1863c4de60dc09bfcb99236f34d97
6
Uoyama, H.; Goushi, K.; Shizu, K.; Nomura, H.; Adachi, C. Highly efficient organic light-emitting diodes from delayed fluorescence. Nature 2012, 492, 234– 238, DOI: 10.1038/nature11687
Google Scholar
6
Highly efficient organic light-emitting diodes from delayed fluorescence
Uoyama, Hiroki; Goushi, Kenichi; Shizu, Katsuyuki; Nomura, Hiroko; Adachi, Chihaya
Nature (London, United Kingdom) (2012), 492 (7428), 234-238CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
The inherent flexibility afforded by mol. design has accelerated the development of a wide variety of org. semiconductors over the past 2 decades. In particular, great advances were made in the development of materials for org. light-emitting diodes (OLEDs), from early devices based on fluorescent mols. to those using phosphorescent mols. In OLEDs, elec. injected charge carriers recombine to form singlet and triplet excitons in a 1:3 ratio; the use of phosphorescent metal-org. complexes exploits the normally nonradiative triplet excitons and so enhances the overall electroluminescence efficiency. Here the authors report a class of metal-free org. electroluminescent mols. in which the energy gap between the singlet and triplet excited states is minimized by design, thereby promoting highly efficient spin up-conversion from nonradiative triplet states to radiative singlet states while maintaining high radiative decay rates, of >106 decays per s. These mols. harness both singlet and triplet excitons for light emission through fluorescence decay channels, leading to an intrinsic fluorescence efficiency >90% and a very high external electroluminescence efficiency, of >19%, which is comparable to that achieved in high-efficiency phosphorescence-based OLEDs.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XhvVamurjL&md5=73e6f816abcb9166d7d4e7676a51f5cf
7
Goushi, K.; Yoshida, K.; Sato, K.; Adachi, C. Organic light-emitting diodes employing efficient reverse intersystem crossing for triplet-to-singlet state conversion. Nat. Photonics 2012, 6, 253– 258, DOI: 10.1038/nphoton.2012.31
Google Scholar
7
Organic light-emitting diodes employing efficient reverse intersystem crossing for triplet-to-singlet state conversion
Goushi, Kenichi; Yoshida, Kou; Sato, Keigo; Adachi, Chihaya
Nature Photonics (2012), 6 (4), 253-258CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
Light emission from org. light-emitting diodes that make use of fluorescent materials have an internal quantum efficiency that is typically limited to no more than 25% due to the creation of non-radiative triplet excited states. Here, we report the use of electron-donating and electron-accepting mols. that allow a very high reverse intersystem crossing of 86.5% between non-radiative triplet and radiative singlet excited states and thus a means of achieving enhanced electroluminescence. Org. light-emitting diodes made using m-MTDATA as the donor material and 3TPYMB as the acceptor material demonstrate that external quantum efficiencies as high as 5.4% can be achieved, and we believe that the approach will offer even higher values in the future as a result of careful material selection.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xjs1SqtbY%253D&md5=4b1e5049bc75aa992f01cde7f58e4bf5
8
Nakanotani, H.; Higuchi, T.; Furukawa, T.; Masui, K.; Morimoto, K.; Numata, M.; Tanaka, H.; Sagara, Y.; Yasuda, T.; Adachi, C. High-efficiency organic light-emitting diodes with fluorescent emitters. Nat. Commun. 2014, 5, 4016 DOI: 10.1038/ncomms5016
Google Scholar
8
High-efficiency organic light-emitting diodes with fluorescent emitters
Nakanotani, Hajime; Higuchi, Takahiro; Furukawa, Taro; Masui, Kensuke; Morimoto, Kei; Numata, Masaki; Tanaka, Hiroyuki; Sagara, Yuta; Yasuda, Takuma; Adachi, Chihaya
Nature Communications (2014), 5 (), 4016CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
Fluorescence-based org. light-emitting diodes have continued to attract interest because of their long operational lifetimes, high color purity of electroluminescence and potential to be manufd. at low cost in next-generation full-color display and lighting applications. In fluorescent mols., however, the exciton prodn. efficiency is limited to 25% due to the deactivation of triplet excitons. Here we report fluorescence-based org. light-emitting diodes that realize external quantum efficiencies as high as 13.4-18% for blue, green, yellow and red emission, indicating that the exciton prodn. efficiency reached nearly 100%. The high performance is enabled by utilization of thermally activated delayed fluorescence mols. as assistant dopants that permit efficient transfer of all elec. generated singlet and triplet excitons from the assistant dopants to the fluorescent emitters. Org. light-emitting diodes employing this exciton harvesting process provide freedom for the selection of emitters from a wide variety of conventional fluorescent mols.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2cXhvF2murjK&md5=d88fbd541737c290739d25c324529ba6
9
Hosokai, T.; Matsuzaki, H.; Nakanotani, H.; Tokumaru, K.; Tsutsui, T.; Furube, A.; Nasu, K.; Nomura, H.; Yahiro, M.; Adachi, C. Evidence and mechanism of efficient thermally activated delayed fluorescence promoted by delocalized excited states. Sci. Adv. 2017, 3, e1603282 DOI: 10.1126/sciadv.1603282
Google Scholar
9
Evidence and mechanism of efficient thermally activated delayed fluorescence promoted by delocalized excited states
Hosokai, Takuya; Matsuzaki, Hiroyuki; Nakanotani, Hajime; Tokumaru, Katsumi; Tsutsui, Tetsuo; Furube, Akihiro; Nasu, Keirou; Nomura, Hiroko; Yahiro, Masayuki; Adachi, Chihaya
Science Advances (2017), 3 (5), e1603282/1-e1603282/9CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)
The design of org. compds. with nearly no gap between the first excited singlet (S1) and triplet (T1) states has been demonstrated to result in an efficient spin-flip transition from the T1 to S1 state, i.e., reverse intersystem crossing (RISC), and facilitate light emission as thermally activated delayed fluorescence (TADF). However, many TADF mols. have shown that a relatively appreciable energy difference between the S1 and T1 states (∼0.2 eV) could also result in a high RISC rate. We revealed from a comprehensive study of optical properties of TADF mols. that the formation of delocalized states is the key to efficient RISC and identified a chem. template for these materials. In addn., simple structural confinement further enhances RISC by suppressing structural relaxation in the triplet states. Our findings aid in designing advanced org. mols. with a high rate of RISC and, thus, achieving the max. theor. electroluminescence efficiency in org. light-emitting diodes.
>> More from SciFinder ^®
https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXkvVCqtrg%253D&md5=a8e7f40b2806362d6bf948fa036cf806
10
de Silva, P. Inverted singlet–triplet gaps and their relevance to thermally activated delayed fluorescence. J. Phys. Chem. Lett. 2019, 10, 5674– 5679, DOI: 10.1021/acs.jpclett.9b02333
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10
Inverted Singlet-Triplet Gaps and Their Relevance to Thermally Activated Delayed Fluorescence
de Silva, Piotr
Journal of Physical Chemistry Letters (2019), 10 (18), 5674-5679CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
The basic design principle for emitters exhibiting thermally activated delayed fluorescence (TADF) is the minimization of the singlet-triplet gap. While typically this gap is pos., a possible inversion of states has been proposed as a pathway to improve the efficiency of org. light-emitting diodes. Despite the efforts to design such emitters, there are very few reports indicating that it is at all possible. We analyze the problem of the gap inversion from the perspective of the electronic structure theory. The key result is that inversion is possible but requires a substantial contribution of double excitations and that commonly used cheap electronic structure methods would fail to predict it.
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Sobolewski, A. L.; Domcke, W. Are heptazine-based organic light-emitting diode chromophores thermally activated delayed fluorescence or inverted singlet–triplet systems?. J. Phys. Chem. Lett. 2021, 12, 6852– 6860, DOI: 10.1021/acs.jpclett.1c01926
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Are Heptazine-Based Organic Light-Emitting Diode Chromophores Thermally Activated Delayed Fluorescence or Inverted Singlet-Triplet Systems?
Sobolewski, Andrzej L.; Domcke, Wolfgang
Journal of Physical Chemistry Letters (2021), 12 (29), 6852-6860CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
Two chromophores derived from heptazine, HAP-3MF and HAP-3TPA, were synthesized and tested as emitters in light-emitting diodes (OLEDs) by Adachi and co-workers. Both emitters were shown to exhibit quantum efficiencies which exceed the theor. max. of conventional fluorescent OLEDs. The enhanced emission efficiency was explained by the mechanism of thermally activated delayed fluorescence (TADF). In the present work, the electronic excitation energies and essential features of the topog. of the excited-state potential-energy surfaces of HAP-3MF and HAP-3TPA have been investigated with a wave function-based ab initio method (ADC(2)). It is found that HAP-3MF is an inverted singlet-triplet (IST) system; i.e., the energies of the S1 and T1 states are robustly inverted in violation of Hund's multiplicity rule. Notably, HAP-3MF presumably is the first IST emitter which was implemented in an OLED device. In HAP-3TPA, on the other hand, the vertical excitation energies of the S1 and T1 states are essentially degenerate. The excited states exhibit vibrational stabilization energies of similar magnitude along different relaxation coordinates, resulting in adiabatic excitation energies which also are nearly degenerate. HAP-3TPA is found to be a chromophore at the borderline of TADF and IST systems. The spectroscopic data reported by Adachi and co-workers for HAP-3MF and HAP-3TPA are analyzed in light of these computational results.
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Pios, S.; Huang, X.; Sobolewski, A. L.; Domcke, W. Triangular boron carbon nitrides: An unexplored family of chromophores with unique properties for photocatalysis and optoelectronics. Phys. Chem. Chem. Phys. 2021, 23, 12968– 12975, DOI: 10.1039/D1CP02026A
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Triangular boron carbon nitrides: an unexplored family of chromophores with unique properties for photocatalysis and optoelectronics
Pios, Sebastian; Huang, Xiang; Sobolewski, Andrzej L.; Domcke, Wolfgang
Physical Chemistry Chemical Physics (2021), 23 (23), 12968-12975CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
It has recently been shown that cycl[3.3.3]azine and heptazine (1,3,4,6,7,9,9b-heptaazaphenalene) as well as related azaphenalenes exhibit inverted singlet and triplet states, i.e., the energy of the lowest singlet excited state (S1) is below the energy of the lowest triplet excited state (T1). This feature is unique among all known arom. chromophores and is of outstanding relevance for applications in photocatalysis and org. optoelectronics. Heptazine is the building block of the polymeric material graphitic carbon nitride which is an extensively explored photocatalyst in hydrogen evolution photocatalysis. Derivs. of heptazine have also been identified as efficient emitters in org. light emitting diodes (OLEDs). In both areas, the inverted singlet-triplet gap of heptazine is a highly beneficial feature. In photocatalysis, the absence of a long-lived triplet state eliminates the activation of atm. oxygen, which is favorable for long-term operational stability. In optoelectronics, singlet-triplet inversion implies the possibility of 100% fluorescence efficiency of electron-hole recombination. However, the absorption and luminescence wavelengths of heptazine and the S1-S0 transition dipole moment are difficult to tune for optimal functionality. In this work, we employed high-level ab initio electronic structure theory to devise and characterize a large family of novel heteroarom. chromophores, the triangular boron carbon nitrides. These novel heterocycles inherit essential spectroscopic features from heptazine, in particular the inverted singlet-triplet gap, while their absorption and luminescence spectra and transition dipole moments are widely tuneable. For applications in photocatalysis, the wavelength of the absorption max. can be tuned to improve the overlap with the solar spectrum at the surface of earth. For applications in OLEDs, the color of emission can be adjusted and the fluorescence yield can be enhanced.
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Ricci, G.; Sancho-García, J.-C.; Olivier, Y. Establishing design strategies for emissive materials with an inverted singlet–triplet energy gap (INVEST): a computational perspective on how symmetry rules the interplay between triplet harvesting and light emission. J. Mater. Chem. C 2022, 10, 12680– 12698, DOI: 10.1039/D2TC02508F
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Establishing design strategies for emissive materials with an inverted singlet-triplet energy gap (INVEST): a computational perspective on how symmetry rules the interplay between triplet harvesting and light emission
Ricci, Gaetano; Sancho-Garcia, Juan-Carlos; Olivier, Yoann
Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2022), 10 (35), 12680-12698CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)
The inversion of the lowest singlet and triplet excited state energy gaps, in fully org. triangle-based compds., can give rise to new exergonic pathways to enhance the performance of org. light-emitting diodes (OLEDs), going beyond the novel yet promising thermally activated delayed fluorescence (TADF) mechanism. The origin of this inversion, arises from the interplay between exchange and electron correlation effects and was extensively studied in the last few years, using wavefunction-based methods. A proper picture of the structure-property relations characterizing these systems is still lacking. The effect of different symmetry point groups (D3h, C2v, C3h and C3v) on the orbital localization was assessed to shed light on the role played by symmetry in detg. the optical features of the triangulene systems (on both S1-T1 inversion and oscillator strengths). The presence of the C2 axis and σv plane (as in the D3h, C2v and C3v groups) turned out to be crit. for ensuring proper orbital localization aimed at minimizing exchange interaction, therefore favoring the inversion process. Adopting the C2v (and its subgroups) symmetry through a proper doping pattern of the triangulene core, by introducing substituents or by merging 2 triangulene cores, is the only way to achieve a neg. ΔEST and a nonzero oscillator strength. The lessons learned from this anal. to establish design rules aimed at helping the identification of inverted singlet-triplet (INVEST) emitters for applications in next-generation OLEDs are summarized.
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Ehrmaier, J.; Huang, X.; Rabe, E. J.; Corp, K. L.; Schlenker, C. W.; Sobolewski, A. L.; Domcke, W. Molecular design of heptazine-based photocatalysts: effect of substituents on photocatalytic efficiency and photostability. J. Phys. Chem. A 2020, 124, 3698– 3710, DOI: 10.1021/acs.jpca.0c00488
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Molecular design of heptazine-based photocatalysts: effect of substituents on photocatalytic efficiency and photostability
Ehrmaier, Johannes; Huang, Xiang; Rabe, Emily J.; Corp, Kathryn L.; Schlenker, Cody W.; Sobolewski, Andrzej L.; Domcke, Wolfgang
Journal of Physical Chemistry A (2020), 124 (19), 3698-3710CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
Recently, a deriv. of the heptazine (tris-triazine) mol., trianisole-heptazine (TAHz), was synthesized and was shown to catalyze the oxidn. of water to hydroxyl radicals under 365 nm LED light in a homogeneous reaction (E. J. Rabe et al.,). The possibility of water photo-oxidn. with a precisely defined mol. catalyst in neat solvents opens new perspectives for clarifying the fundamental reaction mechanisms involved in water oxidn. photocatalysis. In the present work, the effects of chem. substituents on the three CH positions of Hz on the photocatalytic reactivity were explored with wave function-based ab initio electronic-structure calcns. for hydrogen-bonded complexes of Hz and three selected Hz derivs. (TAHz, trichloro-Hz, and tricyano-Hz) with a water mol. While anisole is an electron-donating substituent, Cl is a weakly electron-withdrawing substituent and CN is a strongly electron-withdrawing substituent. It is shown that the barrier for the photoinduced abstraction of an H atom from the water mol. is raised (lowered) by electron-donating (electron-withdrawing) substituents. The highly mobile and reactive hydroxyl radicals generated by water oxidn. can recombine with the reduced chromophore radicals to yield photohydrates. The effect of substituents on the thermodn. of the photohydration reaction was computed. Among the four chromophores studied, TAHz stands out on account of the metastability of its photohydrate, which suggests self-healing of the photocatalyst after oxidn. of TAHzH radicals by OH radicals. In addn., the effect of substituents on the H atom photodetachment reaction from the reduced chromophores, which closes the catalytic cycle, has been investigated. The energy of the repulsive 2πσ* state, which drives the photodetachment reaction is lowered (raised) by electron-donating (electron withdrawing) substituents. All four chromophores exhibit inverted S1/T1 gaps. This feature eliminates long-lived triplet states and thus avoids the activation of mol. oxygen to highly reactive singlet oxygen.
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Ehrmaier, J.; Rabe, E. J.; Pristash, S. R.; Corp, K. L.; Schlenker, C. W.; Sobolewski, A. L.; Domcke, W. Singlet–triplet inversion in heptazine and in polymeric carbon nitrides. J. Phys. Chem. A 2019, 123, 8099– 8108, DOI: 10.1021/acs.jpca.9b06215
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Singlet-Triplet Inversion in Heptazine and in Polymeric Carbon Nitrides
Ehrmaier, Johannes; Rabe, Emily J.; Pristash, Sarah R.; Corp, Kathryn L.; Schlenker, Cody W.; Sobolewski, Andrzej L.; Domcke, Wolfgang
Journal of Physical Chemistry A (2019), 123 (38), 8099-8108CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
According to Hund's rule, the lowest triplet state (T1) is lower in energy than the lowest excited singlet state (S1) in closed-shell mols. The exchange integral lowers the energy of the triplet state and raises the energy of the singlet state of the same orbital character, leading to a pos. singlet-triplet energy gap (ΔST). Exceptions are known for biradicals and charge-transfer excited states of large mols. in which the HOMO and the LUMO are spatially sepd., resulting in a small exchange integral. In the present work, we discovered with ADC(2), CC2, EOM-CCSD, and CASPT2 calcns. that heptazine (1,3,4,6,7,9,9b-heptaazaphenalene or tri-s-triazine) exhibits an inverted S1/T1 energy gap (ΔST ≈ -0.25 eV). This appears to be the first example of a stable closed-shell org. mol. exhibiting S1/T1 inversion at its equil. geometry. The origins of this phenomenon are the nearly pure HOMO-LUMO excitation character of the S1 and T1 states and the lack of spatial overlap of HOMO and LUMO due to a unique structure of these orbitals of heptazine. The S1/T1 inversion is found to be extremely robust, being affected neither by substitution of heptazine nor by oligomerization of heptazine units. Using time-resolved photoluminescence and transient absorption spectroscopy, we investigated the excited-state dynamics of 2,5,8-tris(4-methoxyphenyl)-1,3,4,6,7,9,9b-heptaazaphenalene (TAHz), a chem. stable heptazine deriv., in the presence of external heavy atom sources as well as triplet-quenching oxygen. These spectroscopic data are consistent with TAHz singlet excited state decay in the absence of a low-energy triplet loss channel. The absence of intersystem crossing and an exceptionally low radiative rate result in unusually long S1 lifetimes (of the order of hundreds of nanoseconds in nonaq. solvents). These features of the heptazine chromophore have profound implications for org. optoelectronics as well as for water-splitting photocatalysis with heptazine-based polymers (e.g., graphitic carbon nitride) which have yet to be systematically explored and exploited.
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Li, J.; Nakagawa, T.; MacDonald, J.; Zhang, Q.; Nomura, H.; Miyazaki, H.; Adachi, C. Highly Efficient Organic Light-Emitting Diode Based on a Hidden Thermally Activated Delayed Fluorescence Channel in a Heptazine Derivative. Adv. Mater. 2013, 25, 3319– 3323, DOI: 10.1002/adma.201300575
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Highly Efficient Organic Light-Emitting Diode Based on a Hidden Thermally Activated Delayed Fluorescence Channel in a Heptazine Derivative
Li, Jie; Nakagawa, Tetsuya; Zhang, Qisheng; Nomura, Hiroko; Miyazaki, Hiroshi; Adachi, Chihaya
Advanced Materials (Weinheim, Germany) (2013), 25 (24), 3319-3323CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
The authors have designed and synthesized an orange-red thermally activated delayed fluorescence (TADF) emitter, 4,4',4"-(1,3,3a1,4,6,7,9-heptaazaphenalene-2,5,8-triyl)tris[N,N-bis[4-(tert-butyl)phenyl]aniline] (HAP-3TPA), which has a HAP core as an electron-accepting unit and three electron-donating units of TPA. An org. electroluminescent device (OLED) contg. HAP-3TPA showed high performance with ηext = 17.5 ± 1.3 % , max. luminance of 17000 ± 1600 cd m-2, max. current efficiency and power efficiency of 25.9 + 1.6 cd A-1 and 22.1 ± 1.2 lm W-1, resp., and a turn-one voltage of 4.4 + 0.3 V at a luminance of 100 cd m-2 without any light out-coupling enhancement. Although HAP-3TPA demonstrated very weak TADF in the PL process, upconversion from T1 to S1 was quite efficient under elec. excitation, resulting in high EL efficiency. Thus, in principle, while mols. may show only fluorescence and very faint TADF in PL, they may have an efficient pathway for TADF in EL.
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Li, J.; Zhang, Q.; Nomura, H.; Miyazaki, H.; Adachi, C. Thermally activated delayed fluorescence from 3n π* to 1n π* up-conversion and its application to organic light-emitting diodes. Appl. Phys. Lett. 2014, 105, 013301 DOI: 10.1063/1.4887346
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Thermally activated delayed fluorescence from 3nπ* to 1nπ* up-conversion and its application to organic light-emitting diodes
Li, Jie; Zhang, Qisheng; Nomura, Hiroko; Miyazaki, Hiroshi; Adachi, Chihaya
Applied Physics Letters (2014), 105 (1), 013301/1-013301/4CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
Intense nπ* fluorescence from a nitrogen-rich heterocyclic compd., 2,5,8-tris(4-fluoro-3-methylphenyl)-1,3,4,6,7,9,9b-heptaazaphenalene (HAP-3MF), is demonstrated. The overlap-forbidden nature of the nπ* transition and the higher energy of the 3ππ* state than the 3nπ* one lead to a small energy difference between the lowest singlet (S1) and triplet (T1) excited states of HAP-3MF. Green-emitting HAP-3MF has a moderate photoluminescence quantum yield of 0.26 in both toluene and doped film. However, an org. light-emitting diode contg. HAP-3MF achieved a high external quantum efficiency of 6.0%, indicating that HAP-3MF harvests singlet excitons through a thermally activated T1 → S1 pathway in the electroluminescent process. (c) 2014 American Institute of Physics.
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Li, J.; Nomura, H.; Miyazaki, H.; Adachi, C. Highly efficient exciplex organic light-emitting diodes incorporating a heptazine derivative as an electron acceptor. Chem. Commun. 2014, 50, 6174– 6176, DOI: 10.1039/C4CC01590H
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Highly efficient exciplex organic light-emitting diodes incorporating a heptazine derivative as an electron acceptor
Li, Jie; Nomura, Hiroko; Miyazaki, Hiroshi; Adachi, Chihaya
Chemical Communications (Cambridge, United Kingdom) (2014), 50 (46), 6174-6176CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
Highly efficient exciplex systems incorporating a heptazine deriv. (HAP-3MF) as an electron acceptor and 1,3-di(9H-carbazol-9-yl)benzene (mCP) as an electron donor are developed. An OLED contg. 8 wt.% HAP-3MF:mCP as an emitting layer exhibits a max. external quantum efficiency of 11.3%.
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Ricci, G.; San-Fabián, E.; Olivier, Y.; Sancho-García, J.-C. Singlet-triplet excited-state inversion in heptazine and related molecules: assessment of TD-DFT and ab initio methods. ChemPhysChem 2021, 22, 553– 560, DOI: 10.1002/cphc.202000926
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Singlet-Triplet Excited-State Inversion in Heptazine and Related Molecules: Assessment of TD-DFT and ab initio Methods
Ricci, G.; San-Fabian, E.; Olivier, Y.; Sancho-Garcia, J. C.
ChemPhysChem (2021), 22 (6), 553-560CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)
We have investigated the origin of the S1-T1 energy levels inversion for heptazine, and other N-doped π-conjugated hydrocarbons, leading thus to an unusually neg. singlet-triplet energy gap (ΔEST<0). Since this inversion might rely on substantial doubly-excited configurations to the S1 and/or T1 wavefunctions, we have systematically applied multi-configurational SA-CASSCF and SC-NEVPT2 methods, SCS-cor. CC2 and ADC(2) approaches, and linear-response TD-DFT, to analyze if the latter method could also face this challenging issue. We have also extended the study to B-doped π-conjugated systems, to see the effect of chem. compn. on the results. For all the systems studied, an intricate interplay between the singlet-triplet exchange interaction, the influence of doubly-excited configurations, and the impact of dynamic correlation effects, serves to explain the ΔEST<0 values found for most of the compds., which is not predicted by TD-DFT.
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Sanz-Rodrigo, J.; Ricci, G.; Olivier, Y.; Sancho-Garcia, J.-C. Negative singlet–triplet excitation energy gap in triangle-shaped molecular emitters for efficient triplet harvesting. J. Phys. Chem. A 2021, 125, 513– 522, DOI: 10.1021/acs.jpca.0c08029
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Negative Singlet-Triplet Excitation Energy Gap in Triangle-Shaped Molecular Emitters for Efficient Triplet Harvesting
Sanz-Rodrigo, J.; Ricci, G.; Olivier, Y.; Sancho-Garcia, J. C.
Journal of Physical Chemistry A (2021), 125 (2), 513-522CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
The full harvesting of both singlet and triplet excitons can pave the way toward more efficient mol. light-emission mechanisms (i.e., TADF or thermally activated delayed fluorescence) beyond the spin statistics limit. This TADF mechanism benefits from low (but typically pos.) singlet-triplet energy gaps or ΔEST. Recent research has suggested the possibility of inverting the order of the energy of lowest singlet and triplet excited states, thus opening new pathways to promote light emission without any energy barrier through triplet to singlet conversion, which is systematically investigated here by means of theor. methods. To this end, we have selected a set of heteroatom-substituted triangle-shaped mols. (or triangulenes) for which ΔEST < 0 is predicted. We successfully rationalize the origin of that energy inversion and the reasons for which theor. methods might produce qual. inconsistent predictions depending on how they treat n-tuple excitations (e.g., the large contribution of double excitations for all of the ground and excited states involved). Unfortunately, the time-dependent d. functional theory method is unable to deal with the phys. effects driving this behavior, which prompted us to use more sophisticated ab initio methods here such as SA-CASSCF, SC-NEVPT2, SCS-CC2, and SCS-ADC(2).
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Aizawa, N.; Pu, Y.-J.; Harabuchi, Y.; Nihonyanagi, A.; Ibuka, R.; Inuzuka, H.; Dhara, B.; Koyama, Y.; Nakayama, K.-i.; Maeda, S.; Araoka, F.; Miyajima, D. Delayed fluorescence from inverted singlet and triplet excited states. Nature 2022, 609, 502– 506, DOI: 10.1038/s41586-022-05132-y
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Delayed fluorescence from inverted singlet and triplet excited states
Aizawa, Naoya; Pu, Yong-Jin; Harabuchi, Yu; Nihonyanagi, Atsuko; Ibuka, Ryotaro; Inuzuka, Hiroyuki; Dhara, Barun; Koyama, Yuki; Nakayama, Ken-ichi; Maeda, Satoshi; Araoka, Fumito; Miyajima, Daigo
Nature (London, United Kingdom) (2022), 609 (7927), 502-506CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)
Hund's multiplicity rule states that a higher spin state has a lower energy for a given electronic configuration1. Rephrasing this rule for mol. excited states predicts a pos. energy gap between spin-singlet and spin-triplet excited states, as has been consistent with numerous exptl. observations over almost a century. Here we report a fluorescent mol. that disobeys Hund's rule and has a neg. singlet-triplet energy gap of -11 ± 2 meV. The energy inversion of the singlet and triplet excited states results in delayed fluorescence with short time consts. of 0.2μs, which anomalously decrease with decreasing temp. owing to the emissive singlet character of the lowest-energy excited state. Org. light-emitting diodes (OLEDs) using this mol. exhibited a fast transient electroluminescence decay with a peak external quantum efficiency of 17%, demonstrating its potential implications for optoelectronic devices, including displays, lighting and lasers.
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Kollmar, H.; Staemmler, V. Violation of Hund’s rule by spin polarization in molecules. Theor. Chim. Acta 1978, 48, 223– 239, DOI: 10.1007/BF00549021
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Violation of Hund's rule by spin polarization in molecules
Kollmar, H.; Staemmler, V.
Theoretica Chimica Acta (1978), 48 (3), 223-39CODEN: TCHAAM; ISSN:0040-5744.
Spin polarization effects can lead to violations of Hund's multiplicity rule, particularly for singlet-triplet pairs. In systems with >1 unpaired electron, a dynamic spin polarization is obsd. which depends on the relative spin orientation of the unpaired electrons and is different in open-shell singlet and triplet states. These effects are described by including singly substituted configurations in Cl-type wave functions for the 2 states. In analyzing the contributions of the various singly substituted configurations, a quant. understanding of violations of Hund's rule is obtained; at the same time it is possible to calc. quant. spin polarization contributions to the correlation energies of open-shell singlet and triplet states. A series of model calcns. was performed on systems like square planar H4 and C4H4, nπ* states of H2CO rotated cumulenes, NH and O2 to investigate how strongly spin polarization influences singlet-triplet energy splittings and what are the properties of a mol. that lead to a violation of Hund's multiplicity rule.
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Pollice, R.; Friederich, P.; Lavigne, C.; dos Passos Gomes, G.; Aspuru-Guzik, A. Organic molecules with inverted gaps between first excited singlet and triplet states and appreciable fluorescence rates. Matter 2021, 4, 1654– 1682, DOI: 10.1016/j.matt.2021.02.017
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Organic molecules with inverted gaps between first excited singlet and triplet states and appreciable fluorescence rates
Pollice, Robert; Friederich, Pascal; Lavigne, Cyrille; Gomes, Gabriel dos Passos; Aspuru-Guzik, Alan
Matter (2021), 4 (5), 1654-1682CODEN: MATTCG; ISSN:2590-2385. (Elsevier Inc.)
One recent proposal for designing state-of-the-art emissive materials in org. light-emitting diodes (OLEDs) is the principle of thermally activated delayed fluorescence (TADF). The idea is to enable facile thermal upconversion of excited-state triplets, which are generated upon electron-hole recombination, to excited-state singlets. Minimizing the corresponding singlet-triplet energy difference enables devices with up to 100% internal quantum efficiency. Ideal emissive materials potentially surpassing TADF emitters in other performance parameters should have both neg. singlet-triplet gaps and substantial fluorescence rates to maximize reverse intersystem crossing (ISC) rates from excited triplets to singlets while minimizing ISC rates and triplet state occupation, leading to long-term operational stability. However, mols. with neg. singlet-triplet gaps are extremely rare, and none of them emissive. In this work, based on computational studies, we describe the first mols. with neg. singlet-triplet gaps and considerable fluorescence rates and show that they are more common than hypothesized previously.
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Tučková, L.; Straka, M.; Valiev, R. R.; Sundholm, D. On the origin of the inverted singlet–triplet gap of the 5th generation light-emitting molecules. Phys. Chem. Chem. Phys. 2022, 24, 18713– 18721, DOI: 10.1039/D2CP02364D
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On the origin of the inverted singlet-triplet gap of the 5th generation light-emitting molecules
Tuckova, Lucie; Straka, Michal; Valiev, Rashid R.; Sundholm, Dage
Physical Chemistry Chemical Physics (2022), 24 (31), 18713-18721CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
Excitation energies of the lowest singlet and triplet state of mols. whose first excited singlet state lies energetically below the first triplet state have been studied computationally at (time-dependent) d. functional theory, coupled-cluster, and second-order multiconfiguration perturbation theory levels. The calcns. at the ab initio levels show that the singlet-triplet gap is inverted as compared to the one expected from Hund's rule, whereas all d. functionals yield the triplet state as the lowest excited state. Double excitations responsible for the inverted singlet-triplet gap have been identified. Employing the spin-flip and ΔSCF methods, singlet-triplet inversion was obtained at the d. functional theory level for some of the studied mols.
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Bhattacharyya, K. Can TDDFT render the electronic excited states ordering of Azine derivative? A closer investigation with DLPNO-STEOM-CCSD. Chem. Phys. Lett. 2021, 779, 138827, DOI: 10.1016/j.cplett.2021.138827
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Can TDDFT render the electronic excited states ordering of Azine derivative? A closer investigation with DLPNO-STEOM-CCSD
Bhattacharyya, Kalishankar
Chemical Physics Letters (2021), 779 (), 138827CODEN: CHPLBC; ISSN:0009-2614. (Elsevier B.V.)
TADF materials depend on the small energy gap between the lowest excited singlet and triplet state for an efficient reverse intersystem crossing process. Herein, the first excited singlet (S1) and triplet (T1) state and their gap (ΔEST) are computed based on TDDFT and recently developed coupled-cluster DLPNO-STEOM-CCSD method for Azine deriv. Considerations of higher-order excitations in DLPNO-STEOM-CCSD assign the correct excited state energy level ordering of Azine deriv. while DFT functionals fall short in this context.
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Ghosh, S.; Bhattacharyya, K. Origin of the Failure of Density Functional Theories in Predicting Inverted Singlet–Triplet Gaps. J. Phys. Chem. A 2022, 126, 1378– 1385, DOI: 10.1021/acs.jpca.1c10492
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Origin of the Failure of Density Functional Theories in Predicting Inverted Singlet-Triplet Gaps
Ghosh, Soumen; Bhattacharyya, Kalishankar
Journal of Physical Chemistry A (2022), 126 (8), 1378-1385CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
Recent exptl. and theor. studies have shown several new org. mols. that violate Hund's rule and have the first singlet excited state lower in energy than the first triplet excited state. While many correlated single ref. wave function methods have successfully predicted excited-state energetics of these low-lying states, conventional linear-response time-dependent d. functional theory (TDDFT) fails to predict the correct excited-state energy ordering. In this article, we have explored the performance of combined DFT and wave function methods like doubles-cor. TDDFT and multiconfiguration pair-d. functional theory for the calcn. of inverted singlet-triplet gaps. We have also tested the performance of the excited-state DFT (eDFT) method for this problem. Our results have shown that it is possible to obtain inverted singlet-triplet gaps both by using doubles-cor. TDDFT with a proper choice of double-hybrid functionals or by using eDFT.
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Koseki, S.; Nakajima, T.; Toyota, A. Violation of Hund’s multiplicity rule in the electronically excited states of conjugated hydrocarbons. Can. J. Chem. 1985, 63, 1572– 1579, DOI: 10.1139/v85-267
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27
Violation of Hund's multiplicity rule in the electronically excited states of conjugated hydrocarbons
Koseki, Shiro; Nakajima, Takeshi; Toyota, Azumao
Canadian Journal of Chemistry (1985), 63 (7), 1572-9CODEN: CJCHAG; ISSN:0008-4042.
Violation of Hund's multiplicity rule in the electronically excited states of conjugated hydrocarbons is studied by using the PPP type SCF MO method and the ab initio MO method with STO-3G basis set, both methods being augmented by CI-type treatments. For sym. structures (D2h) of the nonalternant hydrocarbons, propalene, pentalene, and heptalene, the lowest excited singlet state is energetically lower than the corresponding triplet state because of spin polarization (SP) effects. For D2h structures of pentalene and heptalene the open-shell excited singlet state is predicted to be lower in energy than the closed-shell state, with the result that the former is really the ground state. Further, calcns. made by including electron correlation effects reveal that in linear polyenes and polyacenes, the lowest excited singlet minus state (using Pariser's classification of the alternancy symmetry species) is lower in energy than the corresponding triplet state. The energy lowering of the singlet minus state in linear polyenes is due mostly to the mixing with the doubly excited configurations (mm → nn), while the considerable part of it in polyacenes is due to the SP effects.
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Harris, J.; Jones, R. O. The surface energy of a bounded electron gas. J. Phys. F: Met. Phys. 1974, 4, 1170, DOI: 10.1088/0305-4608/4/8/013
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There is no corresponding record for this reference.
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Langreth, D. C.; Perdew, J. Exchange-correlation energy of a metallic surface: Wave-vector analysis. Phys. Rev. B 1977, 15, 2884, DOI: 10.1103/PhysRevB.15.2884
Google Scholar
There is no corresponding record for this reference.
30
Gunnarsson, O.; Lundqvist, B. Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism. Phys. Rev. B 1976, 13, 4274, DOI: 10.1103/PhysRevB.13.4274
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Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
Gunnarsson, O.; Lundqvist, B. I.
Physical Review B: Solid State (1976), 13 (10), 4274-98CODEN: PLRBAQ; ISSN:0556-2805.
The spin-d.-functional (SDF) formalism (e.g., G., et al., 1974-5) was extended to apply to generalized Hamiltonians and to lowest excited states with different types of symmetry. A relation between the exchange-correlation functional and the pair-correlation function was derived, and was used to interpret approx. versions of the theory, esp. the local-spin-d. (LSD) approxn., which can be used in calcn. of the exchange-correlation energy (Exc) in rather inhomogeneous systems. Calcns. done on the homogeneous spin-polarized electron liq., where the charge-d. fluctuations were described by using a plasmon model, provide interpolation formulas for detg. Exc and the exchange-correlation potentials in the LSD approxn. Other properties calcd. for the electron liq. include: bulk modulus at const. magnetization, compressibility at const. magnetic field, and magnetic susceptibility. Applications of the SDF formalism in calcns. of the properties of atoms, mols., and metals are discussed.
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Teale, A. M.; Coriani, S.; Helgaker, T. Accurate calculation and modeling of the adiabatic connection in density functional theory. J. Chem. Phys. 2010, 132, 164115 DOI: 10.1063/1.3380834
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Accurate calculation and modeling of the adiabatic connection in density functional theory
Teale, A. M.; Coriani, S.; Helgaker, T.
Journal of Chemical Physics (2010), 132 (16), 164115/1-164115/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Using a recently implemented technique for the calcn. of the adiabatic connection (AC) of d. functional theory (DFT) based on Lieb maximization with respect to the external potential, the AC is studied for atoms and mols. contg. up to ten electrons: the helium isoelectronic series, the hydrogen mol., the beryllium isoelectronic series, the neon atom, and the water mol. The calcn. of AC curves by Lieb maximization at various levels of electronic-structure theory is discussed. For each system, the AC curve is calcd. using Hartree-Fock (HF) theory, second-order Moller-Plesset (MP2) theory, coupled-cluster singles-and-doubles (CCSD) theory, and coupled-cluster singles-doubles-perturbative-triples CCSD(T) theory, expanding the MOs and the effective external potential in large Gaussian basis sets. The HF AC curve includes a small correlation-energy contribution in the context of DFT, arising from orbital relaxation as the electron-electron interaction is switched on under the constraint that the wave function is always a single determinant. The MP2 and CCSD AC curves recover the bulk of the dynamical correlation energy and their shapes can be understood in terms of a simple energy model constructed from a consideration of the doubles-energy expression at different interaction strengths. Differentiation of this energy expression with respect to the interaction strength leads to a simple two-parameter doubles model (AC-D) for the AC integrand (and hence the correlation energy of DFT) as a function of the interaction strength. The structure of the triples-energy contribution is considered in a similar fashion, leading to a quadratic model for the triples correction to the AC curve (AC-T). From a consideration of the structure of a two-level configuration-interaction (CI) energy expression of the hydrogen mol., a simple two-parameter CI model (AC-CI) is proposed to account for the effects of static correlation on the AC. When parametrized in terms of the same input data, the AC-CI model offers improved performance over the corresponding AC-D model, which is shown to be the lowest-order contribution to the AC-CI model. The utility of the accurately calcd. AC curves for the anal. of std. d. functionals is demonstrated for the BLYP exchange-correlation functional and the interaction-strength-interpolation (ISI) model AC integrand. From the results of this anal., we investigate the performance of our proposed two-parameter AC-D and AC-CI models when a simple d. functional for the AC at infinite interaction strength is employed in place of information at the fully interacting point. The resulting two-parameter correlation functionals offer a qual. correct behavior of the AC integrand with much improved accuracy over previous attempts. The AC integrands in the present work are recommended as a basis for further work, generating functionals that avoid spurious error cancellations between exchange and correlation energies and give good accuracy for the range of densities and types of correlation contained in the systems studied here. (c) 2010 American Institute of Physics.
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Pernal, K. Electron Correlation from the Adiabatic Connection for Multireference Wave Functions. Phys. Rev. Lett. 2018, 120, 013001 DOI: 10.1103/PhysRevLett.120.013001
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Electron Correlation from the Adiabatic Connection for Multireference Wave Functions
Pernal, Katarzyna
Physical Review Letters (2018), 120 (1), 013001CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
A review. An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions. The AC expression recovers dynamic correlation energy and assures a balanced treatment of the correlation energy. Coupling the AC formalism with the extended RPA allows one to find the correlation energy only from ref. one- and two-electron reduced d. matrixes. If the generalized valence bond perfect pairing model is employed a simple closed-form expression for the approx. AC formula is obtained. This results in the overall M5 scaling of the computation cost making the method one of the most efficient multireference approaches accounting for dynamic electron correlation also for the strongly correlated systems.
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Pernal, K. Exact and approximate adiabatic connection formulae for the correlation energy in multireference ground and excited states. J. Chem. Phys. 2018, 149, 204101 DOI: 10.1063/1.5048988
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Exact and approximate adiabatic connection formulae for the correlation energy in multireference ground and excited states
Pernal, Katarzyna
Journal of Chemical Physics (2018), 149 (20), 204101/1-204101/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Recently it has been shown how to employ the adiabatic connection (AC) formalism to obtain correlation energy for multireference wavefunctions [K. Pernal, Phys. Rev. Lett. 120, 013001 (2018)]. Approxns. to the exact AC formulation have been based on assuming that a one-electron reduced d. matrix is const. along the AC path and by employing the extended RPA. In this paper, the importance of these approxns. is examd. by comparing approx. AC integrands with their exact counterparts obtained for the hydrogen mol. in its ground and excited states. Encouraging results obtained for H2 indicate that AC is a viable and promising approach to a correlation energy problem not only for ground but also for excited states of electronic systems. (c) 2018 American Institute of Physics.
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Drwal, D.; Beran, P.; Hapka, M.; Modrzejewski, M.; Sokół, A.; Veis, L.; Pernal, K. Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet–Triplet Gaps of Biradicals. J. Phys. Chem. Lett. 2022, 13, 4570– 4578, DOI: 10.1021/acs.jpclett.2c00993
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Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet-Triplet Gaps of Biradicals
Drwal, Daria; Beran, Pavel; Hapka, Michal; Modrzejewski, Marcin; Sokol, Adam; Veis, Libor; Pernal, Katarzyna
Journal of Physical Chemistry Letters (2022), 13 (20), 4570-4578CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
Strong electron correlation can be captured with multireference wave function methods, but an accurate description of the electronic structure requires accounting for the dynamic correlation, which they miss. In this work, a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The ACn method accounts for terms up to order n in the coupling const., and it is size-consistent and free from instabilities. It employs the multireference RPA and the Cholesky decompn. technique, leading to a computational cost growing with the fifth power of the system size. Because of the dependence on only one- and two-electron reduced d. matrixes, ACn is more efficient than existing ab initio multireference dynamic correlation methods. ACn affords excellent results for singlet-triplet gaps of challenging org. biradicals. The development presented in this work opens new perspectives for accurate calcns. of systems with dozens of strongly correlated electrons.
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Angeli, C.; Cimiraglia, R.; Malrieu, J.-P. n-electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants. J. Chem. Phys. 2002, 117, 9138, DOI: 10.1063/1.1515317
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n-electron valence state perturbation theory: a spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants
Angeli, Celestino; Cimiraglia, Renzo; Malrieu, Jean-Paul
Journal of Chemical Physics (2002), 117 (20), 9138-9153CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
The n-electron valence state perturbation theory is reformulated in a spin-free formalism, concg. on the "strongly contracted" and "partially contracted" variants. The new formulation is based on the introduction of av. values in the unperturbed state of excitation operators which bear resemblance with analogous ones occurring in the extended Koopmans' theorem and in the equations-of-motion technique. Such auxiliary quantities, which allow the second-order perturbation contribution to the energy to be evaluated very efficiently, can be calcd. at the outset provided the unperturbed four-particle spinless d. matrix in the active orbital space is available. A noticeable inequality concerning second-order energy contributions of the same type between the strongly and partially contracted versions is proven to hold. An example concerning the successful calcn. of the potential energy curve for the Cr2 mol. is discussed.
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Bhaskaran-Nair, K.; Brabec, J.; Aprà, E.; van Dam, H. J. J.; Pittner, J.; Kowalski, K. Implementation of the multireference Brillouin-Wigner and Mukherjee’s coupled cluster methods with non-iterative triple excitations utilizing reference-level parallelism. J. Chem. Phys. 2012, 137, 094112 DOI: 10.1063/1.4747698
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Implementation of the multireference Brillouin-Wigner and Mukherjee's coupled cluster methods with non-iterative triple excitations utilizing reference-level parallelism
Bhaskaran-Nair, Kiran; Brabec, Jiri; Apra, Edoardo; van Dam, Hubertus J. J.; Pittner, Jiri; Kowalski, Karol
Journal of Chemical Physics (2012), 137 (9), 094112/1-094112/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
In this paper we discuss the performance of the non-iterative state-specific multireference coupled cluster (SS-MRCC) methods accounting for the effect of triply excited cluster amplitudes. The corrections to the Brillouin-Wigner and Mukherjee's MRCC models based on the manifold of singly and doubly excited cluster amplitudes (BW-MRCCSD and Mk-MRCCSD, resp.) are tested and compared with exact full CI results for small systems (H2O, N2, and Be3). For the larger systems (naphthyne isomers) the BW-MRCC and Mk-MRCC methods with iterative singles, doubles, and non-iterative triples (BW-MRCCSD(T) and Mk-MRCCSD(T)) are compared against the results obtained with single ref. coupled cluster methods. We also report on the parallel performance of the non-iterative implementations based on the use of processor groups. (c) 2012 American Institute of Physics.
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Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. Molpro: a general-purpose quantum chemistry program package. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 242– 253, DOI: 10.1002/wcms.82
Google Scholar
37
Molpro: a general-purpose quantum chemistry program package
Werner, Hans-Joachim; Knowles, Peter J.; Knizia, Gerald; Manby, Frederick R.; Schuetz, Martin
Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (2), 242-253CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
Molpro is a general-purpose quantum chem. program. The original focus was on high-accuracy wave function calcns. for small mols., but using local approxns. combined with explicit correlation treatments, highly accurate coupled-cluster calcns. are now possible for mols. with up to approx. 100 atoms. Recently, multireference correlation treatments were also made applicable to larger mols. Furthermore, an efficient implementation of d. functional theory is available.
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Schäfer, A.; Horn, H.; Ahlrichs, R. Fully optimized contracted Gaussian basis sets for atoms Li to Kr. J. Chem. Phys. 1992, 97, 2571– 2577, DOI: 10.1063/1.463096
Google Scholar
There is no corresponding record for this reference.
39
Pernal, K.; Hapka, M.; Przybytek, M.; Modrzejewski, M.; Sokół, A.; Tucholska, A. GammCor code. https://github.com/pernalk/GAMMCOR, 2023.
Google Scholar
There is no corresponding record for this reference.
40
Aprà, E.; Bylaska, E. J.; de Jong, W. A. NWChem: Past, present, and future. J. Chem. Phys. 2020, 152, 184102 DOI: 10.1063/5.0004997
Google Scholar
40
NWChem: Past, present, and future
Apra, E.; Bylaska, E. J.; de Jong, W. A.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Valiev, M.; van Dam, H. J. J.; Alexeev, Y.; Anchell, J.; Anisimov, V.; Aquino, F. W.; Atta-Fynn, R.; Autschbach, J.; Bauman, N. P.; Becca, J. C.; Bernholdt, D. E.; Bhaskaran-Nair, K.; Bogatko, S.; Borowski, P.; Boschen, J.; Brabec, J.; Bruner, A.; Cauet, E.; Chen, Y.; Chuev, G. N.; Cramer, C. J.; Daily, J.; Deegan, M. J. O.; Dunning, T. H.; Dupuis, M.; Dyall, K. G.; Fann, G. I.; Fischer, S. A.; Fonari, A.; Fruchtl, H.; Gagliardi, L.; Garza, J.; Gawande, N.; Ghosh, S.; Glaesemann, K.; Gotz, A. W.; Hammond, J.; Helms, V.; Hermes, E. D.; Hirao, K.; Hirata, S.; Jacquelin, M.; Jensen, L.; Johnson, B. G.; Jonsson, H.; Kendall, R. A.; Klemm, M.; Kobayashi, R.; Konkov, V.; Krishnamoorthy, S.; Krishnan, M.; Lin, Z.; Lins, R. D.; Littlefield, R. J.; Logsdail, A. J.; Lopata, K.; Ma, W.; Marenich, A. V.; Martin del Campo, J.; Mejia-Rodriguez, D.; Moore, J. E.; Mullin, J. M.; Nakajima, T.; Nascimento, D. R.; Nichols, J. A.; Nichols, P. J.; Nieplocha, J.; Otero-de-la-Roza, A.; Palmer, B.; Panyala, A.; Pirojsirikul, T.; Peng, B.; Peverati, R.; Pittner, J.; Pollack, L.; Richard, R. M.; Sadayappan, P.; Schatz, G. C.; Shelton, W. A.; Silverstein, D. W.; Smith, D. M. A.; Soares, T. A.; Song, D.; Swart, M.; Taylor, H. L.; Thomas, G. S.; Tipparaju, V.; Truhlar, D. G.; Tsemekhman, K.; Van Voorhis, T.; Vazquez-Mayagoitia, A.; Verma, P.; Villa, O.; Vishnu, A.; Vogiatzis, K. D.; Wang, D.; Weare, J. H.; Williamson, M. J.; Windus, T. L.; Wolinski, K.; Wong, A. T.; Wu, Q.; Yang, C.; Yu, Q.; Zacharias, M.; Zhang, Z.; Zhao, Y.; Harrison, R. J.
Journal of Chemical Physics (2020), 152 (18), 184102CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A review. Specialized computational chem. packages have permanently reshaped the landscape of chem. and materials science by providing tools to support and guide exptl. efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principle-driven methodologies to model complex chem. and materials processes. Over the past few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in mol. and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chem. suite, including its history, design principles, parallel tools, current capabilities, outreach, and outlook. (c) 2020 American Institute of Physics.
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Neese, F. The ORCA program system. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 73– 78, DOI: 10.1002/wcms.81
Google Scholar
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The ORCA program system
Neese, Frank
Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (1), 73-78CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
A review. ORCA is a general-purpose quantum chem. program package that features virtually all modern electronic structure methods (d. functional theory, many-body perturbation and coupled cluster theories, and multireference and semiempirical methods). It is designed with the aim of generality, extendibility, efficiency, and user friendliness. Its main field of application is larger mols., transition metal complexes, and their spectroscopic properties. ORCA uses std. Gaussian basis functions and is fully parallelized. The article provides an overview of its current possibilities and documents its efficiency.
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Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988, 38, 3098, DOI: 10.1103/PhysRevA.38.3098
Google Scholar
42
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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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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43
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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Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Results obtained with the correlation energy density functionals of Becke and Lee, Yang and Parr. Chem. Phys. Lett. 1989, 157, 200– 206, DOI: 10.1016/0009-2614(89)87234-3
Google Scholar
44
Results obtained with the correlation energy density functionals of Becke and Lee, Yang and Parr
Miehlich, Burkhard; Savin, Andreas; Stoll, Hermann; Preuss, Heinzwerner
Chemical Physics Letters (1989), 157 (3), 200-6CODEN: CHPLBC; ISSN:0009-2614.
Two recently published d. functionals (Becke, A.D., 1988 and Lee, C. et al., 1988) are used to calc. the correlation energies of first-row atoms, ions and mols. The correlation contributions to ionization energies, electron affinities and dissocn. energies thus obtained are of comparable quality to those of other d. functionals.
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45
Pastorczak, E.; Pernal, K. Correlation Energy from the Adiabatic Connection Formalism for Complete Active Space Wave Functions. J. Chem. Theory Comput. 2018, 14, 3493– 3503, DOI: 10.1021/acs.jctc.8b00213
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45
Correlation Energy from the Adiabatic Connection Formalism for Complete Active Space Wave Functions
Pastorczak, Ewa; Pernal, Katarzyna
Journal of Chemical Theory and Computation (2018), 14 (7), 3493-3503CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
Recently, the adiabatic connection (AC) formula for the electron correlation energy has been proposed for a broad class of multireference wave functions (Pernal, K. Electron Correlation from the Adiabatic Connection for Multireference Wave Functions. Lett. 2018, 120, 013001). We show that the AC formula used together with the extended RPA (ERPA) can be efficiently applied to complete active space (CAS) wave functions to recover the remaining electron correlation. Unlike most of the perturbation theory approaches, the proposed AC-CAS method does not require construction of higher than two-electron reduced d. matrixes, which offers an immediate computational saving. In addn., we show that typically the AC-CAS systematically reduces the errors of both the abs. value of energy and of the energy differences (energy barrier) upon enlarging active spaces for electrons and orbitals. AC-CAS consistently gains in accuracy from including more active electrons. We also propose and study that the performance of the AC0 approach resulting from the first-order expansion of the AC integrand at the coupling const. equal to 0. AC0 avoids solving the full ERPA eigenequation, replacing it with small-dimension eigenproblems, while retaining good accuracy of the AC-CAS method. Low computational cost, compared to AC-CAS or perturbational approaches, makes AC0 the most efficient ab initio approach to capturing electron correlation for the CAS wave functions.
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46
Pastorczak, E.; Pernal, K. Electronic Excited States from the Adiabatic-Connection Formalism with Complete Active Space Wave Functions. J. Phys. Chem. Lett. 2018, 9, 5534– 5538, DOI: 10.1021/acs.jpclett.8b02391
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46
Electronic Excited States from the Adiabatic-Connection Formalism with Complete Active Space Wave Functions
Pastorczak, Ewa; Pernal, Katarzyna
Journal of Physical Chemistry Letters (2018), 9 (18), 5534-5538CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
It is demonstrated how the recently proposed multireference adiabatic-connection (AC) approxn. for electron correlation energy (Pernal, K., Electron Correlation from the Adiabatic Connection for Multireference Wave Functions; Phys. Rev. Lett. 2018, 120, 013001) can be extended to predicting correlation energy in excited states of mols. It is the first successful application of the AC approach to computing excited-states energies of mols. using a complete active space (CAS) wave function as a ref. The unique feature of the AC-CAS approach with respect to popular methods such as CASPT2 and NEVPT2 is that it requires only one- and two-particle reduced d. matrixes, making it possible to efficiently treat large spaces of active electrons. Application of the simpler variant of AC, the AC0, which is based on the first-order expansion of the AC integrand at the uncorrelated system limit, to excited states yields excitation energies with accuracy rivaling that of the NEVPT2 method but at greatly reduced computational cost.
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Pastorczak, E.; Hapka, M.; Veis, L.; Pernal, K. Capturing the Dynamic Correlation for Arbitrary Spin-Symmetry CASSCF Reference with Adiabatic Connection Approaches: Insights into the Electronic Structure of the Tetramethyleneethane Diradical. J. Phys. Chem. Lett. 2019, 10, 4668– 4674, DOI: 10.1021/acs.jpclett.9b01582
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47
Capturing the Dynamic Correlation for Arbitrary Spin-Symmetry CASSCF Reference with Adiabatic Connection Approaches: Insights into the Electronic Structure of the Tetramethyleneethane Diradical
Pastorczak, Ewa; Hapka, Michal; Veis, Libor; Pernal, Katarzyna
Journal of Physical Chemistry Letters (2019), 10 (16), 4668-4674CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
The recently proposed approach to multireference dynamic correlation energy based on the adiabatic connection (AC) is extended to an arbitrary spin symmetry of the ref. state. We show that both the spin-free AC approach and its computationally inexpensive approxn., AC0, when combined with a complete active space wave function, constitute viable alternatives to the perturbation-based and d.-functional-based multiconfiguration methods. In particular, the AC0 approach, thanks to its favorable scaling with the system size and the size of the active space, allows for treating larger systems than its perturbation-based counterparts while maintaining comparable accuracy. We show the method's robustness on illustrative chem. systems, including the elusive tetramethyleneethane (TME) diradical, potential energy surfaces of which present a challenge to most computational approaches. For the latter system, AC0 outperforms other methods, staying in close agreement with the full CI quantum Monte Carlo benchmark. A careful anal. of the contributions to the correlation energy of TME's lowest singlet and triplet states reveals the subtle interplay of the dynamic and static correlation as the key to understanding the shape of the diradical's potential energy surfaces.
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Beran, P.; Matoušek, M.; Hapka, M.; Pernal, K.; Veis, L. Density matrix renormalization group with dynamical correlation via adiabatic connection. J. Chem. Theory Comput. 2021, 17, 7575– 7585, DOI: 10.1021/acs.jctc.1c00896
Google Scholar
48
Density Matrix Renormalization Group with Dynamical Correlation via Adiabatic Connection
Beran, Pavel; Matousek, Mikulas; Hapka, Michal; Pernal, Katarzyna; Veis, Libor
Journal of Chemical Theory and Computation (2021), 17 (12), 7575-7585CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
The quantum chem. version of the d. matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calcns. of strongly correlated mol. systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated mols., in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection (AC) technique which requires only up to two-body active space reduced d. matrixes. We report the encouraging results of this approach on typical candidates for DMRG computations, namely, n-acenes (n = 2 → 7), Fe(II)-porphyrin, and the Fe3S4 cluster.
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Matoušek, M.; Hapka, M.; Veis, L.; Pernal, K. Toward more accurate adiabatic connection approach for multireference wavefunctions. J. Chem. Phys. 2023, 158, 054105 DOI: 10.1063/5.0131448
Google Scholar
49
Toward more accurate adiabatic connection approach for multireference wavefunctions
Matousek, Mikulas; Hapka, Michal; Veis, Libor; Pernal, Katarzyna
Journal of Chemical Physics (2023), 158 (5), 054105CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to compute the dynamic correlation within the complete active space SCF and d. matrix renormalization group (DMRG) models. Practical realizations of AC have been based on two approxns.: (i) fixing one- and two-electron reduced d. matrixes (1- and 2-RDMs) at the zero-coupling const. limit and (ii) extended RPA (ERPA). This work investigates the effect of removing the "fixed-RDM" approxn. in AC. The anal. is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall Hamiltonians. Exact ref. AC integrands are generated from the DMRG full CI solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling const. in the ERPA equations. Calcns. for model mols. indicate that lifting the fixed-RDM approxn. is a viable way toward improving the accuracy of existing AC approxns. (c) 2023 American Institute of Physics.
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Dreuw, A.; Hoffmann, M. T. The inverted singlet-triplet gap: a vanishing myth?. Front. Chem. 2023, 11, 1239604 DOI: 10.3389/fchem.2023.1239604
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50
The inverted singlet-triplet gap: a vanishing myth?
Dreuw, Andreas; Hoffmann, Marvin
Frontiers in Chemistry (Lausanne, Switzerland) (2023), 11 (), 1239604CODEN: FCLSAA; ISSN:2296-2646. (Frontiers Media S.A.)
Mols. with an inverted singlet-triplet gap (STG) between the first excited singlet and triplet states, for example, heptazine, have recently been reported and gained substantial attention since they violate the famous Hund's rule. Utilizing state-of-the-art high-level ab initio methods, the singlet-triplet gap vanishes and approaches zero from below whatever is improved in the theor. description of the mols.: the basis set or the level of electron correlation. Seemingly, the phenomenon of inverted singlet-triplet gaps tends to vanish the closer we observe.
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Abstract
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Figure 1
Figure 1. Structures of the studied molecules. The color codes are as follows: N (blue), C (brown), and H (white).
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Figure 2
Figure 2. Natural orbitals of system 2 corresponding to state-averaged CASSCF(14,14) calculations with one singlet and one triplet states.
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Figure 3
Figure 3. Left panel: ST energy gaps without spin polarization (eq 4). Right panel: ST energy gaps with spin polarization from all occupied-virtual π orbital pairs (eqs 13 and 10). Results obtained with BLYP ground state orbitals vs EOM-CCSD values for the extended test set of molecules.
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Figure 4
Figure 4. Left panel: Contributions from spin polarization to ST energy gaps (second term on the right-hand side of eq 13) vs ST energy gaps without spin polarization (eq 4). Right panel: Molecules corresponding to the lowest and highest HL exchange interaction. Results obtained with BLYP ground state orbitals.
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Figure 5
Figure 5. S₁–T₁ energy gaps for systems 1–6, panel (a). Mean unsigned deviations of the gaps with respect to Mk-MRCCSD(T) values, panel (b). CASSCF, AC0, ACn, and NEVPT2 results correspond to the (14,14) active space.
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Figure 6
Figure 6. S₁–T₁ energy gaps for systems 1–6. 0: no spin polarization (eq 4); sp_π: PT-based model accounting for spin polarization (eq 13); CASSCF: spin polarization from CASSCF(14,14); ACn: spin polarization at the CAS(14,14) level and dynamic correlation via adiabatic connection (eq 15).
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References
This article references 50 other publications.
1. 1
  Tyan, Y.-S. Organic light-emitting-diode lighting overview. J. Photonics Energy 2011, 1, 011009, DOI: 10.1117/1.3529412
  There is no corresponding record for this reference.
2. 2
  Hong, G.; Gan, X.; Leonhardt, C.; Zhang, Z.; Seibert, J.; Busch, J. M.; Bräse, S. A Brief History of OLEDs─Emitter Development and Industry Milestones. Adv. Mater. 2021, 33, 2005630 DOI: 10.1002/adma.202005630
  2
  A Brief History of OLEDs-Emitter Development and Industry Milestones
  Hong, Gloria; Gan, Xuemin; Leonhardt, Celine; Zhang, Zhen; Seibert, Jasmin; Busch, Jasmin M.; Braese, Stefan
  Advanced Materials (Weinheim, Germany) (2021), 33 (9), 2005630CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
  Org. light-emitting diodes (OLEDs) have come a long way ever since their first introduction in 1987 at Eastman Kodak. Today, OLEDs are esp. valued in the display and lighting industry for their promising features. As one of the research fields that equally inspires and drives development in academia and industry, OLED device technol. has continuously evolved over more than 30 years. OLED devices have come forward based on three generations of emitter materials relying on fluorescence (first generation), phosphorescence (second generation), and thermally activated delayed fluorescence (third generation). Furthermore, research in academia and industry toward the fourth generation of OLEDs is in progress. Excerpts from the history of green, orange-red, and blue OLED emitter development on the side of academia and milestones achieved by key players in the industry are included in this report.
  >> More from SciFinder ^®
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhsl2ksLo%253D&md5=c7c3fb2f400d493fb80cfd8019d5372c
3. 3
  Hund, F. Zur Deutung verwickelter Spektren, insbesondere der Elemente Scandium bis Nickel. Z. Phys. 1925, 33, 345– 371, DOI: 10.1007/BF01328319
  3
  The interpretation of complicated spectra
  Hund, F.
  Zeitschrift fuer Physik (1925), 33 (), 345-71CODEN: ZEPYAA; ISSN:0044-3328.
  On the basis of the suggestions of Russel and Saunders, Pauli and Heisenberg on the interaction of electrons in emitting light, the spectral terms of some elements have been correlated to definite quantum nos. which specify the arrangements of the electrons in the atoms. For Sc it is found that the first electron to be added to the Sc+++ ion goes into a 33 orbit giving a doublet 2D term as the normal state of Sc++. The next electron enters a 41 orbit and gives a 3D term for the normal state for the Sc+. The last electron enters a 41 orbit and gives a 2D term for the normal state. The predicted terms for the normal states agree with the exptly. obsd. terms. It is noted that for terms of the same quantum nos. (i. c. the azimuthal quantum nos. of the electrons which do not form a closed shell) that term which has the highest multiplicity lies lowest. Making use of this rule it has been possible to give the type of term (S, P, D, F, G, etc.) and its multiplicity for the normal states of the second short series of the periodic table and for the elements from Sc to Zn. The predicted term agrees with expt. for all cases in which the spectra are known with the exception of Cr. In this case the term for four electrons in the 33 shell and two in the 41 shell was predicted and expt. agrees with five electrons in the 32 shell and one in the 41 shell. The spectra of O, Ne, Sn and Pb are discussed and found to agree with theory. The singly ionized atoms from Ca to Fe inclusive are also considered and excellent agreement between calcn. and expt. is secured.
  >> More from SciFinder ^®
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4. 4
  Li, Z.; Li, Z. R.; Meng, H. Organic Light-Emitting Materials and Devices; CRC Press, 2006.
  There is no corresponding record for this reference.
5. 5
  Endo, A.; Sato, K.; Yoshimura, K.; Kai, T.; Kawada, A.; Miyazaki, H.; Adachi, C. Efficient up-conversion of triplet excitons into a singlet state and its application for organic light emitting diodes. Appl. Phys. Lett. 2011, 98, 083302 DOI: 10.1063/1.3558906
  5
  Efficient up-conversion of triplet excitons into a singlet state and its application for organic light emitting diodes
  Endo, Ayataka; Sato, Keigo; Yoshimura, Kazuaki; Kai, Takahiro; Kawada, Atsushi; Miyazaki, Hiroshi; Adachi, Chihaya
  Applied Physics Letters (2011), 98 (8), 083302/1-083302/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
  A material possessing a small energy gap between its singlet and triplet excited states, ΔE1-3, which allows efficient up-conversion of triplet excitons into a singlet state and leads to efficient thermally activated delayed fluorescence (TADF), is reported. The compd., 2-biphenyl-4,6-bis(12-phenylindolo[2,3-a]carbazol-11-yl)-1,3,5-triazine, breaks the restriction of a large energy gap, with a ΔE1-3 of just 0.11 eV, while maintaining a high fluorescent radiative decay rate (kr ∼ 107). The intense TADF provides a pathway for highly efficient electroluminescence. (c) 2011 American Institute of Physics.
  >> More from SciFinder ^®
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6. 6
  Uoyama, H.; Goushi, K.; Shizu, K.; Nomura, H.; Adachi, C. Highly efficient organic light-emitting diodes from delayed fluorescence. Nature 2012, 492, 234– 238, DOI: 10.1038/nature11687
  6
  Highly efficient organic light-emitting diodes from delayed fluorescence
  Uoyama, Hiroki; Goushi, Kenichi; Shizu, Katsuyuki; Nomura, Hiroko; Adachi, Chihaya
  Nature (London, United Kingdom) (2012), 492 (7428), 234-238CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)
  The inherent flexibility afforded by mol. design has accelerated the development of a wide variety of org. semiconductors over the past 2 decades. In particular, great advances were made in the development of materials for org. light-emitting diodes (OLEDs), from early devices based on fluorescent mols. to those using phosphorescent mols. In OLEDs, elec. injected charge carriers recombine to form singlet and triplet excitons in a 1:3 ratio; the use of phosphorescent metal-org. complexes exploits the normally nonradiative triplet excitons and so enhances the overall electroluminescence efficiency. Here the authors report a class of metal-free org. electroluminescent mols. in which the energy gap between the singlet and triplet excited states is minimized by design, thereby promoting highly efficient spin up-conversion from nonradiative triplet states to radiative singlet states while maintaining high radiative decay rates, of >106 decays per s. These mols. harness both singlet and triplet excitons for light emission through fluorescence decay channels, leading to an intrinsic fluorescence efficiency >90% and a very high external electroluminescence efficiency, of >19%, which is comparable to that achieved in high-efficiency phosphorescence-based OLEDs.
  >> More from SciFinder ^®
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7. 7
  Goushi, K.; Yoshida, K.; Sato, K.; Adachi, C. Organic light-emitting diodes employing efficient reverse intersystem crossing for triplet-to-singlet state conversion. Nat. Photonics 2012, 6, 253– 258, DOI: 10.1038/nphoton.2012.31
  7
  Organic light-emitting diodes employing efficient reverse intersystem crossing for triplet-to-singlet state conversion
  Goushi, Kenichi; Yoshida, Kou; Sato, Keigo; Adachi, Chihaya
  Nature Photonics (2012), 6 (4), 253-258CODEN: NPAHBY; ISSN:1749-4885. (Nature Publishing Group)
  Light emission from org. light-emitting diodes that make use of fluorescent materials have an internal quantum efficiency that is typically limited to no more than 25% due to the creation of non-radiative triplet excited states. Here, we report the use of electron-donating and electron-accepting mols. that allow a very high reverse intersystem crossing of 86.5% between non-radiative triplet and radiative singlet excited states and thus a means of achieving enhanced electroluminescence. Org. light-emitting diodes made using m-MTDATA as the donor material and 3TPYMB as the acceptor material demonstrate that external quantum efficiencies as high as 5.4% can be achieved, and we believe that the approach will offer even higher values in the future as a result of careful material selection.
  >> More from SciFinder ^®
  https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38Xjs1SqtbY%253D&md5=4b1e5049bc75aa992f01cde7f58e4bf5
8. 8
  Nakanotani, H.; Higuchi, T.; Furukawa, T.; Masui, K.; Morimoto, K.; Numata, M.; Tanaka, H.; Sagara, Y.; Yasuda, T.; Adachi, C. High-efficiency organic light-emitting diodes with fluorescent emitters. Nat. Commun. 2014, 5, 4016 DOI: 10.1038/ncomms5016
  8
  High-efficiency organic light-emitting diodes with fluorescent emitters
  Nakanotani, Hajime; Higuchi, Takahiro; Furukawa, Taro; Masui, Kensuke; Morimoto, Kei; Numata, Masaki; Tanaka, Hiroyuki; Sagara, Yuta; Yasuda, Takuma; Adachi, Chihaya
  Nature Communications (2014), 5 (), 4016CODEN: NCAOBW; ISSN:2041-1723. (Nature Publishing Group)
  Fluorescence-based org. light-emitting diodes have continued to attract interest because of their long operational lifetimes, high color purity of electroluminescence and potential to be manufd. at low cost in next-generation full-color display and lighting applications. In fluorescent mols., however, the exciton prodn. efficiency is limited to 25% due to the deactivation of triplet excitons. Here we report fluorescence-based org. light-emitting diodes that realize external quantum efficiencies as high as 13.4-18% for blue, green, yellow and red emission, indicating that the exciton prodn. efficiency reached nearly 100%. The high performance is enabled by utilization of thermally activated delayed fluorescence mols. as assistant dopants that permit efficient transfer of all elec. generated singlet and triplet excitons from the assistant dopants to the fluorescent emitters. Org. light-emitting diodes employing this exciton harvesting process provide freedom for the selection of emitters from a wide variety of conventional fluorescent mols.
  >> More from SciFinder ^®
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9. 9
  Hosokai, T.; Matsuzaki, H.; Nakanotani, H.; Tokumaru, K.; Tsutsui, T.; Furube, A.; Nasu, K.; Nomura, H.; Yahiro, M.; Adachi, C. Evidence and mechanism of efficient thermally activated delayed fluorescence promoted by delocalized excited states. Sci. Adv. 2017, 3, e1603282 DOI: 10.1126/sciadv.1603282
  9
  Evidence and mechanism of efficient thermally activated delayed fluorescence promoted by delocalized excited states
  Hosokai, Takuya; Matsuzaki, Hiroyuki; Nakanotani, Hajime; Tokumaru, Katsumi; Tsutsui, Tetsuo; Furube, Akihiro; Nasu, Keirou; Nomura, Hiroko; Yahiro, Masayuki; Adachi, Chihaya
  Science Advances (2017), 3 (5), e1603282/1-e1603282/9CODEN: SACDAF; ISSN:2375-2548. (American Association for the Advancement of Science)
  The design of org. compds. with nearly no gap between the first excited singlet (S1) and triplet (T1) states has been demonstrated to result in an efficient spin-flip transition from the T1 to S1 state, i.e., reverse intersystem crossing (RISC), and facilitate light emission as thermally activated delayed fluorescence (TADF). However, many TADF mols. have shown that a relatively appreciable energy difference between the S1 and T1 states (∼0.2 eV) could also result in a high RISC rate. We revealed from a comprehensive study of optical properties of TADF mols. that the formation of delocalized states is the key to efficient RISC and identified a chem. template for these materials. In addn., simple structural confinement further enhances RISC by suppressing structural relaxation in the triplet states. Our findings aid in designing advanced org. mols. with a high rate of RISC and, thus, achieving the max. theor. electroluminescence efficiency in org. light-emitting diodes.
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10. 10
  de Silva, P. Inverted singlet–triplet gaps and their relevance to thermally activated delayed fluorescence. J. Phys. Chem. Lett. 2019, 10, 5674– 5679, DOI: 10.1021/acs.jpclett.9b02333
  10
  Inverted Singlet-Triplet Gaps and Their Relevance to Thermally Activated Delayed Fluorescence
  de Silva, Piotr
  Journal of Physical Chemistry Letters (2019), 10 (18), 5674-5679CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  The basic design principle for emitters exhibiting thermally activated delayed fluorescence (TADF) is the minimization of the singlet-triplet gap. While typically this gap is pos., a possible inversion of states has been proposed as a pathway to improve the efficiency of org. light-emitting diodes. Despite the efforts to design such emitters, there are very few reports indicating that it is at all possible. We analyze the problem of the gap inversion from the perspective of the electronic structure theory. The key result is that inversion is possible but requires a substantial contribution of double excitations and that commonly used cheap electronic structure methods would fail to predict it.
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11. 11
  Sobolewski, A. L.; Domcke, W. Are heptazine-based organic light-emitting diode chromophores thermally activated delayed fluorescence or inverted singlet–triplet systems?. J. Phys. Chem. Lett. 2021, 12, 6852– 6860, DOI: 10.1021/acs.jpclett.1c01926
  11
  Are Heptazine-Based Organic Light-Emitting Diode Chromophores Thermally Activated Delayed Fluorescence or Inverted Singlet-Triplet Systems?
  Sobolewski, Andrzej L.; Domcke, Wolfgang
  Journal of Physical Chemistry Letters (2021), 12 (29), 6852-6860CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  Two chromophores derived from heptazine, HAP-3MF and HAP-3TPA, were synthesized and tested as emitters in light-emitting diodes (OLEDs) by Adachi and co-workers. Both emitters were shown to exhibit quantum efficiencies which exceed the theor. max. of conventional fluorescent OLEDs. The enhanced emission efficiency was explained by the mechanism of thermally activated delayed fluorescence (TADF). In the present work, the electronic excitation energies and essential features of the topog. of the excited-state potential-energy surfaces of HAP-3MF and HAP-3TPA have been investigated with a wave function-based ab initio method (ADC(2)). It is found that HAP-3MF is an inverted singlet-triplet (IST) system; i.e., the energies of the S1 and T1 states are robustly inverted in violation of Hund's multiplicity rule. Notably, HAP-3MF presumably is the first IST emitter which was implemented in an OLED device. In HAP-3TPA, on the other hand, the vertical excitation energies of the S1 and T1 states are essentially degenerate. The excited states exhibit vibrational stabilization energies of similar magnitude along different relaxation coordinates, resulting in adiabatic excitation energies which also are nearly degenerate. HAP-3TPA is found to be a chromophore at the borderline of TADF and IST systems. The spectroscopic data reported by Adachi and co-workers for HAP-3MF and HAP-3TPA are analyzed in light of these computational results.
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12. 12
  Pios, S.; Huang, X.; Sobolewski, A. L.; Domcke, W. Triangular boron carbon nitrides: An unexplored family of chromophores with unique properties for photocatalysis and optoelectronics. Phys. Chem. Chem. Phys. 2021, 23, 12968– 12975, DOI: 10.1039/D1CP02026A
  12
  Triangular boron carbon nitrides: an unexplored family of chromophores with unique properties for photocatalysis and optoelectronics
  Pios, Sebastian; Huang, Xiang; Sobolewski, Andrzej L.; Domcke, Wolfgang
  Physical Chemistry Chemical Physics (2021), 23 (23), 12968-12975CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  It has recently been shown that cycl[3.3.3]azine and heptazine (1,3,4,6,7,9,9b-heptaazaphenalene) as well as related azaphenalenes exhibit inverted singlet and triplet states, i.e., the energy of the lowest singlet excited state (S1) is below the energy of the lowest triplet excited state (T1). This feature is unique among all known arom. chromophores and is of outstanding relevance for applications in photocatalysis and org. optoelectronics. Heptazine is the building block of the polymeric material graphitic carbon nitride which is an extensively explored photocatalyst in hydrogen evolution photocatalysis. Derivs. of heptazine have also been identified as efficient emitters in org. light emitting diodes (OLEDs). In both areas, the inverted singlet-triplet gap of heptazine is a highly beneficial feature. In photocatalysis, the absence of a long-lived triplet state eliminates the activation of atm. oxygen, which is favorable for long-term operational stability. In optoelectronics, singlet-triplet inversion implies the possibility of 100% fluorescence efficiency of electron-hole recombination. However, the absorption and luminescence wavelengths of heptazine and the S1-S0 transition dipole moment are difficult to tune for optimal functionality. In this work, we employed high-level ab initio electronic structure theory to devise and characterize a large family of novel heteroarom. chromophores, the triangular boron carbon nitrides. These novel heterocycles inherit essential spectroscopic features from heptazine, in particular the inverted singlet-triplet gap, while their absorption and luminescence spectra and transition dipole moments are widely tuneable. For applications in photocatalysis, the wavelength of the absorption max. can be tuned to improve the overlap with the solar spectrum at the surface of earth. For applications in OLEDs, the color of emission can be adjusted and the fluorescence yield can be enhanced.
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13. 13
  Ricci, G.; Sancho-García, J.-C.; Olivier, Y. Establishing design strategies for emissive materials with an inverted singlet–triplet energy gap (INVEST): a computational perspective on how symmetry rules the interplay between triplet harvesting and light emission. J. Mater. Chem. C 2022, 10, 12680– 12698, DOI: 10.1039/D2TC02508F
  13
  Establishing design strategies for emissive materials with an inverted singlet-triplet energy gap (INVEST): a computational perspective on how symmetry rules the interplay between triplet harvesting and light emission
  Ricci, Gaetano; Sancho-Garcia, Juan-Carlos; Olivier, Yoann
  Journal of Materials Chemistry C: Materials for Optical and Electronic Devices (2022), 10 (35), 12680-12698CODEN: JMCCCX; ISSN:2050-7534. (Royal Society of Chemistry)
  The inversion of the lowest singlet and triplet excited state energy gaps, in fully org. triangle-based compds., can give rise to new exergonic pathways to enhance the performance of org. light-emitting diodes (OLEDs), going beyond the novel yet promising thermally activated delayed fluorescence (TADF) mechanism. The origin of this inversion, arises from the interplay between exchange and electron correlation effects and was extensively studied in the last few years, using wavefunction-based methods. A proper picture of the structure-property relations characterizing these systems is still lacking. The effect of different symmetry point groups (D3h, C2v, C3h and C3v) on the orbital localization was assessed to shed light on the role played by symmetry in detg. the optical features of the triangulene systems (on both S1-T1 inversion and oscillator strengths). The presence of the C2 axis and σv plane (as in the D3h, C2v and C3v groups) turned out to be crit. for ensuring proper orbital localization aimed at minimizing exchange interaction, therefore favoring the inversion process. Adopting the C2v (and its subgroups) symmetry through a proper doping pattern of the triangulene core, by introducing substituents or by merging 2 triangulene cores, is the only way to achieve a neg. ΔEST and a nonzero oscillator strength. The lessons learned from this anal. to establish design rules aimed at helping the identification of inverted singlet-triplet (INVEST) emitters for applications in next-generation OLEDs are summarized.
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14. 14
  Ehrmaier, J.; Huang, X.; Rabe, E. J.; Corp, K. L.; Schlenker, C. W.; Sobolewski, A. L.; Domcke, W. Molecular design of heptazine-based photocatalysts: effect of substituents on photocatalytic efficiency and photostability. J. Phys. Chem. A 2020, 124, 3698– 3710, DOI: 10.1021/acs.jpca.0c00488
  14
  Molecular design of heptazine-based photocatalysts: effect of substituents on photocatalytic efficiency and photostability
  Ehrmaier, Johannes; Huang, Xiang; Rabe, Emily J.; Corp, Kathryn L.; Schlenker, Cody W.; Sobolewski, Andrzej L.; Domcke, Wolfgang
  Journal of Physical Chemistry A (2020), 124 (19), 3698-3710CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  Recently, a deriv. of the heptazine (tris-triazine) mol., trianisole-heptazine (TAHz), was synthesized and was shown to catalyze the oxidn. of water to hydroxyl radicals under 365 nm LED light in a homogeneous reaction (E. J. Rabe et al.,). The possibility of water photo-oxidn. with a precisely defined mol. catalyst in neat solvents opens new perspectives for clarifying the fundamental reaction mechanisms involved in water oxidn. photocatalysis. In the present work, the effects of chem. substituents on the three CH positions of Hz on the photocatalytic reactivity were explored with wave function-based ab initio electronic-structure calcns. for hydrogen-bonded complexes of Hz and three selected Hz derivs. (TAHz, trichloro-Hz, and tricyano-Hz) with a water mol. While anisole is an electron-donating substituent, Cl is a weakly electron-withdrawing substituent and CN is a strongly electron-withdrawing substituent. It is shown that the barrier for the photoinduced abstraction of an H atom from the water mol. is raised (lowered) by electron-donating (electron-withdrawing) substituents. The highly mobile and reactive hydroxyl radicals generated by water oxidn. can recombine with the reduced chromophore radicals to yield photohydrates. The effect of substituents on the thermodn. of the photohydration reaction was computed. Among the four chromophores studied, TAHz stands out on account of the metastability of its photohydrate, which suggests self-healing of the photocatalyst after oxidn. of TAHzH radicals by OH radicals. In addn., the effect of substituents on the H atom photodetachment reaction from the reduced chromophores, which closes the catalytic cycle, has been investigated. The energy of the repulsive 2πσ* state, which drives the photodetachment reaction is lowered (raised) by electron-donating (electron withdrawing) substituents. All four chromophores exhibit inverted S1/T1 gaps. This feature eliminates long-lived triplet states and thus avoids the activation of mol. oxygen to highly reactive singlet oxygen.
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15. 15
  Ehrmaier, J.; Rabe, E. J.; Pristash, S. R.; Corp, K. L.; Schlenker, C. W.; Sobolewski, A. L.; Domcke, W. Singlet–triplet inversion in heptazine and in polymeric carbon nitrides. J. Phys. Chem. A 2019, 123, 8099– 8108, DOI: 10.1021/acs.jpca.9b06215
  15
  Singlet-Triplet Inversion in Heptazine and in Polymeric Carbon Nitrides
  Ehrmaier, Johannes; Rabe, Emily J.; Pristash, Sarah R.; Corp, Kathryn L.; Schlenker, Cody W.; Sobolewski, Andrzej L.; Domcke, Wolfgang
  Journal of Physical Chemistry A (2019), 123 (38), 8099-8108CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  According to Hund's rule, the lowest triplet state (T1) is lower in energy than the lowest excited singlet state (S1) in closed-shell mols. The exchange integral lowers the energy of the triplet state and raises the energy of the singlet state of the same orbital character, leading to a pos. singlet-triplet energy gap (ΔST). Exceptions are known for biradicals and charge-transfer excited states of large mols. in which the HOMO and the LUMO are spatially sepd., resulting in a small exchange integral. In the present work, we discovered with ADC(2), CC2, EOM-CCSD, and CASPT2 calcns. that heptazine (1,3,4,6,7,9,9b-heptaazaphenalene or tri-s-triazine) exhibits an inverted S1/T1 energy gap (ΔST ≈ -0.25 eV). This appears to be the first example of a stable closed-shell org. mol. exhibiting S1/T1 inversion at its equil. geometry. The origins of this phenomenon are the nearly pure HOMO-LUMO excitation character of the S1 and T1 states and the lack of spatial overlap of HOMO and LUMO due to a unique structure of these orbitals of heptazine. The S1/T1 inversion is found to be extremely robust, being affected neither by substitution of heptazine nor by oligomerization of heptazine units. Using time-resolved photoluminescence and transient absorption spectroscopy, we investigated the excited-state dynamics of 2,5,8-tris(4-methoxyphenyl)-1,3,4,6,7,9,9b-heptaazaphenalene (TAHz), a chem. stable heptazine deriv., in the presence of external heavy atom sources as well as triplet-quenching oxygen. These spectroscopic data are consistent with TAHz singlet excited state decay in the absence of a low-energy triplet loss channel. The absence of intersystem crossing and an exceptionally low radiative rate result in unusually long S1 lifetimes (of the order of hundreds of nanoseconds in nonaq. solvents). These features of the heptazine chromophore have profound implications for org. optoelectronics as well as for water-splitting photocatalysis with heptazine-based polymers (e.g., graphitic carbon nitride) which have yet to be systematically explored and exploited.
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16. 16
  Li, J.; Nakagawa, T.; MacDonald, J.; Zhang, Q.; Nomura, H.; Miyazaki, H.; Adachi, C. Highly Efficient Organic Light-Emitting Diode Based on a Hidden Thermally Activated Delayed Fluorescence Channel in a Heptazine Derivative. Adv. Mater. 2013, 25, 3319– 3323, DOI: 10.1002/adma.201300575
  16
  Highly Efficient Organic Light-Emitting Diode Based on a Hidden Thermally Activated Delayed Fluorescence Channel in a Heptazine Derivative
  Li, Jie; Nakagawa, Tetsuya; Zhang, Qisheng; Nomura, Hiroko; Miyazaki, Hiroshi; Adachi, Chihaya
  Advanced Materials (Weinheim, Germany) (2013), 25 (24), 3319-3323CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
  The authors have designed and synthesized an orange-red thermally activated delayed fluorescence (TADF) emitter, 4,4',4"-(1,3,3a1,4,6,7,9-heptaazaphenalene-2,5,8-triyl)tris[N,N-bis[4-(tert-butyl)phenyl]aniline] (HAP-3TPA), which has a HAP core as an electron-accepting unit and three electron-donating units of TPA. An org. electroluminescent device (OLED) contg. HAP-3TPA showed high performance with ηext = 17.5 ± 1.3 % , max. luminance of 17000 ± 1600 cd m-2, max. current efficiency and power efficiency of 25.9 + 1.6 cd A-1 and 22.1 ± 1.2 lm W-1, resp., and a turn-one voltage of 4.4 + 0.3 V at a luminance of 100 cd m-2 without any light out-coupling enhancement. Although HAP-3TPA demonstrated very weak TADF in the PL process, upconversion from T1 to S1 was quite efficient under elec. excitation, resulting in high EL efficiency. Thus, in principle, while mols. may show only fluorescence and very faint TADF in PL, they may have an efficient pathway for TADF in EL.
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17. 17
  Li, J.; Zhang, Q.; Nomura, H.; Miyazaki, H.; Adachi, C. Thermally activated delayed fluorescence from 3n π* to 1n π* up-conversion and its application to organic light-emitting diodes. Appl. Phys. Lett. 2014, 105, 013301 DOI: 10.1063/1.4887346
  17
  Thermally activated delayed fluorescence from 3nπ* to 1nπ* up-conversion and its application to organic light-emitting diodes
  Li, Jie; Zhang, Qisheng; Nomura, Hiroko; Miyazaki, Hiroshi; Adachi, Chihaya
  Applied Physics Letters (2014), 105 (1), 013301/1-013301/4CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
  Intense nπ* fluorescence from a nitrogen-rich heterocyclic compd., 2,5,8-tris(4-fluoro-3-methylphenyl)-1,3,4,6,7,9,9b-heptaazaphenalene (HAP-3MF), is demonstrated. The overlap-forbidden nature of the nπ* transition and the higher energy of the 3ππ* state than the 3nπ* one lead to a small energy difference between the lowest singlet (S1) and triplet (T1) excited states of HAP-3MF. Green-emitting HAP-3MF has a moderate photoluminescence quantum yield of 0.26 in both toluene and doped film. However, an org. light-emitting diode contg. HAP-3MF achieved a high external quantum efficiency of 6.0%, indicating that HAP-3MF harvests singlet excitons through a thermally activated T1 → S1 pathway in the electroluminescent process. (c) 2014 American Institute of Physics.
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18. 18
  Li, J.; Nomura, H.; Miyazaki, H.; Adachi, C. Highly efficient exciplex organic light-emitting diodes incorporating a heptazine derivative as an electron acceptor. Chem. Commun. 2014, 50, 6174– 6176, DOI: 10.1039/C4CC01590H
  18
  Highly efficient exciplex organic light-emitting diodes incorporating a heptazine derivative as an electron acceptor
  Li, Jie; Nomura, Hiroko; Miyazaki, Hiroshi; Adachi, Chihaya
  Chemical Communications (Cambridge, United Kingdom) (2014), 50 (46), 6174-6176CODEN: CHCOFS; ISSN:1359-7345. (Royal Society of Chemistry)
  Highly efficient exciplex systems incorporating a heptazine deriv. (HAP-3MF) as an electron acceptor and 1,3-di(9H-carbazol-9-yl)benzene (mCP) as an electron donor are developed. An OLED contg. 8 wt.% HAP-3MF:mCP as an emitting layer exhibits a max. external quantum efficiency of 11.3%.
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19. 19
  Ricci, G.; San-Fabián, E.; Olivier, Y.; Sancho-García, J.-C. Singlet-triplet excited-state inversion in heptazine and related molecules: assessment of TD-DFT and ab initio methods. ChemPhysChem 2021, 22, 553– 560, DOI: 10.1002/cphc.202000926
  19
  Singlet-Triplet Excited-State Inversion in Heptazine and Related Molecules: Assessment of TD-DFT and ab initio Methods
  Ricci, G.; San-Fabian, E.; Olivier, Y.; Sancho-Garcia, J. C.
  ChemPhysChem (2021), 22 (6), 553-560CODEN: CPCHFT; ISSN:1439-4235. (Wiley-VCH Verlag GmbH & Co. KGaA)
  We have investigated the origin of the S1-T1 energy levels inversion for heptazine, and other N-doped π-conjugated hydrocarbons, leading thus to an unusually neg. singlet-triplet energy gap (ΔEST<0). Since this inversion might rely on substantial doubly-excited configurations to the S1 and/or T1 wavefunctions, we have systematically applied multi-configurational SA-CASSCF and SC-NEVPT2 methods, SCS-cor. CC2 and ADC(2) approaches, and linear-response TD-DFT, to analyze if the latter method could also face this challenging issue. We have also extended the study to B-doped π-conjugated systems, to see the effect of chem. compn. on the results. For all the systems studied, an intricate interplay between the singlet-triplet exchange interaction, the influence of doubly-excited configurations, and the impact of dynamic correlation effects, serves to explain the ΔEST<0 values found for most of the compds., which is not predicted by TD-DFT.
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20. 20
  Sanz-Rodrigo, J.; Ricci, G.; Olivier, Y.; Sancho-Garcia, J.-C. Negative singlet–triplet excitation energy gap in triangle-shaped molecular emitters for efficient triplet harvesting. J. Phys. Chem. A 2021, 125, 513– 522, DOI: 10.1021/acs.jpca.0c08029
  20
  Negative Singlet-Triplet Excitation Energy Gap in Triangle-Shaped Molecular Emitters for Efficient Triplet Harvesting
  Sanz-Rodrigo, J.; Ricci, G.; Olivier, Y.; Sancho-Garcia, J. C.
  Journal of Physical Chemistry A (2021), 125 (2), 513-522CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  The full harvesting of both singlet and triplet excitons can pave the way toward more efficient mol. light-emission mechanisms (i.e., TADF or thermally activated delayed fluorescence) beyond the spin statistics limit. This TADF mechanism benefits from low (but typically pos.) singlet-triplet energy gaps or ΔEST. Recent research has suggested the possibility of inverting the order of the energy of lowest singlet and triplet excited states, thus opening new pathways to promote light emission without any energy barrier through triplet to singlet conversion, which is systematically investigated here by means of theor. methods. To this end, we have selected a set of heteroatom-substituted triangle-shaped mols. (or triangulenes) for which ΔEST < 0 is predicted. We successfully rationalize the origin of that energy inversion and the reasons for which theor. methods might produce qual. inconsistent predictions depending on how they treat n-tuple excitations (e.g., the large contribution of double excitations for all of the ground and excited states involved). Unfortunately, the time-dependent d. functional theory method is unable to deal with the phys. effects driving this behavior, which prompted us to use more sophisticated ab initio methods here such as SA-CASSCF, SC-NEVPT2, SCS-CC2, and SCS-ADC(2).
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21. 21
  Aizawa, N.; Pu, Y.-J.; Harabuchi, Y.; Nihonyanagi, A.; Ibuka, R.; Inuzuka, H.; Dhara, B.; Koyama, Y.; Nakayama, K.-i.; Maeda, S.; Araoka, F.; Miyajima, D. Delayed fluorescence from inverted singlet and triplet excited states. Nature 2022, 609, 502– 506, DOI: 10.1038/s41586-022-05132-y
  21
  Delayed fluorescence from inverted singlet and triplet excited states
  Aizawa, Naoya; Pu, Yong-Jin; Harabuchi, Yu; Nihonyanagi, Atsuko; Ibuka, Ryotaro; Inuzuka, Hiroyuki; Dhara, Barun; Koyama, Yuki; Nakayama, Ken-ichi; Maeda, Satoshi; Araoka, Fumito; Miyajima, Daigo
  Nature (London, United Kingdom) (2022), 609 (7927), 502-506CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)
  Hund's multiplicity rule states that a higher spin state has a lower energy for a given electronic configuration1. Rephrasing this rule for mol. excited states predicts a pos. energy gap between spin-singlet and spin-triplet excited states, as has been consistent with numerous exptl. observations over almost a century. Here we report a fluorescent mol. that disobeys Hund's rule and has a neg. singlet-triplet energy gap of -11 ± 2 meV. The energy inversion of the singlet and triplet excited states results in delayed fluorescence with short time consts. of 0.2μs, which anomalously decrease with decreasing temp. owing to the emissive singlet character of the lowest-energy excited state. Org. light-emitting diodes (OLEDs) using this mol. exhibited a fast transient electroluminescence decay with a peak external quantum efficiency of 17%, demonstrating its potential implications for optoelectronic devices, including displays, lighting and lasers.
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22. 22
  Kollmar, H.; Staemmler, V. Violation of Hund’s rule by spin polarization in molecules. Theor. Chim. Acta 1978, 48, 223– 239, DOI: 10.1007/BF00549021
  22
  Violation of Hund's rule by spin polarization in molecules
  Kollmar, H.; Staemmler, V.
  Theoretica Chimica Acta (1978), 48 (3), 223-39CODEN: TCHAAM; ISSN:0040-5744.
  Spin polarization effects can lead to violations of Hund's multiplicity rule, particularly for singlet-triplet pairs. In systems with >1 unpaired electron, a dynamic spin polarization is obsd. which depends on the relative spin orientation of the unpaired electrons and is different in open-shell singlet and triplet states. These effects are described by including singly substituted configurations in Cl-type wave functions for the 2 states. In analyzing the contributions of the various singly substituted configurations, a quant. understanding of violations of Hund's rule is obtained; at the same time it is possible to calc. quant. spin polarization contributions to the correlation energies of open-shell singlet and triplet states. A series of model calcns. was performed on systems like square planar H4 and C4H4, nπ* states of H2CO rotated cumulenes, NH and O2 to investigate how strongly spin polarization influences singlet-triplet energy splittings and what are the properties of a mol. that lead to a violation of Hund's multiplicity rule.
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23. 23
  Pollice, R.; Friederich, P.; Lavigne, C.; dos Passos Gomes, G.; Aspuru-Guzik, A. Organic molecules with inverted gaps between first excited singlet and triplet states and appreciable fluorescence rates. Matter 2021, 4, 1654– 1682, DOI: 10.1016/j.matt.2021.02.017
  23
  Organic molecules with inverted gaps between first excited singlet and triplet states and appreciable fluorescence rates
  Pollice, Robert; Friederich, Pascal; Lavigne, Cyrille; Gomes, Gabriel dos Passos; Aspuru-Guzik, Alan
  Matter (2021), 4 (5), 1654-1682CODEN: MATTCG; ISSN:2590-2385. (Elsevier Inc.)
  One recent proposal for designing state-of-the-art emissive materials in org. light-emitting diodes (OLEDs) is the principle of thermally activated delayed fluorescence (TADF). The idea is to enable facile thermal upconversion of excited-state triplets, which are generated upon electron-hole recombination, to excited-state singlets. Minimizing the corresponding singlet-triplet energy difference enables devices with up to 100% internal quantum efficiency. Ideal emissive materials potentially surpassing TADF emitters in other performance parameters should have both neg. singlet-triplet gaps and substantial fluorescence rates to maximize reverse intersystem crossing (ISC) rates from excited triplets to singlets while minimizing ISC rates and triplet state occupation, leading to long-term operational stability. However, mols. with neg. singlet-triplet gaps are extremely rare, and none of them emissive. In this work, based on computational studies, we describe the first mols. with neg. singlet-triplet gaps and considerable fluorescence rates and show that they are more common than hypothesized previously.
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24. 24
  Tučková, L.; Straka, M.; Valiev, R. R.; Sundholm, D. On the origin of the inverted singlet–triplet gap of the 5th generation light-emitting molecules. Phys. Chem. Chem. Phys. 2022, 24, 18713– 18721, DOI: 10.1039/D2CP02364D
  24
  On the origin of the inverted singlet-triplet gap of the 5th generation light-emitting molecules
  Tuckova, Lucie; Straka, Michal; Valiev, Rashid R.; Sundholm, Dage
  Physical Chemistry Chemical Physics (2022), 24 (31), 18713-18721CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  Excitation energies of the lowest singlet and triplet state of mols. whose first excited singlet state lies energetically below the first triplet state have been studied computationally at (time-dependent) d. functional theory, coupled-cluster, and second-order multiconfiguration perturbation theory levels. The calcns. at the ab initio levels show that the singlet-triplet gap is inverted as compared to the one expected from Hund's rule, whereas all d. functionals yield the triplet state as the lowest excited state. Double excitations responsible for the inverted singlet-triplet gap have been identified. Employing the spin-flip and ΔSCF methods, singlet-triplet inversion was obtained at the d. functional theory level for some of the studied mols.
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25. 25
  Bhattacharyya, K. Can TDDFT render the electronic excited states ordering of Azine derivative? A closer investigation with DLPNO-STEOM-CCSD. Chem. Phys. Lett. 2021, 779, 138827, DOI: 10.1016/j.cplett.2021.138827
  25
  Can TDDFT render the electronic excited states ordering of Azine derivative? A closer investigation with DLPNO-STEOM-CCSD
  Bhattacharyya, Kalishankar
  Chemical Physics Letters (2021), 779 (), 138827CODEN: CHPLBC; ISSN:0009-2614. (Elsevier B.V.)
  TADF materials depend on the small energy gap between the lowest excited singlet and triplet state for an efficient reverse intersystem crossing process. Herein, the first excited singlet (S1) and triplet (T1) state and their gap (ΔEST) are computed based on TDDFT and recently developed coupled-cluster DLPNO-STEOM-CCSD method for Azine deriv. Considerations of higher-order excitations in DLPNO-STEOM-CCSD assign the correct excited state energy level ordering of Azine deriv. while DFT functionals fall short in this context.
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26. 26
  Ghosh, S.; Bhattacharyya, K. Origin of the Failure of Density Functional Theories in Predicting Inverted Singlet–Triplet Gaps. J. Phys. Chem. A 2022, 126, 1378– 1385, DOI: 10.1021/acs.jpca.1c10492
  26
  Origin of the Failure of Density Functional Theories in Predicting Inverted Singlet-Triplet Gaps
  Ghosh, Soumen; Bhattacharyya, Kalishankar
  Journal of Physical Chemistry A (2022), 126 (8), 1378-1385CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)
  Recent exptl. and theor. studies have shown several new org. mols. that violate Hund's rule and have the first singlet excited state lower in energy than the first triplet excited state. While many correlated single ref. wave function methods have successfully predicted excited-state energetics of these low-lying states, conventional linear-response time-dependent d. functional theory (TDDFT) fails to predict the correct excited-state energy ordering. In this article, we have explored the performance of combined DFT and wave function methods like doubles-cor. TDDFT and multiconfiguration pair-d. functional theory for the calcn. of inverted singlet-triplet gaps. We have also tested the performance of the excited-state DFT (eDFT) method for this problem. Our results have shown that it is possible to obtain inverted singlet-triplet gaps both by using doubles-cor. TDDFT with a proper choice of double-hybrid functionals or by using eDFT.
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27. 27
  Koseki, S.; Nakajima, T.; Toyota, A. Violation of Hund’s multiplicity rule in the electronically excited states of conjugated hydrocarbons. Can. J. Chem. 1985, 63, 1572– 1579, DOI: 10.1139/v85-267
  27
  Violation of Hund's multiplicity rule in the electronically excited states of conjugated hydrocarbons
  Koseki, Shiro; Nakajima, Takeshi; Toyota, Azumao
  Canadian Journal of Chemistry (1985), 63 (7), 1572-9CODEN: CJCHAG; ISSN:0008-4042.
  Violation of Hund's multiplicity rule in the electronically excited states of conjugated hydrocarbons is studied by using the PPP type SCF MO method and the ab initio MO method with STO-3G basis set, both methods being augmented by CI-type treatments. For sym. structures (D2h) of the nonalternant hydrocarbons, propalene, pentalene, and heptalene, the lowest excited singlet state is energetically lower than the corresponding triplet state because of spin polarization (SP) effects. For D2h structures of pentalene and heptalene the open-shell excited singlet state is predicted to be lower in energy than the closed-shell state, with the result that the former is really the ground state. Further, calcns. made by including electron correlation effects reveal that in linear polyenes and polyacenes, the lowest excited singlet minus state (using Pariser's classification of the alternancy symmetry species) is lower in energy than the corresponding triplet state. The energy lowering of the singlet minus state in linear polyenes is due mostly to the mixing with the doubly excited configurations (mm → nn), while the considerable part of it in polyacenes is due to the SP effects.
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28. 28
  Harris, J.; Jones, R. O. The surface energy of a bounded electron gas. J. Phys. F: Met. Phys. 1974, 4, 1170, DOI: 10.1088/0305-4608/4/8/013
  There is no corresponding record for this reference.
29. 29
  Langreth, D. C.; Perdew, J. Exchange-correlation energy of a metallic surface: Wave-vector analysis. Phys. Rev. B 1977, 15, 2884, DOI: 10.1103/PhysRevB.15.2884
  There is no corresponding record for this reference.
30. 30
  Gunnarsson, O.; Lundqvist, B. Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism. Phys. Rev. B 1976, 13, 4274, DOI: 10.1103/PhysRevB.13.4274
  30
  Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism
  Gunnarsson, O.; Lundqvist, B. I.
  Physical Review B: Solid State (1976), 13 (10), 4274-98CODEN: PLRBAQ; ISSN:0556-2805.
  The spin-d.-functional (SDF) formalism (e.g., G., et al., 1974-5) was extended to apply to generalized Hamiltonians and to lowest excited states with different types of symmetry. A relation between the exchange-correlation functional and the pair-correlation function was derived, and was used to interpret approx. versions of the theory, esp. the local-spin-d. (LSD) approxn., which can be used in calcn. of the exchange-correlation energy (Exc) in rather inhomogeneous systems. Calcns. done on the homogeneous spin-polarized electron liq., where the charge-d. fluctuations were described by using a plasmon model, provide interpolation formulas for detg. Exc and the exchange-correlation potentials in the LSD approxn. Other properties calcd. for the electron liq. include: bulk modulus at const. magnetization, compressibility at const. magnetic field, and magnetic susceptibility. Applications of the SDF formalism in calcns. of the properties of atoms, mols., and metals are discussed.
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31. 31
  Teale, A. M.; Coriani, S.; Helgaker, T. Accurate calculation and modeling of the adiabatic connection in density functional theory. J. Chem. Phys. 2010, 132, 164115 DOI: 10.1063/1.3380834
  31
  Accurate calculation and modeling of the adiabatic connection in density functional theory
  Teale, A. M.; Coriani, S.; Helgaker, T.
  Journal of Chemical Physics (2010), 132 (16), 164115/1-164115/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Using a recently implemented technique for the calcn. of the adiabatic connection (AC) of d. functional theory (DFT) based on Lieb maximization with respect to the external potential, the AC is studied for atoms and mols. contg. up to ten electrons: the helium isoelectronic series, the hydrogen mol., the beryllium isoelectronic series, the neon atom, and the water mol. The calcn. of AC curves by Lieb maximization at various levels of electronic-structure theory is discussed. For each system, the AC curve is calcd. using Hartree-Fock (HF) theory, second-order Moller-Plesset (MP2) theory, coupled-cluster singles-and-doubles (CCSD) theory, and coupled-cluster singles-doubles-perturbative-triples CCSD(T) theory, expanding the MOs and the effective external potential in large Gaussian basis sets. The HF AC curve includes a small correlation-energy contribution in the context of DFT, arising from orbital relaxation as the electron-electron interaction is switched on under the constraint that the wave function is always a single determinant. The MP2 and CCSD AC curves recover the bulk of the dynamical correlation energy and their shapes can be understood in terms of a simple energy model constructed from a consideration of the doubles-energy expression at different interaction strengths. Differentiation of this energy expression with respect to the interaction strength leads to a simple two-parameter doubles model (AC-D) for the AC integrand (and hence the correlation energy of DFT) as a function of the interaction strength. The structure of the triples-energy contribution is considered in a similar fashion, leading to a quadratic model for the triples correction to the AC curve (AC-T). From a consideration of the structure of a two-level configuration-interaction (CI) energy expression of the hydrogen mol., a simple two-parameter CI model (AC-CI) is proposed to account for the effects of static correlation on the AC. When parametrized in terms of the same input data, the AC-CI model offers improved performance over the corresponding AC-D model, which is shown to be the lowest-order contribution to the AC-CI model. The utility of the accurately calcd. AC curves for the anal. of std. d. functionals is demonstrated for the BLYP exchange-correlation functional and the interaction-strength-interpolation (ISI) model AC integrand. From the results of this anal., we investigate the performance of our proposed two-parameter AC-D and AC-CI models when a simple d. functional for the AC at infinite interaction strength is employed in place of information at the fully interacting point. The resulting two-parameter correlation functionals offer a qual. correct behavior of the AC integrand with much improved accuracy over previous attempts. The AC integrands in the present work are recommended as a basis for further work, generating functionals that avoid spurious error cancellations between exchange and correlation energies and give good accuracy for the range of densities and types of correlation contained in the systems studied here. (c) 2010 American Institute of Physics.
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32. 32
  Pernal, K. Electron Correlation from the Adiabatic Connection for Multireference Wave Functions. Phys. Rev. Lett. 2018, 120, 013001 DOI: 10.1103/PhysRevLett.120.013001
  32
  Electron Correlation from the Adiabatic Connection for Multireference Wave Functions
  Pernal, Katarzyna
  Physical Review Letters (2018), 120 (1), 013001CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
  A review. An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions. The AC expression recovers dynamic correlation energy and assures a balanced treatment of the correlation energy. Coupling the AC formalism with the extended RPA allows one to find the correlation energy only from ref. one- and two-electron reduced d. matrixes. If the generalized valence bond perfect pairing model is employed a simple closed-form expression for the approx. AC formula is obtained. This results in the overall M5 scaling of the computation cost making the method one of the most efficient multireference approaches accounting for dynamic electron correlation also for the strongly correlated systems.
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33. 33
  Pernal, K. Exact and approximate adiabatic connection formulae for the correlation energy in multireference ground and excited states. J. Chem. Phys. 2018, 149, 204101 DOI: 10.1063/1.5048988
  33
  Exact and approximate adiabatic connection formulae for the correlation energy in multireference ground and excited states
  Pernal, Katarzyna
  Journal of Chemical Physics (2018), 149 (20), 204101/1-204101/8CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Recently it has been shown how to employ the adiabatic connection (AC) formalism to obtain correlation energy for multireference wavefunctions [K. Pernal, Phys. Rev. Lett. 120, 013001 (2018)]. Approxns. to the exact AC formulation have been based on assuming that a one-electron reduced d. matrix is const. along the AC path and by employing the extended RPA. In this paper, the importance of these approxns. is examd. by comparing approx. AC integrands with their exact counterparts obtained for the hydrogen mol. in its ground and excited states. Encouraging results obtained for H2 indicate that AC is a viable and promising approach to a correlation energy problem not only for ground but also for excited states of electronic systems. (c) 2018 American Institute of Physics.
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34. 34
  Drwal, D.; Beran, P.; Hapka, M.; Modrzejewski, M.; Sokół, A.; Veis, L.; Pernal, K. Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet–Triplet Gaps of Biradicals. J. Phys. Chem. Lett. 2022, 13, 4570– 4578, DOI: 10.1021/acs.jpclett.2c00993
  34
  Efficient Adiabatic Connection Approach for Strongly Correlated Systems: Application to Singlet-Triplet Gaps of Biradicals
  Drwal, Daria; Beran, Pavel; Hapka, Michal; Modrzejewski, Marcin; Sokol, Adam; Veis, Libor; Pernal, Katarzyna
  Journal of Physical Chemistry Letters (2022), 13 (20), 4570-4578CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  Strong electron correlation can be captured with multireference wave function methods, but an accurate description of the electronic structure requires accounting for the dynamic correlation, which they miss. In this work, a new approach for the correlation energy based on the adiabatic connection (AC) is proposed. The ACn method accounts for terms up to order n in the coupling const., and it is size-consistent and free from instabilities. It employs the multireference RPA and the Cholesky decompn. technique, leading to a computational cost growing with the fifth power of the system size. Because of the dependence on only one- and two-electron reduced d. matrixes, ACn is more efficient than existing ab initio multireference dynamic correlation methods. ACn affords excellent results for singlet-triplet gaps of challenging org. biradicals. The development presented in this work opens new perspectives for accurate calcns. of systems with dozens of strongly correlated electrons.
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35. 35
  Angeli, C.; Cimiraglia, R.; Malrieu, J.-P. n-electron valence state perturbation theory: A spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants. J. Chem. Phys. 2002, 117, 9138, DOI: 10.1063/1.1515317
  35
  n-electron valence state perturbation theory: a spinless formulation and an efficient implementation of the strongly contracted and of the partially contracted variants
  Angeli, Celestino; Cimiraglia, Renzo; Malrieu, Jean-Paul
  Journal of Chemical Physics (2002), 117 (20), 9138-9153CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  The n-electron valence state perturbation theory is reformulated in a spin-free formalism, concg. on the "strongly contracted" and "partially contracted" variants. The new formulation is based on the introduction of av. values in the unperturbed state of excitation operators which bear resemblance with analogous ones occurring in the extended Koopmans' theorem and in the equations-of-motion technique. Such auxiliary quantities, which allow the second-order perturbation contribution to the energy to be evaluated very efficiently, can be calcd. at the outset provided the unperturbed four-particle spinless d. matrix in the active orbital space is available. A noticeable inequality concerning second-order energy contributions of the same type between the strongly and partially contracted versions is proven to hold. An example concerning the successful calcn. of the potential energy curve for the Cr2 mol. is discussed.
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36. 36
  Bhaskaran-Nair, K.; Brabec, J.; Aprà, E.; van Dam, H. J. J.; Pittner, J.; Kowalski, K. Implementation of the multireference Brillouin-Wigner and Mukherjee’s coupled cluster methods with non-iterative triple excitations utilizing reference-level parallelism. J. Chem. Phys. 2012, 137, 094112 DOI: 10.1063/1.4747698
  36
  Implementation of the multireference Brillouin-Wigner and Mukherjee's coupled cluster methods with non-iterative triple excitations utilizing reference-level parallelism
  Bhaskaran-Nair, Kiran; Brabec, Jiri; Apra, Edoardo; van Dam, Hubertus J. J.; Pittner, Jiri; Kowalski, Karol
  Journal of Chemical Physics (2012), 137 (9), 094112/1-094112/12CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  In this paper we discuss the performance of the non-iterative state-specific multireference coupled cluster (SS-MRCC) methods accounting for the effect of triply excited cluster amplitudes. The corrections to the Brillouin-Wigner and Mukherjee's MRCC models based on the manifold of singly and doubly excited cluster amplitudes (BW-MRCCSD and Mk-MRCCSD, resp.) are tested and compared with exact full CI results for small systems (H2O, N2, and Be3). For the larger systems (naphthyne isomers) the BW-MRCC and Mk-MRCC methods with iterative singles, doubles, and non-iterative triples (BW-MRCCSD(T) and Mk-MRCCSD(T)) are compared against the results obtained with single ref. coupled cluster methods. We also report on the parallel performance of the non-iterative implementations based on the use of processor groups. (c) 2012 American Institute of Physics.
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37. 37
  Werner, H.-J.; Knowles, P. J.; Knizia, G.; Manby, F. R.; Schütz, M. Molpro: a general-purpose quantum chemistry program package. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 242– 253, DOI: 10.1002/wcms.82
  37
  Molpro: a general-purpose quantum chemistry program package
  Werner, Hans-Joachim; Knowles, Peter J.; Knizia, Gerald; Manby, Frederick R.; Schuetz, Martin
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (2), 242-253CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  Molpro is a general-purpose quantum chem. program. The original focus was on high-accuracy wave function calcns. for small mols., but using local approxns. combined with explicit correlation treatments, highly accurate coupled-cluster calcns. are now possible for mols. with up to approx. 100 atoms. Recently, multireference correlation treatments were also made applicable to larger mols. Furthermore, an efficient implementation of d. functional theory is available.
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38. 38
  Schäfer, A.; Horn, H.; Ahlrichs, R. Fully optimized contracted Gaussian basis sets for atoms Li to Kr. J. Chem. Phys. 1992, 97, 2571– 2577, DOI: 10.1063/1.463096
  There is no corresponding record for this reference.
39. 39
  Pernal, K.; Hapka, M.; Przybytek, M.; Modrzejewski, M.; Sokół, A.; Tucholska, A. GammCor code. https://github.com/pernalk/GAMMCOR, 2023.
  There is no corresponding record for this reference.
40. 40
  Aprà, E.; Bylaska, E. J.; de Jong, W. A. NWChem: Past, present, and future. J. Chem. Phys. 2020, 152, 184102 DOI: 10.1063/5.0004997
  40
  NWChem: Past, present, and future
  Apra, E.; Bylaska, E. J.; de Jong, W. A.; Govind, N.; Kowalski, K.; Straatsma, T. P.; Valiev, M.; van Dam, H. J. J.; Alexeev, Y.; Anchell, J.; Anisimov, V.; Aquino, F. W.; Atta-Fynn, R.; Autschbach, J.; Bauman, N. P.; Becca, J. C.; Bernholdt, D. E.; Bhaskaran-Nair, K.; Bogatko, S.; Borowski, P.; Boschen, J.; Brabec, J.; Bruner, A.; Cauet, E.; Chen, Y.; Chuev, G. N.; Cramer, C. J.; Daily, J.; Deegan, M. J. O.; Dunning, T. H.; Dupuis, M.; Dyall, K. G.; Fann, G. I.; Fischer, S. A.; Fonari, A.; Fruchtl, H.; Gagliardi, L.; Garza, J.; Gawande, N.; Ghosh, S.; Glaesemann, K.; Gotz, A. W.; Hammond, J.; Helms, V.; Hermes, E. D.; Hirao, K.; Hirata, S.; Jacquelin, M.; Jensen, L.; Johnson, B. G.; Jonsson, H.; Kendall, R. A.; Klemm, M.; Kobayashi, R.; Konkov, V.; Krishnamoorthy, S.; Krishnan, M.; Lin, Z.; Lins, R. D.; Littlefield, R. J.; Logsdail, A. J.; Lopata, K.; Ma, W.; Marenich, A. V.; Martin del Campo, J.; Mejia-Rodriguez, D.; Moore, J. E.; Mullin, J. M.; Nakajima, T.; Nascimento, D. R.; Nichols, J. A.; Nichols, P. J.; Nieplocha, J.; Otero-de-la-Roza, A.; Palmer, B.; Panyala, A.; Pirojsirikul, T.; Peng, B.; Peverati, R.; Pittner, J.; Pollack, L.; Richard, R. M.; Sadayappan, P.; Schatz, G. C.; Shelton, W. A.; Silverstein, D. W.; Smith, D. M. A.; Soares, T. A.; Song, D.; Swart, M.; Taylor, H. L.; Thomas, G. S.; Tipparaju, V.; Truhlar, D. G.; Tsemekhman, K.; Van Voorhis, T.; Vazquez-Mayagoitia, A.; Verma, P.; Villa, O.; Vishnu, A.; Vogiatzis, K. D.; Wang, D.; Weare, J. H.; Williamson, M. J.; Windus, T. L.; Wolinski, K.; Wong, A. T.; Wu, Q.; Yang, C.; Yu, Q.; Zacharias, M.; Zhang, Z.; Zhao, Y.; Harrison, R. J.
  Journal of Chemical Physics (2020), 152 (18), 184102CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A review. Specialized computational chem. packages have permanently reshaped the landscape of chem. and materials science by providing tools to support and guide exptl. efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principle-driven methodologies to model complex chem. and materials processes. Over the past few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in mol. and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chem. suite, including its history, design principles, parallel tools, current capabilities, outreach, and outlook. (c) 2020 American Institute of Physics.
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41. 41
  Neese, F. The ORCA program system. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2012, 2, 73– 78, DOI: 10.1002/wcms.81
  41
  The ORCA program system
  Neese, Frank
  Wiley Interdisciplinary Reviews: Computational Molecular Science (2012), 2 (1), 73-78CODEN: WIRCAH; ISSN:1759-0884. (Wiley-Blackwell)
  A review. ORCA is a general-purpose quantum chem. program package that features virtually all modern electronic structure methods (d. functional theory, many-body perturbation and coupled cluster theories, and multireference and semiempirical methods). It is designed with the aim of generality, extendibility, efficiency, and user friendliness. Its main field of application is larger mols., transition metal complexes, and their spectroscopic properties. ORCA uses std. Gaussian basis functions and is fully parallelized. The article provides an overview of its current possibilities and documents its efficiency.
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42. 42
  Becke, A. D. Density-functional exchange-energy approximation with correct asymptotic behavior. Phys. Rev. A 1988, 38, 3098, DOI: 10.1103/PhysRevA.38.3098
  42
  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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43. 43
  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
  43
  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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44. 44
  Miehlich, B.; Savin, A.; Stoll, H.; Preuss, H. Results obtained with the correlation energy density functionals of Becke and Lee, Yang and Parr. Chem. Phys. Lett. 1989, 157, 200– 206, DOI: 10.1016/0009-2614(89)87234-3
  44
  Results obtained with the correlation energy density functionals of Becke and Lee, Yang and Parr
  Miehlich, Burkhard; Savin, Andreas; Stoll, Hermann; Preuss, Heinzwerner
  Chemical Physics Letters (1989), 157 (3), 200-6CODEN: CHPLBC; ISSN:0009-2614.
  Two recently published d. functionals (Becke, A.D., 1988 and Lee, C. et al., 1988) are used to calc. the correlation energies of first-row atoms, ions and mols. The correlation contributions to ionization energies, electron affinities and dissocn. energies thus obtained are of comparable quality to those of other d. functionals.
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45. 45
  Pastorczak, E.; Pernal, K. Correlation Energy from the Adiabatic Connection Formalism for Complete Active Space Wave Functions. J. Chem. Theory Comput. 2018, 14, 3493– 3503, DOI: 10.1021/acs.jctc.8b00213
  45
  Correlation Energy from the Adiabatic Connection Formalism for Complete Active Space Wave Functions
  Pastorczak, Ewa; Pernal, Katarzyna
  Journal of Chemical Theory and Computation (2018), 14 (7), 3493-3503CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  Recently, the adiabatic connection (AC) formula for the electron correlation energy has been proposed for a broad class of multireference wave functions (Pernal, K. Electron Correlation from the Adiabatic Connection for Multireference Wave Functions. Lett. 2018, 120, 013001). We show that the AC formula used together with the extended RPA (ERPA) can be efficiently applied to complete active space (CAS) wave functions to recover the remaining electron correlation. Unlike most of the perturbation theory approaches, the proposed AC-CAS method does not require construction of higher than two-electron reduced d. matrixes, which offers an immediate computational saving. In addn., we show that typically the AC-CAS systematically reduces the errors of both the abs. value of energy and of the energy differences (energy barrier) upon enlarging active spaces for electrons and orbitals. AC-CAS consistently gains in accuracy from including more active electrons. We also propose and study that the performance of the AC0 approach resulting from the first-order expansion of the AC integrand at the coupling const. equal to 0. AC0 avoids solving the full ERPA eigenequation, replacing it with small-dimension eigenproblems, while retaining good accuracy of the AC-CAS method. Low computational cost, compared to AC-CAS or perturbational approaches, makes AC0 the most efficient ab initio approach to capturing electron correlation for the CAS wave functions.
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46. 46
  Pastorczak, E.; Pernal, K. Electronic Excited States from the Adiabatic-Connection Formalism with Complete Active Space Wave Functions. J. Phys. Chem. Lett. 2018, 9, 5534– 5538, DOI: 10.1021/acs.jpclett.8b02391
  46
  Electronic Excited States from the Adiabatic-Connection Formalism with Complete Active Space Wave Functions
  Pastorczak, Ewa; Pernal, Katarzyna
  Journal of Physical Chemistry Letters (2018), 9 (18), 5534-5538CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  It is demonstrated how the recently proposed multireference adiabatic-connection (AC) approxn. for electron correlation energy (Pernal, K., Electron Correlation from the Adiabatic Connection for Multireference Wave Functions; Phys. Rev. Lett. 2018, 120, 013001) can be extended to predicting correlation energy in excited states of mols. It is the first successful application of the AC approach to computing excited-states energies of mols. using a complete active space (CAS) wave function as a ref. The unique feature of the AC-CAS approach with respect to popular methods such as CASPT2 and NEVPT2 is that it requires only one- and two-particle reduced d. matrixes, making it possible to efficiently treat large spaces of active electrons. Application of the simpler variant of AC, the AC0, which is based on the first-order expansion of the AC integrand at the uncorrelated system limit, to excited states yields excitation energies with accuracy rivaling that of the NEVPT2 method but at greatly reduced computational cost.
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47. 47
  Pastorczak, E.; Hapka, M.; Veis, L.; Pernal, K. Capturing the Dynamic Correlation for Arbitrary Spin-Symmetry CASSCF Reference with Adiabatic Connection Approaches: Insights into the Electronic Structure of the Tetramethyleneethane Diradical. J. Phys. Chem. Lett. 2019, 10, 4668– 4674, DOI: 10.1021/acs.jpclett.9b01582
  47
  Capturing the Dynamic Correlation for Arbitrary Spin-Symmetry CASSCF Reference with Adiabatic Connection Approaches: Insights into the Electronic Structure of the Tetramethyleneethane Diradical
  Pastorczak, Ewa; Hapka, Michal; Veis, Libor; Pernal, Katarzyna
  Journal of Physical Chemistry Letters (2019), 10 (16), 4668-4674CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)
  The recently proposed approach to multireference dynamic correlation energy based on the adiabatic connection (AC) is extended to an arbitrary spin symmetry of the ref. state. We show that both the spin-free AC approach and its computationally inexpensive approxn., AC0, when combined with a complete active space wave function, constitute viable alternatives to the perturbation-based and d.-functional-based multiconfiguration methods. In particular, the AC0 approach, thanks to its favorable scaling with the system size and the size of the active space, allows for treating larger systems than its perturbation-based counterparts while maintaining comparable accuracy. We show the method's robustness on illustrative chem. systems, including the elusive tetramethyleneethane (TME) diradical, potential energy surfaces of which present a challenge to most computational approaches. For the latter system, AC0 outperforms other methods, staying in close agreement with the full CI quantum Monte Carlo benchmark. A careful anal. of the contributions to the correlation energy of TME's lowest singlet and triplet states reveals the subtle interplay of the dynamic and static correlation as the key to understanding the shape of the diradical's potential energy surfaces.
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48. 48
  Beran, P.; Matoušek, M.; Hapka, M.; Pernal, K.; Veis, L. Density matrix renormalization group with dynamical correlation via adiabatic connection. J. Chem. Theory Comput. 2021, 17, 7575– 7585, DOI: 10.1021/acs.jctc.1c00896
  48
  Density Matrix Renormalization Group with Dynamical Correlation via Adiabatic Connection
  Beran, Pavel; Matousek, Mikulas; Hapka, Michal; Pernal, Katarzyna; Veis, Libor
  Journal of Chemical Theory and Computation (2021), 17 (12), 7575-7585CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)
  The quantum chem. version of the d. matrix renormalization group (DMRG) method has established itself as one of the methods of choice for calcns. of strongly correlated mol. systems. Despite its great ability to capture strong electronic correlation in large active spaces, it is not suitable for computations of dynamical electron correlation. In this work, we present a new approach to the electronic structure problem of strongly correlated mols., in which DMRG is responsible for a proper description of the strong correlation, whereas dynamical correlation is computed via the recently developed adiabatic connection (AC) technique which requires only up to two-body active space reduced d. matrixes. We report the encouraging results of this approach on typical candidates for DMRG computations, namely, n-acenes (n = 2 → 7), Fe(II)-porphyrin, and the Fe3S4 cluster.
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49. 49
  Matoušek, M.; Hapka, M.; Veis, L.; Pernal, K. Toward more accurate adiabatic connection approach for multireference wavefunctions. J. Chem. Phys. 2023, 158, 054105 DOI: 10.1063/5.0131448
  49
  Toward more accurate adiabatic connection approach for multireference wavefunctions
  Matousek, Mikulas; Hapka, Michal; Veis, Libor; Pernal, Katarzyna
  Journal of Chemical Physics (2023), 158 (5), 054105CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  A multiconfigurational adiabatic connection (AC) formalism is an attractive approach to compute the dynamic correlation within the complete active space SCF and d. matrix renormalization group (DMRG) models. Practical realizations of AC have been based on two approxns.: (i) fixing one- and two-electron reduced d. matrixes (1- and 2-RDMs) at the zero-coupling const. limit and (ii) extended RPA (ERPA). This work investigates the effect of removing the "fixed-RDM" approxn. in AC. The anal. is carried out for two electronic Hamiltonian partitionings: the group product function- and the Dyall Hamiltonians. Exact ref. AC integrands are generated from the DMRG full CI solver. Two AC models are investigated, employing either exact 1- and 2-RDMs or their second-order expansions in the coupling const. in the ERPA equations. Calcns. for model mols. indicate that lifting the fixed-RDM approxn. is a viable way toward improving the accuracy of existing AC approxns. (c) 2023 American Institute of Physics.
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50. 50
  Dreuw, A.; Hoffmann, M. T. The inverted singlet-triplet gap: a vanishing myth?. Front. Chem. 2023, 11, 1239604 DOI: 10.3389/fchem.2023.1239604
  50
  The inverted singlet-triplet gap: a vanishing myth?
  Dreuw, Andreas; Hoffmann, Marvin
  Frontiers in Chemistry (Lausanne, Switzerland) (2023), 11 (), 1239604CODEN: FCLSAA; ISSN:2296-2646. (Frontiers Media S.A.)
  Mols. with an inverted singlet-triplet gap (STG) between the first excited singlet and triplet states, for example, heptazine, have recently been reported and gained substantial attention since they violate the famous Hund's rule. Utilizing state-of-the-art high-level ab initio methods, the singlet-triplet gap vanishes and approaches zero from below whatever is improved in the theor. description of the mols.: the basis set or the level of electron correlation. Seemingly, the phenomenon of inverted singlet-triplet gaps tends to vanish the closer we observe.
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Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.3c00781.
- Expressions: Hamiltonian matrix elements of doubly excited states, energy differences of doubly excited states. Tables: ST energy gaps from sp models, ST energy gaps in cc-pVDZ and cc-pVQZ basis sets, singlet- and triplet-state energies for systems 1–6, energy characteristics for all heptazine-derived systems from the extended set. Figures: CASSCF(14,14) orbitals for the S₁ and T₁ states, ST energy gaps from sp models with HF orbitals vs EOM-CCSD for an extended set of molecules. Geometries of systems 1–6 (PDF)
- Geometries_xyz_extended_set (ZIP)
- ct3c00781_si_001.pdf (5.52 MB)
- ct3c00781_si_002.zip (79.95 kb)
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Role of Spin Polarization and Dynamic Correlation in Singlet–Triplet Gap Inversion of Heptazine DerivativesClick to copy article linkArticle link copied!

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Inverting S1–T1 Energy Gaps by Including Dynamic Spin Polarization

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Effect of Dynamic Correlation Energy

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Role of Spin Polarization and Dynamic Correlation in Singlet–Triplet Gap Inversion of Heptazine Derivatives
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Inverting S₁–T₁ Energy Gaps by Including Dynamic Spin Polarization