**Cite This:**

*J. Am. Chem. Soc.*2023, 145, 45, 24558-24567

# Accurate and Efficient Spin–Phonon Coupling and Spin Dynamics Calculations for Molecular SolidsClick to copy article linkArticle link copied!

- Rizwan NabiRizwan NabiDepartment of Chemistry, University of Manchester, Manchester M13 9PL, U.K.More by Rizwan Nabi
- Jakob K. StaabJakob K. StaabDepartment of Chemistry, University of Manchester, Manchester M13 9PL, U.K.More by Jakob K. Staab
- Andrea MattioniAndrea MattioniDepartment of Chemistry, University of Manchester, Manchester M13 9PL, U.K.More by Andrea Mattioni
- Jon G. C. KragskowJon G. C. KragskowDepartment of Chemistry, University of Manchester, Manchester M13 9PL, U.K.Department of Chemistry, University of Bath, Bath BA2 7AY, U.K.More by Jon G. C. Kragskow
- Daniel RetaDaniel RetaDepartment of Chemistry, University of Manchester, Manchester M13 9PL, U.K.Faculty of Chemistry, University of the Basque Country UPV/EHU, 20018 Donostia, SpainDonostia International Physics Center (DIPC), 20018 Donostia, SpainIKERBASQUE, Basque Foundation for Science, 48013 Bilbao, SpainMore by Daniel Reta
- Jonathan M. Skelton
*****Jonathan M. SkeltonDepartment of Chemistry, University of Manchester, Manchester M13 9PL, U.K.*****Email: [email protected]More by Jonathan M. Skelton - Nicholas F. Chilton
*****Nicholas F. ChiltonDepartment of Chemistry, University of Manchester, Manchester M13 9PL, U.K.*****Email: [email protected]More by Nicholas F. Chilton

## Abstract

Molecular materials are poised to play a significant role in the development of future optoelectronic and quantum technologies. A crucial aspect of these areas is the role of spin–phonon coupling and how it facilitates energy transfer processes such as intersystem crossing, quantum decoherence, and magnetic relaxation. Thus, it is of significant interest to be able to accurately calculate the molecular spin–phonon coupling and spin dynamics in the condensed phase. Here, we demonstrate the maturity of *ab initio* methods for calculating spin–phonon coupling by performing a case study on a single-molecule magnet and showing quantitative agreement with the experiment, allowing us to explore the underlying origins of its spin dynamics. This feat is achieved by leveraging our recent developments in analytic spin–phonon coupling calculations in conjunction with a new method for including the infinite electrostatic potential in the calculations. Furthermore, we make the first *ab initio* determination of phonon lifetimes and line widths for a molecular magnet to prove that the commonplace Born–Markov assumption for the spin dynamics is valid, but such “exact” phonon line widths are not essential to obtain accurate magnetic relaxation rates. Calculations using this approach are facilitated by the open-source packages we have developed, enabling cost-effective and accurate spin–phonon coupling calculations on molecular solids.

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### License Summary*

You are free to share(copy and redistribute) this article in any medium or format and to adapt(remix, transform, and build upon) the material for any purpose, even commercially within the parameters below:

Creative Commons (CC): This is a Creative Commons license.

Attribution (BY): Credit must be given to the creator.

*Disclaimer

This summary highlights only some of the key features and terms of the actual license. It is not a license and has no legal value. Carefully review the actual license before using these materials.

### License Summary*

You are free to share(copy and redistribute) this article in any medium or format and to adapt(remix, transform, and build upon) the material for any purpose, even commercially within the parameters below:

Creative Commons (CC): This is a Creative Commons license.

Attribution (BY): Credit must be given to the creator.

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## Introduction

*via*the Orbach mechanism, for which the characteristic time has an exponential temperature dependence τ = τ

_{0}exp(

*U*

_{eff}/

*k*

_{B}

*T*) with a characteristic phonon time scale τ

_{0}and an energy barrier

*U*

_{eff}. In the best-performing SMMs, this is driven by high-energy optic phonons. (15,16) At lower temperatures, the populations of high-energy phonons are very low, and the Orbach mechanism is suppressed. In this regime, the spin dynamics are instead dominated by two-phonon Raman mechanisms driven by low-energy (pseudo)acoustic phonons, showing a power law temperature dependence of τ in the range of

*T*

^{–1}–

*T*

^{–7}. (17) Other mechanisms pertinent to the spin dynamics of SMMs, such as the direct and quantum tunneling of magnetization (QTM) mechanisms, (11) are not discussed here as they are either not relevant in zero magnetic field (direct) or are only active at very low temperatures (QTM; usually <10 K).

^{i}Pr

_{5})][B(C

_{6}F

_{5})

_{4}] (Cp* = pentamethyl cyclopentadienyl) (18) and more recently for the mixed-valence Cp

^{iPr5}DyI

_{3}DyCp

^{iPr5}(Cp

^{iPr5}= pentaisopropyl cyclopentadienyl), which shows strong magnetic exchange coupling mediated by the Ln–Ln half-σ bond. (19) In both cases, a large axial magnetic anisotropy is imposed by the cyclopentadienyl ligands, leading to large

*U*

_{eff}values and slow Orbach relaxation. For [Dy(Cp

^{ttt})

_{2}][B(C

_{6}F

_{5})

_{4}] (Cp

^{ttt}= C

_{5}H

_{2}-1,2,4-

^{t}Bu), (15) it has been demonstrated that the comparatively slow spin dynamics in the Raman regime for this class of materials results from a separation in energy between the very high-energy optical phonons (due to the conjugated five-membered rings being the only ligands in the first coordination sphere) and low-energy pseudoacoustic phonons (due to the soft intermolecular potential energy of the bulky cation–anion pair). (20) Variation of the cyclopentadienyl substituents can have a significant effect on the spin dynamics (15,18,21) since it impacts both the magnetic anisotropy and the vibrational spectrum. (22) Despite these successes, control of the spin dynamics through chemical modification remains an open challenge for the design of improved SMMs and indeed any molecular spin system, and given the vastness of chemical space, strategies employing machine learning are likely to be particularly promising. (23)

*ab initio*methods for calculating molecular spin–phonon coupling and modeling spin dynamics. (22,24−27) Such methods are crucial to leverage the computational material design procedures (28) that have proven very successful in solid-state chemistry (29,30) to discover new and improved molecular materials with desirable spin dynamics. However, for this to be a viable approach, the calculations must approach experimental accuracy. Just recently, Lunghi and co-workers presented a landmark study: the first fully

*ab initio*simulation of Raman spin dynamics for an SMM. (31) Taking inspiration from their work, we herein introduce a number of further developments, resulting in the most accurate

*ab initio*simulation of molecular spin dynamics to date. We focus on the high-performance Dy(III) SMM, [Dy(bbpen)Br] (

**1**, Figure 1), (32) chosen because of its small unit cell size, relatively high-symmetry space group (

*C*222

_{1}), and excellent SMM performance, although we note that the methodology described herein is equally applicable to any other molecular magnet, and numerous other such preliminary studies are underway in our group. We perform the first

*ab initio*calculation of the phonon line widths for a molecular magnet to show that: i)phonon lifetimes are orders of magnitude shorter than the spin lifetimes in this compound, justifying the commonly assumed Born–Markov approximation for molecular spin dynamics, (22,31) and ii) the phonon line widths are highly energy- and wavevector-dependent, with full width at half maximum (fwhm) values varying between 0.1 and 40 cm

^{–1}at 300 K. We find that the spin dynamics are relatively insensitive to the choice of line width model, with similar results obtained using a fixed line width or a thermodynamic approximation, (25) and thus our work suggests that the burden of performing expensive phonon line width calculations for other molecules may not be required for accurate spin dynamics simulations. Furthermore, we show that the use of finite slab methods leads to significant errors and that accurate treatment of the electrostatic (Madelung) potential of the infinite crystal lattice is essential to achieve quantitative accuracy. Our open-source tools implement a computationally inexpensive and accurate method to calculate the infinite crystalline electrostatic potential, including its effect on the spin–phonon coupling terms, which vastly improves the agreement with the experiment. This work thus paves the way for accurate and efficient spin–phonon calculations on solid-state molecular systems with applicability beyond molecular magnetism.

## Methods

**1**in the gas phase or an infinite perfectly periodic crystal of

**1**); (2) calculation of the vibrations (gas phase) or phonons (crystalline phase); (3) calculation of the electronic structure of a single molecule of

**1**(either on its own in the gas phase or embedded in an electrostatic representation of the crystal); (4) calculation of the spin–phonon coupling between the vibrational/phonon modes and the electronic states in

**1**(again, either on its own in the gas phase or embedded in an electrostatic representation of a crystal); and (5) calculation of the magnetic relaxation rates.

**1**in the gas phase was performed with Gaussian09d (33) using the PBE functional and the D3 semiempirical dispersion correction. (34,35) Density functional theory (DFT) is based on a single configuration wave function and therefore struggles with the multiconfigurational ground state arising from near-degenerate 4f electronic configurations. To avoid this, we substituted Dy(III) for the chemically and structurally analogous Y(III), which has no 4f electrons, and used the Stuttgart RSC 1997 effective core potential (ECP) and associated valence basis set for Y and the cc-pVDZ basis sets for all other atoms. (36) We found a root-mean-square deviation (RMSD) for all the atomic positions compared to the experimental crystal structure of 0.13 Å. We then calculated the vibrational modes of the gas-phase molecule of

**1**using analytic methods in Gaussian09d, where the isotopic mass of Y was set as the isotopic mass of Dy.

**1**was performed using the primitive cell, with starting atomic positions and unit cell parameters obtained from the Cambridge Structural Database (CCDC: 1416543), using periodic density functional theory (DFT) as implemented in VASP 5.4.4. (37−40) The PBE functional (34) with the D3 semiempirical dispersion correction (35) was employed to model the electron exchange and correlation. To avoid the multiconfigurational ground state of Dy(III) in this case, we used a 4f-in-core ECP for Dy(III); we have previously verified that both Y(III) substitution and a 4f-in-core ECP give the same results. All ion cores were modeled with projector augmented wave (PAW) pseudopotentials, (41,42) and the valence electronic structure was modeled using a plane-wave basis set with an energy cutoff of 800 eV and Γ-point Brillouin zone sampling, with both parameters determined

*via*explicit convergence testing. Starting from the 128-atom primitive cell of the published X-ray structure of

**1**, the atomic positions and unit cell parameters were optimized to tight tolerances of 10

^{–8}eV on the electronic total energy and 10

^{–2}eV Å

^{–1}on the forces. Phonon calculations were then performed with the optimized crystal structure of

**1**using the finite-difference method implemented in Phonopy (43) and Phono3py. (44) In this approach, the Phonopy code is used to generate a series of distorted structures (with each independent atom shifted along each independent

*xyz*coordinate, one by one, by 0.01 Å) and the forces on the atoms in each distorted structure are calculated using VASP, where the outputs are combined with Phonopy again to obtain the Hessian matrix of second derivatives of the energy with respect to coordinates. The Hessian is then “mass-weighted” using the atomic masses to give the dynamical matrix, which is diagonalized to give the normal modes of vibration and squared frequencies. The process is slightly more involved than this, as the calculations are periodic, and we refer the interested reader to our recent Tutorial Review, which covers this in detail. (45) The Phono3py code is similarly used to generate a sequence of distorted structures in which pairs of atoms are displaced to obtain the third-order force constants, which are combined with the harmonic frequencies and eigenvectors to determine the phonon lifetimes and line widths. A 2 × 2 × 1 supercell with 512 atoms was employed to determine the second-order force constants in Phonopy, (43) while the third-order force constants were determined for the primitive cell (i.e., a 1 × 1 × 1 cell) using Phono3py, (44) and the phonon frequencies and line widths were evaluated on uniform 2 × 2 × 2, 3 × 3 × 3, 4 × 4 × 4, and 5 × 5 × 5

*q*-point grids using Fourier interpolation with Phono3py.

**1**. However, for adapting our method to the crystalline phase, we note that the CASSCF is not compatible with periodic wave functions, and hence, we must bridge the gap between the phonons described in the infinite periodic crystal and the electronic structure described with a finite model. The simplest approach is a finite slab of unit cells cropped from the infinite periodic crystal (approach 1), but we find that this has its shortcomings, and hence, we have implemented a more accurate method accounting for the infinite crystalline electrostatic potential (approach 2); both methods are implemented in our

*spin_phonon_suite*code (version 1.4.1). (51)

### Approach 1: Finite Slab Expansions

*q*on a Γ-centered

*q*-point sampling grid with

*q*

_{1}×

*q*

_{2}×

*q*

_{3}subdivisions is commensurate with a

*q*

_{1}×

*q*

_{2}×

*q*

_{3}finite slab cell expansion in the real space (i.e., the slab is of the correct size to contain an integer number of phonon wavelengths for all the

*q*on the sampling grid). For a given

*q*-point grid, we build the required

*q*

_{1}×

*q*

_{2}×

*q*

_{3}finite slab, redefined by translation to position a single molecule of

**1**in the center. The electrostatic potential of the finite slab is accounted for by assigning the remaining atoms (excluding the central molecule) their CHELPG charges determined as outlined above.

### Approach 2: Infinite Crystalline Electrostatic Potential *via* Conductor Screening

**1**in the center of the spherical array. All remaining atoms in the spherical array are assigned their CHELPG charges (outlined above), and the entire array is embedded in a perfect conductor reaction field cavity with a radius of 40 Å using the Kirkwood solvent model with ε = ∞. (52) The displacement vectors for phonons corresponding to arbitrary

*q*

_{1}×

*q*

_{2}×

*q*

_{3}grids can then be mapped onto the spherical array as required.

*S*= 5/2 states (

^{6}H and

^{6}F terms) for a 9-in-7 active space (4f

^{9}configuration) using the second-order Douglas–Kroll–Hess relativistic decoupling, (54) the Cholesky “atomic compact” resolution of the identity method for approximating the two-electron integrals, (55) and ANO-RCC basis sets for all atoms (VTZP for Dy, VDZP for the first coordination sphere, and VDZ for all other atoms). (56,57) These 18 spin-free states are then mixed with SO coupling, and the lowest 16 resulting states (the

^{6}H

_{15/2}multiplet) are projected onto a crystal field (CF) Hamiltonian acting in the (2

*J*+ 1)-dimensional |

*m*

_{J}⟩ basis, using our

*angmom_suite*code (version 1.17.1). (58) The spin–phonon coupling parameters for each phonon mode, defined by band index

*j*and wavevector

*q*, are the derivatives of the CF parameters along the phonon normal mode vectors. (22,26,45,59) To compute these, we first obtain the derivatives of the CF parameters with respect to Cartesian atomic coordinates using an analytic linear vibronic coupling (LVC) model (60) and then convert to the normal mode basis using the linear combination of atomic displacements specified by the mode displacement vector. (45) This is done for all vibrational modes of the gas-phase model and all phonon modes at all

*q*-points in the sampling mesh for the crystalline-phase model.

*Tau*code (commit e058b24959), (61) considering Orbach and Raman rates, (26,45,62) given by eqs 40, 41, and 46–49 in reference. (45) There are two forms of the Raman mechanism, which arise from their derivation using different orders of perturbation theory: (26,45,62) the Raman-I mechanism (first-order in spin–phonon coupling, second-order in time) does not depend on the magnitude of an external magnetic field, (63) while the Raman-II mechanism (second-order in spin–phonon coupling, first-order in time) has a quadratic dependence on the field and vanishes in zero field. (20) Since our experiments are performed in zero field, we do not consider the Raman-II mechanism, and we therefore refer to the Raman-I mechanism simply as “the Raman mechanism” throughout. In the context of magnetic relaxation in SMMs, the two-phonon Raman mechanism concerns coupling between the two states of the ground Kramers doublet, and our calculations are thus restricted to this pair of states. Derivation of the Raman rate expressions adopts the secular approximation, which assumes that no degeneracies exist in the electronic eigenstates, (26,31,45) and thus, we must introduce an energy gap between the two states of the ground Kramers doublet. Indeed, this occurs in experiments due to the presence of a dipolar magnetic field and/or the driving AC magnetic field, and we therefore apply a magnetic field of 2 Oe along the main magnetic axis of the molecule, splitting the ground doublet by ca. 0.002 cm

^{–1}. The Raman mechanism involves pairs of phonons, and the rate is obtained as the double integral over their lineshapes. (26,45,60) We restrict the domain of the phonon energies to 0 ≤ ω ≲ ω

_{cut}, where ω

_{cut}= 267 cm

^{–1}is chosen as the minimum in the phonon density of states (DoS) above the low-energy pseudoacoustic peak (Figure 2c). The cutoff is applied to avoid divergences in the Raman rates, as the denominator of eqs 46–49 in ref (45) goes to zero when ℏω is resonant with a CF excitation, and the chosen value is sufficiently smaller than the first crystal field excitation of ca. 420 cm

^{–1}. The double integral is transformed into a one-dimensional integral due to the conservation of energy

*via*the Dirac delta function and is performed over anti-Lorentzian phonon lineshapes (eq 11 in ref (45)) to an equivalent range of μ ± 2σ (95%) using the trapezoidal method with 40 equidistant steps (anti-Lorentzian lineshapes are used to ensure that the DoS goes to zero at zero energy).

## Results and Discussion

### Phonons and Phonon Line Widths

**1**is a monometallic Dy(III) molecule with a pentagonal bipyramidal coordination geometry. The molecule crystallizes in the orthorhombic space group

*C*222

_{1}with half a molecule in the asymmetric unit and two complete molecules in the conventional unit cell (Figure 1). (32) To obtain the phonon spectrum of

**1**, we first optimize the unit cell parameters and atomic positions of

**1**with periodic DFT (see the Methods), starting from the experimental crystal structure, and observe only very small changes: the optimized cell parameters are very similar to the measured values (Table S1), and we find an RMSD for all atomic positions of only 0.10 Å. This indicates that our chosen methodology is a good approximation to the molecular forces. We then obtain the second derivatives of the energy (first derivative of the forces) with respect to the atomic positions using numerical finite differences and construct the dynamical matrix to determine the normal modes of vibration by matrix diagonalization (see the Methods). (45)

^{–1}(Figure 2b), while the complete spectrum extends up to 3500 cm

^{–1}and at higher frequencies comprises relatively flat bands of intramolecular modes (Figure 2c). Phonons have finite lifetimes τ

_{qj}due to a variety of scattering processes, which means that the intrinsic line widths Γ

_{qj}= ℏ/τ

_{qj}(where Γ

_{qj}is the Lorentzian fwhm line width) vary as a function of energy and wavevector and are intrinsically temperature-dependent through the populations of the modes involved in the scattering processes. (44) We have previously treated phonon line widths as an empirical parameter, (22) while Lunghi et al. proposed a simplified model for an effective phonon line width based on the NVT canonical ensemble (eq 1) (25)

_{qj}and line widths Γ

_{qj}from first principles, we calculated third-order (anharmonic) force constants with a similar numerical finite-difference method (see the Methods) and modeled the phonon–phonon scattering processes explicitly for a grid of wavevectors

*q*at a series of temperatures. (44) Here, we have used 2 × 2 × 2, 3 × 3 × 3, 4 × 4 × 4, and 5 × 5 × 5

*q*-point grids with 6, 8, 21, and 27 unique

*q*-points, respectively, and performed the calculations at 10, 20, 30, 40, 50, 60, and 300 K. The

*ab initio*line widths vary both as a function of wavevector and mode energy (Figure 3a), but we find that their behavior is relatively insensitive to the choice of grid (Figure S2). There is also a marked temperature dependence (Figures S3 and S4), arising from larger scattering probabilities as the phonons are more heavily populated at elevated temperature, (44) which above 30 K is well approximated as Γ ∝

*T*, in agreement with the high-temperature limit of eq 1. (25) However, the line widths predicted by eq 1 differ substantially from our

*ab initio*calculated values, especially at low and high phonon energies (Figure 3a). The

*ab initio*phonon line widths for

**1**at 300 K are on the order of 0.1–40 cm

^{–1}(corresponding to lifetimes on the order of 100–0.1 ps), and some modes become much longer lived at low temperatures with lifetimes of up to 4.5 ns (line widths of 0.001 cm

^{–1}) at 10 K. However, even the longest of these

*ab initio*lifetimes is still orders of magnitude shorter than the experimental spin lifetimes for this compound, which are seconds to hundreds of microseconds, justifying the commonly assumed Born–Markov approximation for molecular spin dynamics. (22,31) To the best of our knowledge, the present study represents one of very few explicit calculations of the phonon line widths and lifetimes for a molecular crystal and the only such calculation for a molecular magnet.

*q*-point grid and applying Gaussian or Lorentzian smoothing functions with an arbitrary line width (e.g., Figure 2b). Here, because we have calculated the mode-dependent line widths from first principles, we can directly construct the DoS without an artificial smoothing function (Figure 3b). The resulting low-energy DoS is sharply featured when using a small 2 × 2 × 2

*q*-point grid due to the coarse sampling of the Brillouin zone. The low-energy DoS as ω → 0, determined solely by the three acoustic modes, is expected to be a quadratic function of frequency, (64) and this behavior in the low-energy DoS is better approximated using a larger 5 × 5 × 5

*q*-point grid to sample the dispersion of these modes more accurately, although we note that this grid still does not fully capture the low-energy dispersion (cf. Figure 2b). We also note that using a small grid would be more problematic at lower temperatures given the drastic narrowing of the line widths (Figure S5). Given the similar profiles of the line widths obtained with different grids (Figure S2), the difference in the DoS obtained with the different

*q*-point sampling in Figure 3b can be attributed to better integration of the reciprocal space. We note that the issue of a sharply featured DoS can potentially be avoided by using a suitable fixed phonon line width, and a line width of Γ = 10 cm

^{–1}gives a smooth DoS even with a comparatively sparse 2 × 2 × 2

*q*-point grid (Figure S6).

### Spin Dynamics and Crystalline Electrostatic Potential

*ab initio*phonon line widths on the spin dynamics, we proceeded to calculate the spin–phonon coupling and magnetic relaxation rates (see the Methods). We first examined the spin dynamics under the gas-phase ansatz by optimizing the geometry and obtaining the vibrational modes of an isolated molecule of

**1**(see the Methods). The calculated single-phonon Orbach magnetic relaxation rates, using the gas-phase vibrational modes and fixed line widths, show excellent agreement with the experimental measurements at high temperature (Figure S7). As we have shown previously, the absolute rates show a significant dependence on the choice of line width, (15,22,65) with broader line widths leading to faster relaxation rates. This behavior occurs for single-phonon processes because there is only one possible phonon energy ℏω = |

*E*

_{f}–

*E*

_{i}| that can cause a spin transition between any pair of states i and f (where

*E*

_{i}and

*E*

_{f}are the initial and final electronic state energies, respectively), and a larger line width gives a larger probability of overlap between |

*E*

_{f}–

*E*

_{i}| and the calculated vibrational energies. We find that the best agreement is obtained with Γ = 1 cm

^{–1}(Figure S7), which is consistent with the approximate center of the distribution of

*ab initio*phonon line widths at 50 K (Figure 3a).

*q*-point grids on which the

*ab initio*frequencies and line widths were obtained. However, it is known that the crystalline electrostatic potential converges very slowly in real space, and finite slab expansions of lattice charges do not correctly approach the exact potential. (66) This is because atomic charges within a unit cell are only balanced by their periodic neighboring charges, and so the surfaces of a finite slab remain charged, generating a static electric field that deviates from that in the infinite crystal. (66) This is clearly observed in the electrostatic potential map, where there is an obvious lack of symmetry for the finite slab expansions compared to the exact result for an infinite crystal (Figure 4) and also in the corresponding equilibrium electronic CF splitting for

**1**calculated with different electrostatic potentials (Figure S8). We note that we checked larger slabs up to a 9 × 9 × 9 expansion and still did not observe convergence (Figure S8). The electrostatic potential can be converged very quickly in reciprocal space using Ewald summation, (67) but this method is not available in OpenMolcas. (53) Luckily, there are two methods that can be employed to address this issue: the first uses an extra set of charges external to the crystalline slab as fitting parameters to replicate the exact infinite crystalline potential (68,69) and the second places an approximately spherical array of unit cells in a perfect conductor to screen the charges directly, (70) thus approximating the infinite crystalline potential very closely. The first method is not compatible with our analytic “one-shot” LVC method for obtaining the spin–phonon coupling coefficients, (60) and we have therefore used the conductor screening method, which allows us to obtain spin–phonon coupling coefficients corrected for the infinite crystalline electrostatic potential (see the Methods).

*q*-point grids to assess the impact of Brillouin zone integration on the phonons and spin dynamics.

*q*-point grids: the rates obtained with Γ = 0.1 and 10 cm

^{–1}differ by a factor of ∼19 at 60 K in the gas-phase calculations, reducing to factors of ∼8 and ∼2 for solid-state calculations with 2 × 2 × 2 and 5 × 5 × 5 grids, respectively. We next calculated the two-phonon Raman rates with fixed line widths, which are in excellent agreement with the experimental rates (Figure S11). We note that the choice of line width has a larger effect in this region than in the single-phonon Orbach region and that, counterintuitively, the two-phonon Raman rates have a negative correlation with line width, i.e., the rates become slower with larger line widths, which is the opposite behavior to the single-phonon rates. This can be explained by the fact that for the Raman mechanism, only the difference in the phonon energy ℏω–ℏω′ must match the difference in electronic energy

*E*

_{f}–

*E*

_{i}, which allows many pairs of phonons to cause a transition between the ground doublet states. (45) When the line widths are larger, the phonon lineshapes extend to higher energies, resulting in smaller Bose–Einstein occupation factors and hence a reduction in the magnitude of these contributions.

^{–1}differ by a factor of 1.5 at 60 K for the 2 × 2 × 2 grid, which reduces to 1.2 for the 5 × 5 × 5 grid). We also note that the increased sensitivity of the magnetic relaxation rates in the Raman region to the choice of phonon line width compared to the Orbach region could provide an explanation for the increase in the distribution of magnetic relaxation rates for this compound as the temperature is decreased, i.e., the presence of crystalline disorder, shown to correlate with the width of the distributions of magnetic relaxation rates, (71) has more of an effect on the Raman rates, which tend to dominate as the temperature is reduced.

*ab initio*phonon line widths. In the Orbach region, the rates obtained using mode- and temperature-dependent line widths coincide with the fixed line width calculations using Γ = 1 cm

^{–1}(Figure S10). In the Raman region, the rates obtained with mode- and temperature-dependent line widths are close to those obtained with fixed Γ = 10 cm

^{–1}at 60 K but increasingly approach the smaller fixed line width calculations at lower temperature, crossing the Γ = 0.1 cm

^{–1}rates between 20 and 10 K (Figure S11). As the Raman rates are more strongly affected by the choice of line width than the Orbach rates, it is unsurprising that the extreme narrowing of some of the

*ab initio*phonon line widths at low temperatures has a marked impact on the relaxation rates. However, we note that the profile of the relaxation rates calculated using

*ab initio*mode- and temperature-dependent line widths does not agree with the experimental data at the lowest temperatures and in particular level off at low temperature, while the experimental rates continue to decrease. We therefore suggest that the extreme narrowing of the

*ab initio*line widths at low temperatures is overestimated and that there are likely other sources of phonon scattering (such as boundary effects, impurities, defects, and/or disorder) in real crystals that would lead to shorter phonon lifetimes, and therefore broader line widths, at lower temperature than those estimated by our DFT calculations on a perfect infinite crystal.

^{–1}, Γ = 417 cm

^{–1}at 300 K from eq 1, but is ca. 1–10 cm

^{–1}as calculated

*ab initio*, Figures S3 and S4) such that the numerical integration over the phonon lineshapes when computing the Raman mechanism becomes problematic, and we therefore only report these results for

*T*≤ 46 K. We have also previously shown that the NVT line widths of the high-energy phonons drastically narrow at low temperature, resulting in unphysical Orbach rates, (22) which again we find here when using anti-Lorentzian lineshapes. Nevertheless, we find that in both the Orbach and Raman regions, the NVT expression gives rates that are close to those obtained using a fixed Γ = 10 cm

^{–1}(Figures S12 and S13) and in fact gives rates nearly identical to those obtained by fixing the line widths to their

*ab initio*calculated values at 300 K, which themselves agree well with the rates obtained using the mode- and temperature-dependent line widths above ca. 30 K (Figures S12 and S13). Overall, however, excellent agreement with the experimental rates can be obtained using a simple fixed line width of Γ = 0.1 cm

^{–1}(Figure 5), but, there is little difference to using Γ = 1 cm

^{–1}when the largest 5 × 5 × 5

*q*-point grid is employed (Figure S14).

*ab initio*methodology, we are in the unique position to reliably decompose our calculations and learn which phonon modes are important for the Raman mechanism in compound

**1**. As the Raman rates are calculated as sums over pairs of modes involved in the scattering process (eqs 46–49 in reference (45)), we can examine the contribution that every pair makes to the total rate; here, we do so using the modes obtained with the 2 × 2 × 2

*q*-point grid with fixed Γ = 1 cm

^{–1}for simplicity.

^{–1}at

*=*

**q***Y*(0.5, −0.5, 0) and one of the doubly degenerate modes with ℏ

*ω*= 19.98 cm

^{–1}at

*=*

**q***T*(0.5, −0.5, 0.5), and between one of the doubly degenerate modes with ℏ

*ω*= 27.41 cm

^{–1}at

*= (0.5, 0, 0.5) and ℏω = 27.66 cm*

**q**^{–1}at

*=*

**q***Y*(0.5, −0.5, 0). These are all off-Γ acoustic modes that mix substantially with the low-energy pseudoacoustic spectrum (Figure 2a). At higher temperatures where the Raman mechanism is almost overtaken by the Orbach mechanism (e.g., 40 K; Table S3), significant contributions arise from scattering between higher energy modes. One pair has ℏ

*ω*= 154.68 cm

^{–1}(mode 42 at

*=*

**q***Y*(0.5, −0.5, 0), corresponding to an asymmetric N

_{py}–Dy–N

_{py}stretch) and ℏω = 154.74 cm

^{–1}(degenerate modes 43 and 44 at

*=*

**q***Z*, corresponding to a pinching of the phenoxide O atoms parallel to the Dy–Br axis accompanied by a rotation of the O atoms around the Dy–Br axis). A second pair has ℏω = 113.65 cm

^{–1}(degenerate modes 29 and 30 at

*=*

**q***T*(0.5, −0.5, 0.5), a twisting of the phenoxide and pyridine rings around their tethers) and ℏω = 114.47 cm

^{–1}(mode 30 at

*= (0.5, 0, 0), which is a pinching of the pyridyl N and phenoxide O atoms parallel to the Dy–Br axis).*

**q**^{–1}) from our Raman relaxation rate calculations leads to a barely perceptible change in the total rate of only <11% (Table S4). Removing all modes listed in Table S3 and their symmetry equivalents leads to a slightly more substantial reduction of 27% at 40 K, but it is not until we additionally remove the pseudoacoustic modes between 25 and 60 cm

^{–1}that contribute to the first peak in the phonon DoS (Figure 2b) that we obtain a 66% average reduction in the Raman rates across the 10–40 K region (Table S4). The pseudoacoustic modes involve molecular rotations and twists, some of which are accompanied by wagging of the Dy–Br bond, which also occurs at low energies given the large mass of Br. The terminal bromide ligand can therefore be associated with increasing Raman relaxation rates in

**1**, along with the flexible backbone of the bbpen ligand, as described above.

## Conclusions

*ab initio*calculation of the phonon lifetimes and line widths and demonstrated that (i) the Born–Markov approximation is justified for Dy(III) single-molecule magnets, and (ii) that the choice of the phonon line width model is not crucial to describe molecular spin dynamics, given an adequate integration of reciprocal space. Hence, the large computational burden of obtaining

*ab initio*line widths is not justified for this application, and either the NVT approximation or a simple fixed line width on the order of Γ = 0.1–10 cm

^{–1}is the most transferrable and economic method for molecular spin dynamics calculations. Indeed, we are currently exploring the present method applied to other molecular magnets, including those based on different metal ions, and find excellent agreement with experiment. The open-source tools we have developed and used herein thus open the door to quantitatively accurate and efficient spin–phonon calculations on molecular solids.

## Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.3c06015.

Convergence testing, optimized unit cell parameters,

*ab initio*calculated line widths, DoS plots, magnetic relaxation rates under different approximations, and contributions to Raman relaxation (PDF)

## 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.

## Acknowledgments

The authors thank the Royal Society for a University Research Fellowship (URF191320 to N.F.C.), UK Research and Innovation for a Future Leaders Fellowship (MR/T043121/1 to J.M.S.), the European Research Council for a Starting Grant (StG-851504 to N.F.C.), and the Computational Shared Facility at The University of Manchester for access to computational resources. *Via* our membership of the UK’s HEC Materials Chemistry Consortium, which is funded by the UK Engineering and Physical Sciences Research Council (EP/R029431), this work used the ARCHER2 UK National Supercomputing Service (https://www.archer2.ac.uk). Raw data supporting this publication have been deposited on FigShare (doi: 10.48420/22148963).

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However, the sub-200-fs lifetimes of the redox-active metal-to-ligand charge transfer (MLCT) excited states typically encountered in these compds. have largely precluded their widespread use3. Here we show that the MLCT lifetime of an iron(II) complex can be manipulated using information from excited-state quantum coherences as a guide to implementing synthetic modifications that can disrupt the reaction coordinate assocd. with MLCT decay. We developed a structurally tunable mol. platform in which vibronic coherences-i.e., coherences reflecting a coupling of vibrational and electronic degrees of freedom-were obsd. in ultrafast time-resolved absorption measurements after MLCT excitation of the mol. Following visualization of the vibrational modes assocd. with these coherences, we synthetically modified an iron(II) chromophore to interfere with these specific at. motions. 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Ultrafast transient absorption spectroscopy in soln. reveals oscillations superimposed on the decay traces due to a vibrational wavepacket. Based on complementary measurements and calcns. on the monomer Mn(acac)3, the wavepacket motion in the trinuclear SMM is constrained along the Jahn-Teller axis due to the μ3-oxo and μ-oxime bridges. The results provide new possibilities for optical control of the magnetization in SMMs on fs timescales and open up new mol.-design challenges to control the wavepacket motion in the excited state of polynuclear transition-metal complexes.**6**Serrano, D.; Kuppusamy, S. K.; Heinrich, B.; Fuhr, O.; Hunger, D.; Ruben, M.; Goldner, P. 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However, so far, few cryst. materials have shown an environment quiet enough to fully exploit REI properties. This hinders further progress, in particular towards REI-contg. integrated nanophotonics devices. Mol. systems can provide such capability but generally lack spin states. If, however, mol. systems do have spin states, they show broad optical lines that severely limit optical-to-spin coherent interfacing. Here we report on europium mol. crystals that exhibit linewidths in the tens of kilohertz range, orders of magnitude narrower than those of other mol. systems. We harness this property to demonstrate efficient optical spin initialization, coherent storage of light using an at. frequency comb, and optical control of ion-ion interactions towards implementation of quantum gates. 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Performing any useful computation demands much more than realizing a robust qubit-one also needs a large no. of qubits and a reliable manner with which to integrate them into a complex circuitry that can store and process information and implement quantum algorithms. This 'scalability' is arguably one of the challenges for which a chem.-based bottom-up approach is best-suited. Mols., being much more versatile than atoms, and yet microscopic, are the quantum objects with the highest capacity to form non-trivial ordered states at the nanoscale and to be replicated in large nos. using chem. tools.**11**Gatteschi, D.; Sessoli, R.; Villain, J.*Molecular Nanomagnets*; Oxford University Press, 2006.Google ScholarThere is no corresponding record for this reference.**12**Chilton, N. F. Molecular Magnetism.*Annu. Rev. Mater. 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The above topics are complemented by an overview of pertinent electronic structure methods and, in a look towards the future, an overview of the state of the art in measurement and modeling of mol. spin-phonon coupling.**13**Escalera-Moreno, L.; J Baldoví, J.; Gaita-Ariño, A.; Coronado, E. Spin States, Vibrations and Spin Relaxation in Molecular Nanomagnets and Spin Qubits: A Critical Perspective.*Chem. Sci.*2018,*9*(13), 3265– 3275, DOI: 10.1039/C7SC05464EGoogle Scholar13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXjvFWqu78%253D&md5=0687f59f35f9c3cda5e476eaea5ed284Spin states, vibrations and spin relaxation in molecular nanomagnets and spin qubits: a critical perspectiveEscalera-Moreno, Luis; Baldovi, Jose J.; Gaita-Arino, Alejandro; Coronado, EugenioChemical Science (2018), 9 (13), 3265-3275CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)Very recently the closely related fields of mol. spin qubits, single ion magnets and single atom magnets have been shaken by unexpected results. We have witnessed a jump in the phase memory times of spin qubits from a few microseconds to almost a millisecond in a vanadium complex, magnetic hysteresis up to 60 K in a dysprosium-based magnetic mol. and magnetic memory up to 30 K in a holmium atom deposited on a surface. With single-mol. magnets being more than two decades old, this rapid improvement in the phys. properties is surprising and its explanation deserves urgent attention. The general assumption of focusing uniquely on the energy barrier is clearly insufficient to model magnetic relaxation. Other factors, such as vibrations that couple to spin states, need to be taken into account. In fact, this coupling is currently recognized to be the key factor that accounts for the slow relaxation of magnetization at higher temps. Herein we will present a crit. perspective of the recent advances in mol. nanomagnetism towards the goal of integrating spin-phonon interactions into the current computational methodologies of spin relaxation. This presentation will be placed in the context of the well-known models developed in solid state physics, which, as we will explain, are severely limited for mol. systems.**14**Lunghi, A.; Sanvito, S. The Limit of Spin Lifetime in Solid-State Electronic Spins.*J. Phys. Chem. Lett.*2020,*11*(15), 6273– 6278, DOI: 10.1021/acs.jpclett.0c01681Google Scholar14https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtl2rsrfP&md5=3c6e646b3b537f46e159933629c0b465The Limit of Spin Lifetime in Solid-State Electronic SpinsLunghi, Alessandro; Sanvito, StefanoJournal of Physical Chemistry Letters (2020), 11 (15), 6273-6278CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)The development of spin qubits for quantum technologies requires their protection from the main source of finite-temp. decoherence: at. vibrations. Here the authors eliminate one of the main barriers to the progress in this field by providing a complete 1st-principles picture of spin relaxation that includes up to 2-phonon processes. Method is based on machine learning and electronic structure theory and makes the prediction of spin lifetime in realistic systems feasible. The authors study a prototypical V-based mol. qubit and reveal that the spin lifetime at high temp. is limited by Raman processes due to a small no. of THz intramol. vibrations. These findings effectively change the conventional understanding of spin relaxation in this class of materials and open new avenues for the rational design of long-living spin systems.**15**Goodwin, C. A. P.; Ortu, F.; Reta, D.; Chilton, N. F.; Mills, D. P. Molecular Magnetic Hysteresis at 60 K in Dysprosocenium.*Nature*2017,*548*(7668), 439– 442, DOI: 10.1038/nature23447Google Scholar15https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhtlyisbfF&md5=8bc379889e7ac64db1802a4e14fed96eMolecular magnetic hysteresis at 60 kelvin in dysprosoceniumGoodwin, Conrad A. P.; Ortu, Fabrizio; Reta, Daniel; Chilton, Nicholas F.; Mills, David P.Nature (London, United Kingdom) (2017), 548 (7668), 439-442CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)Lanthanides were studied extensively for potential applications in quantum information processing and high-d. data storage at the mol. and at. scale. Exptl. achievements include reading and manipulating single nuclear spins, exploiting at. clock transitions for robust qubits and, most recently, magnetic data storage in single atoms. Single-mol. magnets exhibit magnetic hysteresis of mol. origin-a magnetic memory effect and a prerequisite of data storage-and so far lanthanide examples have exhibited this phenomenon at the highest temps. However, in the nearly 25 years since the discovery of single-mol. magnets, hysteresis temps. have increased from 4 K to only ∼14 K using a consistent magnetic field sweep rate of ∼20 Oe per s, although higher temps. were achieved by using very fast sweep rates (for example, 30 K with 200 Oe per s). Here the authors report a hexa-tert-butyldysprosocenium complex-[Dy(Cpttt)2][B(C6F5)4], with Cpttt = {C5H2tBu3-1,2,4} and tBu = CMe3-which exhibits magnetic hysteresis at temps. of up to 60 K at a sweep rate of 22 Oe per s. The authors observe a clear change in the relaxation dynamics at this temp., which persists in magnetically dild. samples, suggesting that the origin of the hysteresis is the localized metal-ligand vibrational modes that are unique to dysprosocenium. Ab initio calcns. of spin dynamics demonstrate that magnetic relaxation at high temps. is due to local mol. vibrations. With judicious mol. design, magnetic data storage in single mols. at temps. above liq. nitrogen should be possible.**16**Lunghi, A.; Totti, F.; Sanvito, S.; Sessoli, R. Intra-Molecular Origin of the Spin-Phonon Coupling in Slow-Relaxing Molecular Magnets.*Chem. Sci.*2017,*8*(9), 6051– 6059, DOI: 10.1039/C7SC02832FGoogle Scholar16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXht1GrtrvP&md5=b72061032d53ce16e8f9869479e52355Intra-molecular origin of the spin-phonon coupling in slow-relaxing molecular magnetsLunghi, Alessandro; Totti, Federico; Sanvito, Stefano; Sessoli, RobertaChemical Science (2017), 8 (9), 6051-6059CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)We perform a systematic investigation of the spin-phonon coupling leading to spin relaxation in the prototypical mononuclear single mol. magnet [(tpaPh)Fe]-. In particular we analyze in detail the nature of the most relevant vibrational modes giving rise to the relaxation. Our fully ab initio calcns., where the phonon modes are evaluated at the level of d. functional theory and the spin-phonon coupling by mapping post-Hartree-Fock electronic structures onto an effective spin Hamiltonian, reveal that acoustic phonons are not active in the spin-phonon relaxation process of dil. SMMs crystals. Furthermore, we find that intra-mol. vibrational modes produce anisotropy tensor modulations orders of magnitude higher than those assocd. to rotations. In light of these results we are able to suggest new designing rules for spin-long-living SMMs which go beyond the tailoring of static mol. features but fully take into account dynamical features of the vibrational thermal bath evidencing those internal mol. distortions more relevant to the spin dynamics.**17**Abragam, A.; Bleaney, B.*Electron Paramagnetic Resonance of Transition Ions*; Oxford University Press, 1970.Google ScholarThere is no corresponding record for this reference.**18**Guo, F.-S.; Day, B. M.; Chen, Y.-C.; Tong, M.-L.; Mansikkamäki, A.; Layfield, R. A. Magnetic Hysteresis up to 80 K in a Dysprosium Metallocene Single-Molecule Magnet.*Science*2018,*362*(6421), 1400– 1403, DOI: 10.1126/science.aav0652Google Scholar18https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisFeksL3F&md5=13d4c594df879bd5b507078447ab9af2Magnetic hysteresis up to 80 kelvin in a dysprosium metallocene single-molecule magnetGuo, Fu-Sheng; Day, Benjamin M.; Chen, Yan-Cong; Tong, Ming-Liang; Mansikkamaeki, Akseli; Layfield, Richard A.Science (Washington, DC, United States) (2018), 362 (6421), 1400-1403CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)Single-mol. magnets (SMMs) contg. only one metal center may represent the lower size limit for mol.-based magnetic information storage materials. Their current drawback is that all SMMs require liq.-helium cooling to show magnetic memory effects. We now report a chem. strategy to access the dysprosium metallocene cation [(CpiPr5)Dy(Cp*)]+ (CpiPr5, penta-iso-propylcyclopentadienyl; Cp*, pentamethylcyclopentadienyl), which displays magnetic hysteresis above liq.-nitrogen temps. An effective energy barrier to reversal of the magnetization of Ueff = 1541 wave no. is also measured. The magnetic blocking temp. of TB = 80 K for this cation overcomes an essential barrier toward the development of nanomagnet devices that function at practical temps.**19**Gould, C. A.; McClain, K. R.; Reta, D.; Kragskow, J. G. C.; Marchiori, D. A.; Lachman, E.; Choi, E.-S.; Analytis, J. G.; Britt, R. D.; Chilton, N. F.; Harvey, B. G.; Long, J. R. Ultrahard Magnetism from Mixed-Valence Dilanthanide Complexes with Metal-Metal Bonding.*Science*2022,*375*(6577), 198– 202, DOI: 10.1126/science.abl5470Google Scholar19https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhvV2lsbk%253D&md5=ebf15df0aa5b317333b45859719de25fUltrahard magnetism from mixed-valence dilanthanide complexes with metal-metal bondingGould, Colin A.; McClain, K. Randall; Reta, Daniel; Kragskow, Jon G. C.; Marchiori, David A.; Lachman, Ella; Choi, Eun-Sang; Analytis, James G.; Britt, R. David; Chilton, Nicholas F.; Harvey, Benjamin G.; Long, Jeffrey R.Science (Washington, DC, United States) (2022), 375 (6577), 198-202CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)Metal-metal bonding interactions can engender outstanding magnetic properties in bulk materials and mols., and examples abound for the transition metals. Extending this paradigm to the lanthanides, herein we report mixed-valence dilanth anide complexes (CpiPr5)2Ln2I3 (Ln is Gd, Tb, or Dy; CpiPr5, pentaisopropylcyclopentadienyl), which feature a singly occupied lanthanide-lanthanide σ-bonding orbital of 5dz2 parentage, as detd. by structural, spectroscopic, and computational analyses. Valence delocalization, wherein the d electron is equally shared by the two lanthanide centers, imparts strong parallel alignment of the σ-bonding and f electrons on both lanthanides according to Hund's rules. The combination of a well-isolated high-spin ground state and large magnetic anisotropy in (CpiPr5)2Dy2I3 gives rise to an enormous coercive magnetic field with a lower bound of 14 T at temps. as high as 60 K.**20**Chiesa, A.; Cugini, F.; Hussain, R.; Macaluso, E.; Allodi, G.; Garlatti, E.; Giansiracusa, M.; Goodwin, C. A. P.; Ortu, F.; Reta, D.; Skelton, J. M.; Guidi, T.; Santini, P.; Solzi, M.; De Renzi, R.; Mills, D. P.; Chilton, N. F.; Carretta, S. Understanding Magnetic Relaxation in Single-Ion Magnets with High Blocking Temperature.*Phys. Rev. B*2020,*101*(17), 174402 DOI: 10.1103/PhysRevB.101.174402Google Scholar20https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsFequrfK&md5=c8334ba3e94991645831b1b0a005de83Understanding magnetic relaxation in single-ion magnets with high blocking temperatureChiesa, A.; Cugini, F.; Hussain, R.; Macaluso, E.; Allodi, G.; Garlatti, E.; Giansiracusa, M.; Goodwin, C. A. P.; Ortu, F.; Reta, D.; Skelton, J. M.; Guidi, T.; Santini, P.; Solzi, M.; De Renzi, R.; Mills, D. P.; Chilton, N. F.; Carretta, S.Physical Review B (2020), 101 (17), 174402CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)The recent discovery of single-ion magnets with magnetic hysteresis above liq.-nitrogen temps. placed these compds. among the best candidates to realize high-d. storage devices. Starting from a prototypical dysprosocenium mol., showing hysteresis up to 60 K, we derive here a general recipe to design high-blocking-temp. rare-earth single-ion magnets. The complex magnetic relaxation is unraveled by combining magnetization and NMR measurements with inelastic neutron scattering expts. and ab initio calcns., thus disentangling the different mechanisms and identifying the key ingredients behind slow relaxation.**21**Randall McClain, K.; Gould, C. A.; Chakarawet, K.; Teat, S.; Groshens, T. J.; Long, J. R.; Harvey, B. G. High-Temperature Magnetic Blocking and Magneto-Structural Correlations in a Series of Dysprosium(III) Metallocenium Single-Molecule Magnets.*Chem. Sci.*2018,*9*, 8492– 8503, DOI: 10.1039/C8SC03907KGoogle Scholar21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhvFCjsrjN&md5=1223684628a7d022399fa5a032335ba5High-temperature magnetic blocking and magneto-structural correlations in a series of dysprosium(III) metallocenium single-molecule magnetsRandall McClain, K.; Gould, Colin A.; Chakarawet, Khetpakorn; Teat, Simon J.; Groshens, Thomas J.; Long, Jeffrey R.; Harvey, Benjamin G.Chemical Science (2018), 9 (45), 8492-8503CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)A series of dysprosium(III) metallocenium salts, [Dy(CpiPr4R)2][B(C6F5)4] (R = H (1), Me (2), Et (3), iPr (4)), was synthesized by reaction of DyI3 with the corresponding known NaCpiPr4R (R = H, iPr) and novel NaCpiPr4R (R = Me, Et) salts at high temp., followed by iodide abstraction with [H(SiEt3)2][B(C6F5)4]. Variation of the substituents in this series results in substantial changes in mol. structure, with more sterically-encumbering cyclopentadienyl ligands promoting longer Dy-C distances and larger Cp-Dy-Cp angles. Dc and ac magnetic susceptibility data reveal that these structural changes have a considerable impact on the magnetic relaxation behavior and operating temp. of each compd. In particular, the magnetic relaxation barrier increases as the Dy-C distance decreases and the Cp-Dy-Cp angle increases. An overall 45 K increase in the magnetic blocking temp. is obsd. across the series, with compds. 2-4 exhibiting the highest 100 s blocking temps. yet reported for a single-mol. magnet. Compd. 2 possesses the highest operating temp. of the series with a 100 s blocking temp. of 62 K. Concomitant increases in the effective relaxation barrier and the max. magnetic hysteresis temp. are obsd., with 2 displaying a barrier of 1468 cm-1 and open magnetic hysteresis as high as 72 K at a sweep rate of 3.1 mT s-1. Magneto-structural correlations are discussed with the goal of guiding the synthesis of future high operating temp. DyIII metallocenium single-mol. magnets.**22**Reta, D.; Kragskow, J. G. C.; Chilton, N. F. Ab Initio Prediction of High-Temperature Magnetic Relaxation Rates in Single-Molecule Magnets.*J. Am. Chem. Soc.*2021,*143*(15), 5943– 5950, DOI: 10.1021/jacs.1c01410Google Scholar22https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXnvF2gu7w%253D&md5=2f860e9ac222235f2792d230259e57fbAb Initio Prediction of High-Temperature Magnetic Relaxation Rates in Single-Molecule MagnetsReta, Daniel; Kragskow, Jon G. C.; Chilton, Nicholas F.Journal of the American Chemical Society (2021), 143 (15), 5943-5950CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)Organometallic mols. based on [Dy(CpR)2]+ cations (where CpR is a substituted cyclopentadienyl anion) have emerged as clear front-runners in the search for high-temp. single-mol. magnets. Within this family of structurally similar mols., significant variations in their magnetic properties are seen, demonstrating the importance of understanding magneto-structural relationships to develop more efficient design strategies. Here we develop an ab initio spin dynamics methodol. and show that it is capable of quant. prediction of relative relaxation rates in the Orbach region. Applying it to all reported [Dy(CpR)2]+ cations allows us understand differences in their relaxation dynamics, highlighting that the main discriminant is the magnitude of the crystal field splitting, rather than differences in spin-vibrational coupling. We subsequently employ the method to predict relaxation rates for a series of hypothetical organometallic sandwich compds., revealing an upper limit to the effective barrier to magnetic relaxation of around 2100-2200 K, which has been reached by existing compds. Our conclusion is that further improvements to monometallic single-mol. magnets require moving vibrational modes off-resonance with electronic excitations.**23**Lunghi, A.; Sanvito, S. Surfing Multiple Conformation-Property Landscapes via Machine Learning: Designing Single-Ion Magnetic Anisotropy.*J. Phys. Chem. C*2020,*124*(10), 5802– 5806, DOI: 10.1021/acs.jpcc.0c01187Google Scholar23https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXivVaktLw%253D&md5=22d2b08703e9a20cb543a12f1d1cc041Surfing Multiple Conformation-Property Landscapes via Machine Learning: Designing Single-Ion Magnetic AnisotropyLunghi, Alessandro; Sanvito, StefanoJournal of Physical Chemistry C (2020), 124 (10), 5802-5806CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)Computational statistical disciplines, such as machine learning, are leading to a paradigm shift in the way the authors conceive the design of new compds., offering a way to directly design the best compd. for specific applications. This approach, known as reverse engineering, requires the construction of models able to efficiently predict continuous structure-property maps. Here, the authors show that machine learning offers such a possibility by designing a model that predicts both the energy and magnetic properties as a function of the mol. structure of a single-ion magnet. This model is then used to explore the mol. conformational landscapes in search of structures that maximize magnetic anisotropy. The authors find that a 5% change in one of the coordination angles leads to a ∼50% increase in the anisotropy. This approach can be applied to any structure-property relation and paves the way for a machine-learning-driven optimization of chem. compds.**24**Escalera-Moreno, L.; Suaud, N.; Gaita-Ariño, A.; Coronado, E. Determining Key Local Vibrations in the Relaxation of Molecular Spin Qubits and Single-Molecule Magnets.*J. Phys. Chem. Lett.*2017,*8*, 1695– 1700, DOI: 10.1021/acs.jpclett.7b00479Google Scholar24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXltVSqtrw%253D&md5=efae85248b706be0d5e6897009782538Determining Key Local Vibrations in the Relaxation of Molecular Spin Qubits and Single-Molecule MagnetsEscalera-Moreno, L.; Suaud, N.; Gaita-Arino, A.; Coronado, E.Journal of Physical Chemistry Letters (2017), 8 (7), 1695-1700CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)To design mol. spin qubits and nanomagnets operating at high temps., there is an urgent need to understand the relationship between vibrations and spin relaxation processes. Herein we develop a simple first-principles methodol. to det. the modulation that vibrations exert on spin energy levels. This methodol. is applied to [Cu(mnt)2]2- (mnt2- = 1,2-dicyanoethylene-1,2-dithiolate), a highly coherent complex. By theor. identifying the most relevant vibrational modes, we are able to offer general strategies to chem. design more resilient magnetic mols., where the energy of the spin states is not coupled to vibrations.**25**Lunghi, A.; Totti, F.; Sessoli, R.; Sanvito, S. The Role of Anharmonic Phonons in Under-Barrier Spin Relaxation of Single Molecule Magnets.*Nat. Commun.*2017,*8*, 14620 DOI: 10.1038/ncomms14620Google Scholar25https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC1czjtFahug%253D%253D&md5=af55f4e5f2641e56670ec5651e0d608aThe role of anharmonic phonons in under-barrier spin relaxation of single molecule magnetsLunghi Alessandro; Totti Federico; Sessoli Roberta; Lunghi Alessandro; Sanvito StefanoNature communications (2017), 8 (), 14620 ISSN:.The use of single molecule magnets in mainstream electronics requires their magnetic moment to be stable over long times. One can achieve such a goal by designing compounds with spin-reversal barriers exceeding room temperature, namely with large uniaxial anisotropies. Such strategy, however, has been defeated by several recent experiments demonstrating under-barrier relaxation at high temperature, a behaviour today unexplained. Here we propose spin-phonon coupling to be responsible for such anomaly. With a combination of electronic structure theory and master equations we show that, in the presence of phonon dissipation, the relevant energy scale for the spin relaxation is given by the lower-lying phonon modes interacting with the local spins. These open a channel for spin reversal at energies lower than that set by the magnetic anisotropy, producing fast under-barrier spin relaxation. Our findings rationalize a significant body of experimental work and suggest a possible strategy for engineering room temperature single molecule magnets.**26**Lunghi, A. Toward Exact Predictions of Spin-Phonon Relaxation Times: An Ab Initio Implementation of Open Quantum Systems Theory.*Sci. Adv.*2022,*8*(31), eabn7880 DOI: 10.1126/sciadv.abn7880Google ScholarThere is no corresponding record for this reference.**27**Albino, A.; Benci, S.; Tesi, L.; Atzori, M.; Torre, R.; Sanvito, S.; Sessoli, R.; Lunghi, A. First-Principles Investigation of Spin–Phonon Coupling in Vanadium-Based Molecular Spin Quantum Bits.*Inorg. Chem.*2019,*58*(15), 10260– 10268, DOI: 10.1021/acs.inorgchem.9b01407Google Scholar27https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhsVaqtL3E&md5=ecf53e227cb269283c657c52364625dcFirst-Principles Investigation of Spin-Phonon Coupling in Vanadium-Based Molecular Spin Quantum BitsAlbino, Andrea; Benci, Stefano; Tesi, Lorenzo; Atzori, Matteo; Torre, Renato; Sanvito, Stefano; Sessoli, Roberta; Lunghi, AlessandroInorganic Chemistry (2019), 58 (15), 10260-10268CODEN: INOCAJ; ISSN:0020-1669. (American Chemical Society)Paramagnetic mols. can show long spin-coherence times, which make them good candidates as quantum bits (qubits). Reducing the efficiency of the spin-phonon interaction is the primary challenge toward achieving long coherence times over a wide temp. range in soft mol. lattices. The lack of a microscopic understanding about the role of vibrations in spin relaxation strongly undermines the possibility of chem. designing better-performing mol. qubits. Here we report a first-principles characterization of the main mechanism contributing to the spin-phonon coupling for a class of vanadium(IV) mol. qubits. Post-Hartree-Fock and d. functional theory methods are used to det. the effect of both intermol. and intramol. vibrations on modulation of the Zeeman energy for four mols. showing different coordination geometries and ligands. This comparative study provides the first insight into the role played by coordination geometry and ligand-field strength in detg. the spin-lattice relaxation time of mol. qubits, opening an avenue to the rational design of new compds.**28**Shevlin, S.; Castro, B.; Li, X. Computational Materials Design.*Nat. Mater.*2021,*20*(6), 727, DOI: 10.1038/s41563-021-01038-8Google Scholar28https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB2c7gtVeluw%253D%253D&md5=6e7825cd82f936741e7b83ce17404140Computational materials designShevlin Stephen; Castro Bruno; Li XinNature materials (2021), 20 (6), 727 ISSN:.There is no expanded citation for this reference.**29**Butler, K. T.; Frost, J. M.; Skelton, J. M.; Svane, K. L.; Walsh, A. Computational Materials Design of Crystalline Solids.*Chem. Soc. Rev.*2016,*45*(22), 6138– 6146, DOI: 10.1039/C5CS00841GGoogle Scholar29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XksVajt7c%253D&md5=f9695a25b788f726dc66ed4ac4ae65fbComputational materials design of crystalline solidsButler, Keith T.; Frost, Jarvist M.; Skelton, Jonathan M.; Svane, Katrine L.; Walsh, AronChemical Society Reviews (2016), 45 (22), 6138-6146CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)The modeling of materials properties and processes from first principles is becoming sufficiently accurate as to facilitate the design and testing of new systems in silico. Computational materials science is both valuable and increasingly necessary for developing novel functional materials and composites that meet the requirements of next-generation technol. A range of simulation techniques are being developed and applied to problems related to materials for energy generation, storage and conversion including solar cells, nuclear reactors, batteries, fuel cells, and catalytic systems. Such techniques may combine crystal-structure prediction (global optimization), data mining (materials informatics) and high-throughput screening with elements of machine learning. We explore the development process assocd. with computational materials design, from setting the requirements and descriptors to the development and testing of new materials. As a case study, we critically review progress in the fields of thermoelecs. and photovoltaics, including the simulation of lattice thermal cond. and the search for Pb-free hybrid halide perovskites. Finally, a no. of universal chem.-design principles are advanced.**30**Nolan, A. M.; Zhu, Y.; He, X.; Bai, Q.; Mo, Y. Computation-Accelerated Design of Materials and Interfaces for All-Solid-State Lithium-Ion Batteries.*Joule*2018,*2*(10), 2016– 2046, DOI: 10.1016/j.joule.2018.08.017Google Scholar30https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhvFOrsb%252FI&md5=c4feeea90a614cdda2f06b973a5492afComputation-Accelerated Design of Materials and Interfaces for All-Solid-State Lithium-Ion BatteriesNolan, Adelaide M.; Zhu, Yizhou; He, Xingfeng; Bai, Qiang; Mo, YifeiJoule (2018), 2 (10), 2016-2046CODEN: JOULBR; ISSN:2542-4351. (Cell Press)A review. The all-solid-state lithium-ion battery is a promising next-generation battery technol. However, the realization of all-solid-state batteries is impeded by limited understanding of solid electrolyte materials and solid electrolyte-electrode interfaces. In this review, we present an overview of recently developed computation techniques and their applications in understanding and advancing materials and interfaces in all-solid-state batteries. We review the role of ab initio mol. dynamics simulations in studying fast ion conductors and discuss the capabilities of thermodn. calcns. powered by materials databases for identifying the chem. and electrochem. stability of solid electrolyte materials and solid electrolyte-electrode interfaces. We highlight the computational studies in the design and discovery of new solid electrolyte materials and outline design guidelines for solid electrolytes and their interfaces. We conclude with discussion of future directions in computation techniques, materials development, and interface engineering for all-solid-state lithium-ion batteries.**31**Briganti, M.; Santanni, F.; Tesi, L.; Totti, F.; Sessoli, R.; Lunghi, A. A Complete Ab Initio View of Orbach and Raman Spin–Lattice Relaxation in a Dysprosium Coordination Compound.*J. Am. Chem. Soc.*2021,*143*(34), 13633– 13645, DOI: 10.1021/jacs.1c05068Google Scholar31https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhvVSqs7%252FL&md5=ae99249136f2543532fc8fbdfdcc288fA Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination CompoundBriganti, Matteo; Santanni, Fabio; Tesi, Lorenzo; Totti, Federico; Sessoli, Roberta; Lunghi, AlessandroJournal of the American Chemical Society (2021), 143 (34), 13633-13645CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)The unique electronic and magnetic properties of lanthanide mol. complexes place them at the forefront of the race toward high-temp. single-mol. magnets and magnetic quantum bits. The design of compds. of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its max. potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chem. beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-mol. magnet. Computational predictions are in agreement with the exptl. detn. of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temp., is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive anal. of spin-phonon coupling mechanism reveals that mol. vibrations beyond the ion's first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chem. sound design rules tackling every aspect of spin relaxation at any temp.**32**Liu, J.; Chen, Y.-C.; Liu, J.-L.; Vieru, V.; Ungur, L.; Jia, J.-H.; Chibotaru, L. F.; Lan, Y.; Wernsdorfer, W.; Gao, S.; Chen, X.-M.; Tong, M.-L. A Stable Pentagonal Bipyramidal Dy(III) Single-Ion Magnet with a Record Magnetization Reversal Barrier over 1000 K.*J. Am. Chem. Soc.*2016,*138*(16), 5441– 5450, DOI: 10.1021/jacs.6b02638Google Scholar32https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28Xls1Gru7s%253D&md5=913ebcfdd033b556209ebcccdfb268e0A Stable Pentagonal Bipyramidal Dy(III) Single-Ion Magnet with a Record Magnetization Reversal Barrier over 1000 KLiu, Jiang; Chen, Yan-Cong; Liu, Jun-Liang; Vieru, Veacheslav; Ungur, Liviu; Jia, Jian-Hua; Chibotaru, Liviu F.; Lan, Yanhua; Wernsdorfer, Wolfgang; Gao, Song; Chen, Xiao-Ming; Tong, Ming-LiangJournal of the American Chemical Society (2016), 138 (16), 5441-5450CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)Single-mol. magnets (SMMs) with a large spin reversal barrier were recognized to exhibit slow magnetic relaxation that can lead to a magnetic hysteresis loop. Synthesis of highly stable SMMs with both large energy barriers and significantly slow relaxation times is challenging. Here, the authors report two highly stable and neutral Dy(III) classical coordination compds. with pentagonal bipyramidal local geometry that exhibit SMM behavior. Weak intermol. interactions in the undiluted single crystals are 1st obsd. for mononuclear lanthanide SMMs by micro-SQUID measurements. The study of magnetic relaxation reveals the thermally activated quantum tunneling of magnetization through the 3rd excited Kramers doublet, owing to the increased axial magnetic anisotropy and weaker transverse magnetic anisotropy. As a result, pronounced magnetic hysteresis loops up to 14 K are obsd., and the effective energy barrier (Ueff = 1025 K) for relaxation of magnetization reached a breakthrough among the SMMs.**33**Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J.*Gaussian 09*, revision D.01; Gaussian, Inc.: Wallingford CT, 2013.Google ScholarThere is no corresponding record for this reference.**34**Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple.*Phys. Rev. Lett.*1996,*77*(18), 3865– 3868, DOI: 10.1103/PhysRevLett.77.3865Google Scholar34https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XmsVCgsbs%253D&md5=55943538406ee74f93aabdf882cd4630Generalized gradient approximation made simplePerdew, John P.; Burke, Kieron; Ernzerhof, MatthiasPhysical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.**35**Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu.*J. Chem. Phys.*2010,*132*(15), 154104 DOI: 10.1063/1.3382344Google Scholar35https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXkvVyks7o%253D&md5=2bca89d904579d5565537a0820dc2ae8A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-PuGrimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, HelgeJournal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.**36**Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen.*J. Chem. Phys.*1989,*90*(2), 1007– 1023, DOI: 10.1063/1.456153Google Scholar36https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL1MXksVGmtrk%253D&md5=c6cd67a3748dc61692a9cb622d2694a0Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogenDunning, Thom H., Jr.Journal of Chemical Physics (1989), 90 (2), 1007-23CODEN: JCPSA6; ISSN:0021-9606.Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.**37**Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals.*Phys. Rev. B*1993,*47*(1), 558– 561, DOI: 10.1103/PhysRevB.47.558Google Scholar37https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3sXlt1Gnsr0%253D&md5=c9074f6e1afc534b260d29dd1846e350Ab initio molecular dynamics of liquid metalsKresse, G.; Hafner, J.Physical Review B: Condensed Matter and Materials Physics (1993), 47 (1), 558-61CODEN: PRBMDO; ISSN:0163-1829.The authors present ab initio quantum-mech. mol.-dynamics calcns. based on the calcn. of the electronic ground state and of the Hellmann-Feynman forces in the local-d. approxn. at each mol.-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using sub-space alignment. This approach avoids the instabilities inherent in quantum-mech. mol.-dynamics calcns. for metals based on the use of a factitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows one to perform simulations over several picoseconds.**38**Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal--Amorphous-Semiconductor Transition in Germanium.*Phys. Rev. B*1994,*49*(20), 14251– 14269, DOI: 10.1103/PhysRevB.49.14251Google Scholar38https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2cXkvFKrtL4%253D&md5=c5dddfd01394e53720fb4c3a3ccfd6c0Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germaniumKresse, G.; Hafner, J.Physical Review B: Condensed Matter and Materials Physics (1994), 49 (20), 14251-69CODEN: PRBMDO; ISSN:0163-1829.The authors present ab initio quantum-mech. mol.-dynamics simulations of the liq.-metal-amorphous-semiconductor transition in Ge. The simulations are based on (a) finite-temp. d.-functional theory of the 1-electron states, (b) exact energy minimization and hence calcn. of the exact Hellmann-Feynman forces after each mol.-dynamics step using preconditioned conjugate-gradient techniques, (c) accurate nonlocal pseudopotentials, and (d) Nose' dynamics for generating a canonical ensemble. This method gives perfect control of the adiabaticity of the electron-ion ensemble and allows the authors to perform simulations over >30 ps. The computer-generated ensemble describes the structural, dynamic, and electronic properties of liq. and amorphous Ge in very good agreement with expt.. The simulation allows the authors to study in detail the changes in the structure-property relation through the metal-semiconductor transition. The authors report a detailed anal. of the local structural properties and their changes induced by an annealing process. The geometrical, bounding, and spectral properties of defects in the disordered tetrahedral network are studied and compared with expt.**39**Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set.*Comput. Mater. Sci.*1996,*6*(1), 15– 50, DOI: 10.1016/0927-0256(96)00008-0Google Scholar39https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XmtFWgsrk%253D&md5=779b9a71bbd32904f968e39f39946190Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis setKresse, G.; Furthmuller, J.Computational Materials Science (1996), 6 (1), 15-50CODEN: CMMSEM; ISSN:0927-0256. (Elsevier)The authors present a detailed description and comparison of algorithms for performing ab-initio quantum-mech. calcns. using pseudopotentials and a plane-wave basis set. The authors will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temp. d.-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N2atoms scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge d. including a new special preconditioning optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. The authors have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio mol.-dynamics package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.**40**Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set.*Phys. Rev. B*1996,*54*(16), 11169– 11186, DOI: 10.1103/PhysRevB.54.11169Google Scholar40https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28Xms1Whu7Y%253D&md5=9c8f6f298fe5ffe37c2589d3f970a697Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setKresse, G.; Furthmueller, J.Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.**41**Kresse, G.; Hafner, J. Norm-Conserving and Ultrasoft Pseudopotentials for First-Row and Transition Elements.*J. Phys.: Condens. Matter*1994,*6*(40), 8245– 8257, DOI: 10.1088/0953-8984/6/40/015Google Scholar41https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2cXms1Cjsr4%253D&md5=401c0f2ca351bb8484b70bc9bcaed11eNorm-conserving and ultrasoft pseudopotentials for first-row and transition elementsKresse, G.; Hafner, J.Journal of Physics: Condensed Matter (1994), 6 (40), 8245-57CODEN: JCOMEL; ISSN:0953-8984.The construction of accurate pseudopotentials with good convergence properties for the first-row and transition elements is discussed. By combining an improved description of the pseudo-wavefunction inside the cut-off radius with the concept of ultrasoft pseudopotentials introduced by Vanderbilt optimal compromise between transferability and plane-wave convergence can be achieved. With the new pseudopotentials, basis sets with no more than 75-100 plane waves per atom are sufficient to reproduce the results obtained with the most accurate norm-conserving pseudopotentials.**42**Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method.*Phys. Rev. B*1999,*59*(3), 1758– 1775, DOI: 10.1103/PhysRevB.59.1758Google Scholar42https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXkt12nug%253D%253D&md5=78a73e92a93f995982fc481715729b14From ultrasoft pseudopotentials to the projector augmented-wave methodKresse, G.; Joubert, D.Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.**43**Togo, A.; Tanaka, I. First Principles Phonon Calculations in Materials Science.*Scr. Mater.*2015,*108*, 1– 5, DOI: 10.1016/j.scriptamat.2015.07.021Google Scholar43https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXht1GltLbE&md5=5b0b051b706cef43bfbb682a583fd4adFirst principles phonon calculations in materials scienceTogo, Atsushi; Tanaka, IsaoScripta Materialia (2015), 108 (), 1-5CODEN: SCMAF7; ISSN:1359-6462. (Elsevier Ltd.)Phonon plays essential roles in dynamical behaviors and thermal properties, which are central topics in fundamental issues of materials science. The importance of first principles phonon calcns. cannot be overly emphasized. Phonopy is an open source code for such calcns. launched by the present authors, which has been world-widely used. Here we demonstrate phonon properties with fundamental equations and show examples how the phonon calcns. are applied in materials science.**44**Togo, A.; Chaput, L.; Tanaka, I. Distributions of Phonon Lifetimes in Brillouin Zones.*Phys. Rev. B*2015,*91*(9), 094306 DOI: 10.1103/PhysRevB.91.094306Google Scholar44https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXovVyrtLg%253D&md5=d9b81b8d71595c2cc5a1aef413b113caDistributions of phonon lifetimes in Brillouin zonesTogo, Atsushi; Chaput, Laurent; Tanaka, IsaoPhysical Review B: Condensed Matter and Materials Physics (2015), 91 (9), 094306/1-094306/31CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Lattice thermal conductivities of zincblende- and wurtzite-type compds. with 33 combinations of elements are calcd. with the single-mode relaxation-time approxn. and a full soln. of the linearized phonon Boltzmann equation from first-principles anharmonic lattice dynamics calcns. In nine zincblende-type compds., distributions of phonon linewidths (inverse phonon lifetimes) are discussed in detail. The phonon linewidths vary nonsmoothly with respect to wave vector, which is explained from the imaginary parts of the self-energies. It is presented that detailed combination of phonon-phonon interaction strength and three-phonon selection rule is critically important to det. phonon lifetime for these compds. This indicates difficulty to predict phonon lifetime quant. without anharmonic force consts. However, it is shown that joint d. of states weighted by phonon nos., which is calcd. only from harmonic force consts., can be potentially used for a screening of the lattice thermal cond. of materials.**45**Kragskow, J. G. C.; Mattioni, A.; Staab, J. K.; Reta, D.; Skelton, J. M.; Chilton, N. F. Spin–Phonon Coupling and Magnetic Relaxation in Single-Molecule Magnets.*Chem. Soc. Rev.*2023,*52*(14), 4567– 4585, DOI: 10.1039/D2CS00705CGoogle Scholar45https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXhtlCjsL7I&md5=0b1b2a3e3e75b276e82836775e0b37beSpin-phonon coupling and magnetic relaxation in single-molecule magnetsKragskow, Jon G. C.; Mattioni, Andrea; Staab, Jakob K.; Reta, Daniel; Skelton, Jonathan M.; Chilton, Nicholas F.Chemical Society Reviews (2023), 52 (14), 4567-4585CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)A review. Electron-phonon coupling is important in many phys. phenomena, e.g. photosynthesis, catalysis and quantum information processing, but its impacts are difficult to grasp on the microscopic level. One area attracting wide interest is that of single-mol. magnets, which is motivated by searching for the ultimate limit in the miniaturization of binary data storage media. The utility of a mol. to store magnetic information is quantified by the timescale of its magnetic reversal processes, also known as magnetic relaxation, which is limited by spin-phonon coupling. Several recent accomplishments of synthetic organometallic chem. have led to the observation of mol. magnetic memory effects at temps. above that of liq. nitrogen. These discoveries have highlighted how far chem. design strategies for maximising magnetic anisotropy have come, but have also highlighted the need to characterize the complex interplay between phonons and mol. spin states. The crucial step is to make a link between magnetic relaxation and chem. motifs, and so be able to produce design criteria to extend mol. magnetic memory. The basic physics assocd. with spin-phonon coupling and magnetic relaxation was outlined in the early 20th century using perturbation theory, and has more recently been recast in the form of a general open quantum systems formalism and tackled with different levels of approxns. It is the purpose of this Tutorial Review to introduce the topics of phonons, mol. spin-phonon coupling, and magnetic relaxation, and to outline the relevant theories in connection with both the traditional perturbative texts and the more modern open quantum systems methods.**46**Breneman, C. M.; Wiberg, K. B. Determining Atom-Centered Monopoles from Molecular Electrostatic Potentials. The Need for High Sampling Density in Formamide Conformational Analysis.*J. Comput. Chem.*1990,*11*(3), 361– 373, DOI: 10.1002/jcc.540110311Google Scholar46https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3cXitFGrtr4%253D&md5=459ad3de5200b9d914d2cd8c896f387aDetermining atom-centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysisBreneman, Curt M.; Wiberg, Kenneth B.Journal of Computational Chemistry (1990), 11 (3), 361-73CODEN: JCCHDD; ISSN:0192-8651.An improved method for computing potential-derived charges is described which is based upon the CHELP program available from QCPE. This approach (CHELPG) is shown to be considerably less dependent upon mol. orientation than the original CHELP program. In the second part of this work, the CHELPG point selection algorithm was used to analyze the changes in the potential-derived charges in formamide during rotation about the C-N bond. In order to achieve a level of rotational invariance less than 10% of the magnitude of the electronic effects studied, an equally-spaced array of points 0.3 Å apart was required. Points found to be greater than 2.8 Å from any nucleus were eliminated, along with all points contained within the defined VDW distances from each of the atoms. The results are compared to those obtained by using CHELP. Even when large nos. of points (ca. 3000) were sampled using the CHELP selection routine, the results did not indicate a satisfactory level of rotational invariance. On the basis of these results, the original CHELP program was inadequate for analyzing internal rotations.**47**Chan, W.-T.; Fournier, R. Binding of Ammonia to Small Copper and Silver Clusters.*Chem. Phys. Lett.*1999,*315*(3), 257– 265, DOI: 10.1016/S0009-2614(99)01195-1Google Scholar47https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXotVKrsr8%253D&md5=979ba9910e96eb8552412eb2060e6d58Binding of ammonia to small copper and silver clustersChan, W.-T.; Fournier, R.Chemical Physics Letters (1999), 315 (3,4), 257-265CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)Equil. geometries, harmonic frequencies, and thermochem. data are reported for the metal cluster-NH3 complexes Agn(NH3) and Cun(NH3) (n=1,2,3,4), Ag4(NH3)2, and Cu4(NH3)2 calcd. by a d. functional method. The calcd. shifts in NH3 umbrella mode frequency correlate with the obsd. shifts and the calcd. enthalpies of complexation. The preferred site for NH3 adsorption and the calcd. bond enthalpies can be rationalized by considering at. charges obtained from a natural population anal. and polarization of the metal electron d.**48**Valdés, Á.; Prosmiti, R.; Villarreal, P.; Delgado-Barrio, G. HeBr2 Complex: Ground-State Potential and Vibrational Dynamics from Ab Initio Calculations.*Mol. Phys.*2004,*102*(21–22), 2277– 2283, DOI: 10.1080/00268970412331290634Google Scholar48https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXhtFGmu73N&md5=87238d42143bcb3255cfed8b55f9be47HeBr2 complex: Ground-state potential and vibrational dynamics from ab initio calculationsValdes, Alvaro; Prosmiti, Rita; Villarreal, Pablo; Delgado-Barrio, GerardoMolecular Physics (2004), 102 (21-22), 2277-2283CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)The three-dimensional interaction potential for HeBr2 was studied using a coupled-cluster (CCSD(T)) method. In our calcns., the Stuttgart group (SDD) effective-core potentials, augmented with diffusion (sp) and polarization (3df) functions (denoted SDD + G(3df)), basis sets are employed for the bromine atoms. For the He atom, the augmented correlation-consistent aug-cc-pV5Z basis set, supplemented with a set of bond functions, is used. The potential energy surface is constructed by fitting the CCSD(T) calcd. ab initio data to an anal. expression. The present ground-state potential for HeBr2 shows a double-min. topol., with wells for both linear and T-shaped configurations. Bound-state calcns. are carried out and the lowest vibrational levels are assigned to linear and T-shaped isomers. Dissocn. energies and vibrationally averaged structures for both species are detd. and found to be in very good agreement with the available exptl. data.**49**Lei, M.; Wang, N.; Zhu, L.; Tang, H. Peculiar and Rapid Photocatalytic Degradation of Tetrabromodiphenyl Ethers over Ag/TiO2 Induced by Interaction between Silver Nanoparticles and Bromine Atoms in the Target.*Chemosphere*2016,*150*, 536– 544, DOI: 10.1016/j.chemosphere.2015.10.048Google Scholar49https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhslKktLfN&md5=74176daf90d1056376d066d2a0be5c4ePeculiar and rapid photocatalytic degradation of tetrabromodiphenyl ethers over Ag/TiO2 induced by interaction between silver nanoparticles and bromine atoms in the targetLei, Ming; Wang, Nan; Zhu, Lihua; Tang, HeqingChemosphere (2016), 150 (), 536-544CODEN: CMSHAF; ISSN:0045-6535. (Elsevier Ltd.)As a typical moderately-brominated diphenylethers, 2,2,4,4-tetrabromodiphenyl ether (BDE47) is hardly debrominated by a conventional TiO2-mediated photocatalysis. However, its reductive debromination was rapid achieved over silver nanoparticle-loaded TiO2 (Ag/TiO2) in UV-irradiated anoxic acetonitrile-water within 13 min. An "Ag-promoted electron transfer and C-Br cleavage" concept was proposed based on exptl. results and d. functional theory calcns. Ag0 exerted affinity interaction with bromine atoms, and the storing of electrons on Ag0 increased the binding interaction, which elongated the C-Br bond of BDE47 and facilitated its cleavage. The initiating of the BDE47 debromination on Ag0 required an induction period to enrich a crit. amt. of electrons, leading to a stronger driving force for both injecting electron to BDE47 and stretching the C-Br bond. Stronger photo-excitation, higher polar solvent, and a moderate Ag0 load strengthened the interfacial electron transfer over Ag/TiO2, and thereby shortening the induction time and accelerating the BDE47 degrdn.**50**Ungur, L.; Chibotaru, L. F. Ab Initio Crystal Field for Lanthanides.*Chem. – Eur. J.*2017,*23*(15), 3708– 3718, DOI: 10.1002/chem.201605102Google Scholar50https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXjtVehsLg%253D&md5=7449a485b779634f64c774721976ed5fAb Initio Crystal Field for LanthanidesUngur, Liviu; Chibotaru, Liviu F.Chemistry - A European Journal (2017), 23 (15), 3708-3718CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)An ab initio methodol. for the first-principle derivation of crystal-field (CF) parameters for lanthanides is described. The methodol. is applied to the anal. of CF parameters in [Tb(Pc)2]- (Pc = phthalocyanine) and Dy4K2 ([Dy4K2O(OtBu)12]) complexes, and compared with often used approx. and model descriptions. It is found that the application of geometry symmetrization, and the use of electrostatic point-charge and phenomenol. CF models, lead to unacceptably large deviations from predictions based on ab initio calcns. for exptl. geometry. It is shown how the predictions of std. CASSCF (Complete Active Space SCF) calcns. (with 4f orbitals in the active space) can be systematically improved by including effects of dynamical electronic correlation (CASPT2 step) and by admixing electronic configurations of the 5d shell. This is exemplified for the well-studied Er-trensal complex (H3trensal = 2,2',2"-tris(salicylideneimido)trimethylamine). The electrostatic contributions to CF parameters in this complex, calcd. with true charge distributions in the ligands, yield less than half of the total CF splitting, thus pointing to the dominant role of covalent effects. This anal. allows the conclusion that ab initio crystal field is an essential tool for the decent description of lanthanides.**51**spin_phonon_suite. https://gitlab.com/chilton-group/spin_phonon_suite (accessed Aug 21, 2023).Google ScholarThere is no corresponding record for this reference.**52**Karlstroem, G. New Approach to the Modeling of Dielectric Media Effects in Ab Initio Quantum Chemical Calculations.*J. Phys. Chem. A*1988,*92*(5), 1315– 1318, DOI: 10.1021/j100316a060Google ScholarThere is no corresponding record for this reference.**53**Li Manni, G.; Fdez Galván, I.; Alavi, A.; Aleotti, F.; Aquilante, F.; Autschbach, J.; Avagliano, D.; Baiardi, A.; Bao, J. J.; Battaglia, S.; Birnoschi, L.; Blanco-González, A.; Bokarev, S. I.; Broer, R.; Cacciari, R.; Calio, P. B.; Carlson, R. K.; Carvalho Couto, R.; Cerdán, L.; Chibotaru, L. F.; Chilton, N. F.; Church, J. R.; Conti, I.; Coriani, S.; Cuéllar-Zuquin, J.; Daoud, R. E.; Dattani, N.; Decleva, P.; de Graaf, C.; Delcey, M. G.; De Vico, L.; Dobrautz, W.; Dong, S. S.; Feng, R.; Ferré, N.; Filatov Gulak, M.; Gagliardi, L.; Garavelli, M.; González, L.; Guan, Y.; Guo, M.; Hennefarth, M. R.; Hermes, M. R.; Hoyer, C. E.; Huix-Rotllant, M.; Jaiswal, V. K.; Kaiser, A.; Kaliakin, D. S.; Khamesian, M.; King, D. S.; Kochetov, V.; Krośnicki, M.; Kumaar, A. A.; Larsson, E. D.; Lehtola, S.; Lepetit, M.-B.; Lischka, H.; López Ríos, P.; Lundberg, M.; Ma, D.; Mai, S.; Marquetand, P.; Merritt, I. C. D.; Montorsi, F.; Mörchen, M.; Nenov, A.; Nguyen, V. H. A.; Nishimoto, Y.; Oakley, M. S.; Olivucci, M.; Oppel, M.; Padula, D.; Pandharkar, R.; Phung, Q. M.; Plasser, F.; Raggi, G.; Rebolini, E.; Reiher, M.; Rivalta, I.; Roca-Sanjuán, D.; Romig, T.; Safari, A. A.; Sánchez-Mansilla, A.; Sand, A. M.; Schapiro, I.; Scott, T. R.; Segarra-Martí, J.; Segatta, F.; Sergentu, D.-C.; Sharma, P.; Shepard, R.; Shu, Y.; Staab, J. K.; Straatsma, T. P.; Sørensen, L. K.; Tenorio, B. N. C.; Truhlar, D. G.; Ungur, L.; Vacher, M.; Veryazov, V.; Voß, T. A.; Weser, O.; Wu, D.; Yang, X.; Yarkony, D.; Zhou, C.; Zobel, J. P.; Lindh, R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry.*J. Chem. Theory Comput.*2023,*19*, 6933– 6991, DOI: 10.1021/acs.jctc.3c00182Google Scholar53https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXhtVert7zL&md5=9c537979f7071e510b139e143620f3aaThe OpenMolcas Web: A Community-Driven Approach to Advancing Computational ChemistryLi Manni, Giovanni; Fdez. Galvan, Ignacio; Alavi, Ali; Aleotti, Flavia; Aquilante, Francesco; Autschbach, Jochen; Avagliano, Davide; Baiardi, Alberto; Bao, Jie J.; Battaglia, Stefano; Birnoschi, Letitia; Blanco-Gonzalez, Alejandro; Bokarev, Sergey I.; Broer, Ria; Cacciari, Roberto; Calio, Paul B.; Carlson, Rebecca K.; Carvalho Couto, Rafael; Cerdan, Luis; Chibotaru, Liviu F.; Chilton, Nicholas F.; Church, Jonathan Richard; Conti, Irene; Coriani, Sonia; Cuellar-Zuquin, Juliana; Daoud, Razan E.; Dattani, Nike; Decleva, Piero; de Graaf, Coen; Delcey, Mickael G.; De Vico, Luca; Dobrautz, Werner; Dong, Sijia S.; Feng, Rulin; Ferre, Nicolas; Filatov, Michael; Gagliardi, Laura; Garavelli, Marco; Gonzalez, Leticia; Guan, Yafu; Guo, Meiyuan; Hennefarth, Matthew R.; Hermes, Matthew R.; Hoyer, Chad E.; Huix-Rotllant, Miquel; Jaiswal, Vishal Kumar; Kaiser, Andy; Kaliakin, Danil S.; Khamesian, Marjan; King, Daniel S.; Kochetov, Vladislav; Krosnicki, Marek; Kumaar, Arpit Arun; Larsson, Ernst D.; Lehtola, Susi; Lepetit, Marie-Bernadette; Lischka, Hans; Lopez Rios, Pablo; Lundberg, Marcus; Ma, Dongxia; Mai, Sebastian; Marquetand, Philipp; Merritt, Isabella C. D.; Montorsi, Francesco; Moerchen, Maximilian; Nenov, Artur; Nguyen, Vu Ha Anh; Nishimoto, Yoshio; Oakley, Meagan S.; Olivucci, Massimo; Oppel, Markus; Padula, Daniele; Pandharkar, Riddhish; Phung, Quan Manh; Plasser, Felix; Raggi, Gerardo; Rebolini, Elisa; Reiher, Markus; Rivalta, Ivan; Roca-Sanjuan, Daniel; Romig, Thies; Safari, Arta Anushirwan; Sanchez-Mansilla, Aitor; Sand, Andrew M.; Schapiro, Igor; Scott, Thais R.; Segarra-Marti, Javier; Segatta, Francesco; Sergentu, Dumitru-Claudiu; Sharma, Prachi; Shepard, Ron; Shu, Yinan; Staab, Jakob K.; Straatsma, Tjerk P.; Soerensen, Lasse Kragh; Tenorio, Bruno Nunes Cabral; Truhlar, Donald G.; Ungur, Liviu; Vacher, Morgane; Veryazov, Valera; Voss, Torben Arne; Weser, Oskar; Wu, Dihua; Yang, Xuchun; Yarkony, David; Zhou, Chen; Zobel, J. Patrick; Lindh, RolandJournal of Chemical Theory and Computation (2023), 19 (20), 6933-6991CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)A review. In this article the recent developments of the open-source OpenMolcas chem. software environment, since spring 2020, are described, with the main focus on novel functionalities that are accessible in the stable branch of the package and/or via interfaces with other packages. These community developments span a wide range of topics in computational chem., and are presented in thematic sections assocd. with electronic structure theory, electronic spectroscopy simulations, analytic gradients and mol. structure optimizations, ab initio mol. dynamics, and other new features. This report represents a useful summary of these developments, and it offers a solid overview of the chem. phenomena and processes that OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.**54**Reiher, M. Douglas–Kroll–Hess Theory: A Relativistic Electrons-Only Theory for Chemistry.*Theor. Chem. Acc.*2006,*116*(1–3), 241– 252, DOI: 10.1007/s00214-005-0003-2Google Scholar54https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xns1Sqs7Y%253D&md5=32bd8fff4b0c49e80dcd3c97af2f34f4Douglas-Kroll-Hess Theory: A relativistic electrons-only theory for chemistryReiher, MarkusTheoretical Chemistry Accounts (2006), 116 (1-3), 241-252CODEN: TCACFW; ISSN:1432-881X. (Springer GmbH)A review. A unitary transformation allows to sep. (block-diagonalize) the Dirac Hamiltonian into two parts one part: solely describes electrons, while the other gives rise to neg.-energy states, which are the so-called positronic states. The block-diagonal form of the Hamiltonian no longer accounts for the coupling of both kinds of states. The pos.-energy ('electrons-only') part can serve as a 'fully' relativistic electrons-only theory, which can be understood as a rigorous basis for chem. Recent developments of the Douglas-Kroll-Hess (DKH) method allowed to derive a sequence of expressions, which approx. this electrons-only Hamiltonian up to arbitrary-order. While all previous work focused on the numerical stability and accuracy of these arbitrary-order DKH Hamiltonians, conceptual issues and paradoxa of the method were mostly left aside. In this work, the conceptual side of DKH theory is revisited in order to identify essential aspects of the theory to be distinguished from purely computational consideration.**55**Aquilante, F.; Gagliardi, L.; Pedersen, T. B.; Lindh, R. Atomic Cholesky Decompositions: A Route to Unbiased Auxiliary Basis Sets for Density Fitting Approximation with Tunable Accuracy and Efficiency.*J. Chem. Phys.*2009,*130*(15), 154107 DOI: 10.1063/1.3116784Google Scholar55https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXkslaqsbY%253D&md5=42b21986fd7324f3540f96521dd6e62cAtomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiencyAquilante, Francesco; Gagliardi, Laura; Pedersen, Thomas Bondo; Lindh, RolandJournal of Chemical Physics (2009), 130 (15), 154107/1-154107/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Cholesky decompn. of the at. two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the d. fitting approxn. In order to increase computational performance while maintaining accuracy, we propose here to reduce the no. of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decompn. Test calcns. show that this procedure is most beneficial in conjunction with highly contracted AO basis sets such as at. natural orbitals, and that the error resulting from the second decompn. is negligible. We also demonstrate theor. as well as computationally that the locality of the fitting coeffs. can be controlled by means of the decompn. threshold even with the long-ranged Coulomb metric. Cholesky decompn.-based auxiliary basis sets are thus ideally suited for local d. fitting approxns. (c) 2009 American Institute of Physics.**56**Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.; Widmark, P.-O. New Relativistic ANO Basis Sets for Transition Metal Atoms.*J. Phys. Chem. A*2005,*109*(29), 6575– 6579, DOI: 10.1021/jp0581126Google Scholar56https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXls1Ohsbo%253D&md5=b8f2a0bb7b0edaed9b6e4580224001daNew Relativistic ANO Basis Sets for Transition Metal AtomsRoos, Bjoern O.; Lindh, Roland; Malmqvist, Per-Aake; Veryazov, Valera; Widmark, Per-OlofJournal of Physical Chemistry A (2005), 109 (29), 6575-6579CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)New basis sets of the at. natural orbital (ANO) type have been developed for the first, second, and third row transition metal atoms. The ANOs have been obtained from the av. d. matrix of the ground and lowest excited states of the atom, the pos. and neg. ions, and the atom in an elec. field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calcns. of ionization energies, electron affinities, and excitation energies for all atoms and polarizabilities for spherically sym. atoms. These calcns. include spin-orbit coupling using a variation-perturbation approach. Computed ionization energies have an accuracy better than 0.2 eV in most cases. The accuracy of computed electron affinities is the same except in cases where the exptl. values are smaller than 0.5 eV. Accurate results are obtained for the polarizabilities of atoms with spherical symmetry. Multiplet levels are presented for some of the third row transition metals.**57**Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.; Widmark, P.-O. Main Group Atoms and Dimers Studied with a New Relativistic ANO Basis Set.*J. Phys. Chem. A*2004,*108*(15), 2851– 2858, DOI: 10.1021/jp031064+Google Scholar57https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3sXpvFGksLs%253D&md5=0376f88ebbc6bd69daee46c198d463eeMain Group Atoms and Dimers Studied with a New Relativistic ANO Basis SetRoos, Bjoern O.; Lindh, Roland; Malmqvist, Per-Aake; Veryazov, Valera; Widmark, Per-OlofJournal of Physical Chemistry A (2004), 108 (15), 2851-2858CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)New basis sets of the at. natural orbital (ANO) type have been developed for the main group and rare gas atoms. The ANO's have been obtained from the av. d. matrix of the ground and lowest excited states of the atom, the pos. and neg. ions, and the dimer at its equil. geometry. Scalar relativistic effects are included through the use of a Douglas-Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calcns. of ionization energies, electron affinities, and excitation energies for all atoms and the ground-state potentials for the dimers. These calcns. include spin-orbit coupling using the RASSCF State Interaction (RASSI-SO) method. The spin-orbit splitting for the lowest at. term is reproduced with an accuracy of better than 0.05 eV, except for row 5, where it is 0.15 eV. Ionization energies and electron affinities have an accuracy better than 0.2 eV, and at. polarizabilities for the spherical atoms are computed with errors smaller than 2.5%. Computed bond energies for the dimers are accurate to better than 0.15 eV in most cases (the dimers for row 5 excluded).**58**angmom_suite. https://gitlab.com/chilton-group/angmom_suite (accessed Aug 21, 2023).Google ScholarThere is no corresponding record for this reference.**59**Kragskow, J. G. C.; Marbey, J.; Buch, C. D.; Nehrkorn, J.; Ozerov, M.; Piligkos, S.; Hill, S.; Chilton, N. F. Analysis of Vibronic Coupling in a 4f Molecular Magnet with FIRMS.*Nat. Commun.*2022,*13*(1), 825 DOI: 10.1038/s41467-022-28352-2Google Scholar59https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XjsVGrtr8%253D&md5=dbe8805fe522125b8c05fa3420cac0cdAnalysis of vibronic coupling in a 4f molecular magnet with FIRMSKragskow, Jon G. C.; Marbey, Jonathan; Buch, Christian D.; Nehrkorn, Joscha; Ozerov, Mykhaylo; Piligkos, Stergios; Hill, Stephen; Chilton, Nicholas F.Nature Communications (2022), 13 (1), 825CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)Vibronic coupling, the interaction between mol. vibrations and electronic states, is a fundamental effect that profoundly affects chem. processes. In the case of mol. magnetic materials, vibronic, or spin-phonon, coupling leads to magnetic relaxation, which equates to loss of magnetic memory and loss of phase coherence in mol. magnets and qubits, resp. The study of vibronic coupling is challenging, and most exptl. evidence is indirect. Here we employ far-IR magnetospectroscopy to directly probe vibronic transitions in [Yb(trensal)] (where H3trensal = 2,2,2-tris(salicylideneimino)trimethylamine). We find intense signals near electronic states, which we show arise due to an ''envelope effect'' in the vibronic coupling Hamiltonian, which we calc. fully ab initio to simulate the spectra. We subsequently show that vibronic coupling is strongest for vibrational modes that simultaneously distort the first coordination sphere and break the C3 symmetry of the mol. With this knowledge, vibrational modes could be identified and engineered to shift their energy towards or away from particular electronic states to alter their impact. Hence, these findings provide new insights towards developing general guidelines for the control of vibronic coupling in mols.**60**Staab, J. K.; Chilton, N. F. Analytic Linear Vibronic Coupling Method for First-Principles Spin-Dynamics Calculations in Single-Molecule Magnets.*J. Chem. Theory Comput.*2022,*18*(11), 6588– 6599, DOI: 10.1021/acs.jctc.2c00611Google Scholar60https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38Xis1Ohur3J&md5=e423b88538384f7e0384d827cee433dcAnalytic Linear Vibronic Coupling Method for First-Principles Spin-Dynamics Calculations in Single-Molecule MagnetsStaab, Jakob K.; Chilton, Nicholas F.Journal of Chemical Theory and Computation (2022), 18 (11), 6588-6599CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)Accurate modeling of vibronically driven magnetic relaxation from ab initio calcns. is of paramount importance to the design of next-generation single-mol. magnets (SMMs). Previous theor. studies have been relying on numerical differentiation to obtain spin-phonon couplings in the form of derivs. of spin Hamiltonian parameters. In this work, we introduce a novel approach to obtain these derivs. fully anal. by combining the linear vibronic coupling (LVC) approach with analytic complete active space SCF derivs. and nonadiabatic couplings computed at the equil. geometry with a single electronic structure calcn. We apply our analytic approach to the computation of Orbach and Raman relaxation rates for a bis-cyclobutadienyl Dy(III) sandwich complex in the frozen-soln. phase, where the soln. environment is modeled by electrostatic multipole expansions, and benchmark our findings against results obtained using conventional numerical derivs. and a fully electronic description of the whole system. We demonstrate that our LVC approach exhibits high accuracy over a wide range of coupling strengths and enables significant computational savings due to its analytic, "single-shot" nature. Evidently, this offers great potential for advancing the simulation of a wide range of vibronic coupling phenomena in magnetism and spectroscopy, ultimately aiding the design of high-performance SMMs. Considering different environmental representations, we find that a point charge model shows the best agreement with the ref. calcn., including the full electronic environment, but note that the main source of discrepancies obsd. in the magnetic relaxation rates originates from the approx. equil. electronic structure computed using the electrostatic environment models rather than from the couplings.**61**tau. https://gitlab.com/chilton-group/tau (accessed Aug 21, 2023).Google ScholarThere is no corresponding record for this reference.**62**Shrivastava, K. N. Theory of Spin–Lattice Relaxation.*Phys. Status Solidi B*1983,*117*(2), 437– 458, DOI: 10.1002/pssb.2221170202Google Scholar62https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL3sXktFGisrY%253D&md5=9f186f6be6ed2a4dfb360fcdfcb952d5Theory of spin-lattice relaxationShrivastava, K. N.Physica Status Solidi B: Basic Research (1983), 117 (2), 437-58CODEN: PSSBBD; ISSN:0370-1972.A review with 46 refs. Topics include: the spin-lattice interaction, the direct process, the Raman process, the sum process, the Orbach process, the 3-phonon process, the local mode process, and the collision process.**63**Ho, L. T. A.; Chibotaru, L. F. Spin-Lattice Relaxation of Magnetic Centers in Molecular Crystals at Low Temperature.*Phys. Rev. B*2018,*97*(2), 024427 DOI: 10.1103/PhysRevB.97.024427Google Scholar63https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltVCqu7g%253D&md5=0a3742a91ac20c5e5e7304e842f8a44aSpin-lattice relaxation of magnetic centers in molecular crystals at low temperatureHo, Le Tuan Anh; Chibotaru, Liviu F.Physical Review B (2018), 97 (2), 024427CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)We study the spin-phonon relaxation rate of both Kramers and non-Kramers mol. magnets in strongly dild. samples at low temp. Using the "rotational" contribution to the spin-phonon Hamiltonian, universal formulas for the relaxation rate are obtained. Intriguingly, these formulas are all entirely expressed via measurable or ab initio computable phys. quantities. Moreover, they are also independent of the energy gaps to excited states involved in the relaxation process. These obtained expressions for direct and Raman processes offer an easy way to det. the lowest limit of the spin-phonon relaxation of any spin system based on magnetic properties of the ground doublet only. In addn., some intriguing properties of Raman process are also found. Particularly, Raman process in Kramers system is found dependent on the magnetic field's orientation but independent of its magnitude, meanwhile, the same process in non-Kramers system is significantly reduced out of resonance, i.e., for an applied external field. Interestingly, Raman process is demonstrated to vary as T9 for both systems. Application of the theory to a recently investigated cobalt(II) complex shows that it can provide a reasonably good description for the relaxation. Based on these findings, a strategy in developing efficient single-mol. magnets by enhancing the mech. rigidity of the mol. unit is proposed.**64**Dove, M. T.*Introduction to Lattice Dynamics*; Cambridge topics in mineral physics and chemistry; Cambridge University Press: Cambridge ; New York, 1993.Google ScholarThere is no corresponding record for this reference.**65**Evans, P.; Reta, D.; Whitehead, G. F. S.; Chilton, N. F.; Mills, D. P. Bis-Monophospholyl Dysprosium Cation Showing Magnetic Hysteresis at 48 K.*J. Am. Chem. Soc.*2019,*141*(50), 19935– 19940, DOI: 10.1021/jacs.9b11515Google Scholar65https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXit1SnsbzL&md5=bdae8e6b829adb3cb921ae07805875c4Bis-Monophospholyl Dysprosium Cation Showing Magnetic Hysteresis at 48 KEvans, Peter; Reta, Daniel; Whitehead, George F. S.; Chilton, Nicholas F.; Mills, David P.Journal of the American Chemical Society (2019), 141 (50), 19935-19940CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)Single-mol. magnets (SMMs) have potential applications in high-d. data storage, but magnetic relaxation times at elevated temps. must be increased to make them practically useful. Bis-cyclopentadienyl lanthanide sandwich complexes have emerged as the leading candidates for SMMs that show magnetic memory at liq. nitrogen temps., but the relaxation mechanisms mediated by arom. C5 rings have not been fully established. Here we synthesize a bis-monophospholyl dysprosium SMM [Dy(Dtp)2][Al{OC(CF3)3}4] (1, Dtp = {P(CtBuCMe)2}) by the treatment of in situ-prepd. "[Dy(Dtp)2(C3H5)]" with [HNEt3][Al{OC(CF3)3}4]. SQUID magnetometry reveals that 1 has an effective barrier to magnetization reversal of 1,760 K (1,223 cm-1) and magnetic hysteresis up to 48 K. Ab initio calcn. of the spin dynamics reveal that transitions out of the ground state are slower in 1 than in the first reported dysprosocenium SMM, [Dy(Cpttt)2][B(C6F5)4] (Cpttt = C5H2tBu3-1,2,4), however relaxation is faster in 1 overall due to the compression of electronic energies and to vibrational modes being brought on-resonance by the chem. and structural changes introduced by the bis-Dtp framework. With the prepn. and anal. of 1 we are thus able to further refine our understanding of relaxation processes operating in bis-C5/C4P sandwich lanthanide SMMs, which is the necessary first step towards rationally achieving higher magnetic blocking temps. in these systems in future.**66**Smith, E. R.; Rowlinson, J. S. Electrostatic Energy in Ionic Crystals.*Proc. R. Soc. London, Ser. A*1997,*375*(1763), 475– 505, DOI: 10.1098/rspa.1981.0064Google ScholarThere is no corresponding record for this reference.**67**Ewald, P. P. Die Berechnung Optischer Und Elektrostatischer Gitterpotentiale.*Ann. Phys.*1921,*369*(3), 253– 287, DOI: 10.1002/andp.19213690304Google ScholarThere is no corresponding record for this reference.**68**Derenzo, S. E.; Klintenberg, M. K.; Weber, M. J. Determining Point Charge Arrays That Produce Accurate Ionic Crystal Fields for Atomic Cluster Calculations.*J. Chem. Phys.*2000,*112*(5), 2074– 2081, DOI: 10.1063/1.480776Google Scholar68https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXnsFWqtg%253D%253D&md5=7892892b36bc1eb18234d1c5780ee01cDetermining point charge arrays that produce accurate ionic crystal fields for atomic cluster calculationsDerenzo, Stephen E.; Klintenberg, Mattias K.; Weber, Marvin J.Journal of Chemical Physics (2000), 112 (5), 2074-2081CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)In performing at. cluster calcns. of local electronic structure defects in ionic crystals, the crystal is often modeled as a central cluster of 5-50 ions embedded in an array of point charges. For most crystals, however, a finite three-dimensional repeated array of unit cells generates electrostatic potentials that are in significant disagreement with the Madelung (infinite crystal) potentials computed by the Ewald method. This is illustrated for the cubic crystal CaF2. We present a novel algorithm for solving this problem for any crystal whose unit cell information is known: (1) the unit cell is used to generate a neutral array contg. typically 10 000 point charges at their normal crystallog. positions; (2) the array is divided into zone 1 (a vol. defined by the at. cluster of interest), zone 2 (several hundred addnl. point charges that together with zone 1 fill a spherical vol.), and zone 3 (all other point charges); (3) the Ewald formula is used to compute the site potentials at all point charges in zones 1 and 2; (4) a system of simultaneous linear equations is solved to find the zone 3 charge values that make the zone 1 and zone 2 site potentials exactly equal to their Ewald values and the total charge and dipole moments equal to zero, and (5) the soln. is checked at 1000 addnl. points randomly chosen in zone 1. The method is applied to 33 different crystal types with 50-71 ions in zone 1. In all cases the accuracy detd. in step 5 steadily improves as the sizes of zones 2 and 3 are increased, reaching a typical rms error of 1 μV in zone 1 for 500 point charges in zone 2 and 10 000 in zone 3.**69**Rivera, M.; Dommett, M.; Crespo-Otero, R. ONIOM(QM:QM′) Electrostatic Embedding Schemes for Photochemistry in Molecular Crystals.*J. Chem. Theory Comput.*2019,*15*(4), 2504– 2516, DOI: 10.1021/acs.jctc.8b01180Google Scholar69https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXkslaitrk%253D&md5=46534739fc9ceab577f97a0f4e4580dbONIOM(QM:QM') electrostatic embedding schemes for photochemistry in molecular crystalsRivera, Miguel; Dommett, Michael; Crespo-Otero, RachelJournal of Chemical Theory and Computation (2019), 15 (4), 2504-2516CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)Understanding photoinduced processes in mol. crystals is central to the design of highly emissive materials such as org. lasers and org. light-emitting diodes. The modeling of such processes is, however, hindered by the lack of excited state methodologies tailored for these systems. Embedding approaches based on the Ewald sum can be used in conjunction with excited state electronic structure methods to model the localized excitations which characterize these materials. In this article, we describe the implementation of a two-level ONIOM(QM:QM') point charge embedding approach based on the Ewald method, the ONIOM Ewald embedded cluster (OEEC) model. An alternative self-consistent method is also considered to simulate the response of the environment to the excitation. Two mol. crystals with opposing photochem. behavior were used to benchmark the results with single ref. and multireference methods. We obsd. that the inclusion of an explicit ground state cluster surrounding the QM region was imperative for the exploration of the excited state potential energy surfaces. Using OEEC, accurate absorption and emission energies as well as S1-S0 conical intersections were obtained for both crystals. We discuss the implications of the use of these embedding schemes considering the degree of localization of the excitation. The methods discussed herein are implemented in an open source platform (fromage, https://github.com/Crespo-Otero-group/fromage) which acts as an interface between popular electronic structure codes (Gaussian, Turbomole, and Molcas).**70**Fraser, L. M.; Foulkes, W. M. C.; Rajagopal, G.; Needs, R. J.; Kenny, S. D.; Williamson, A. J. Finite-Size Effects and Coulomb Interactions in Quantum Monte Carlo Calculations for Homogeneous Systems with Periodic Boundary Conditions.*Phys. Rev. B*1996,*53*(4), 1814– 1832, DOI: 10.1103/PhysRevB.53.1814Google Scholar70https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XptV2jsw%253D%253D&md5=8766705cf1df20e8f6a3bed60aa04bcdFinite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditionsFraser, Louisa M.; Foulkes, W. M. C.; Rajagopal, G.; Needs, R. J.; Kenny, S. D.; Williamson, A. J.Physical Review B: Condensed Matter (1996), 53 (4), 1814-32CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)Quantum Monte Carlo (QMC) calcns. are only possible in finite systems and so solids and liqs. must be modeled using small simulation cells subject to periodic boundary conditions. The resulting finite-size errors are often cor. using data from the local-d. functional or Hartree-Fock calcns., but systematic errors remain after these corrections have been applied. The results of the authors' jellium QMC calcns. for simulation cells contg. more than 600 electrons conform that the residual errors are significant and decay very slowly as the system size increases. They are sensitive to the form of the model Coulomb interaction used in the simulation cell Hamiltonian; the usual choice, exemplified by the Ewald summation technique, is not the best. The finite-size errors can be greatly reduced and the speed of the calcns. increased by a factor of 20 if a better choice is made. Finite-size effects plague most methods used for extended Coulomb systems and many of the ideas in this paper are quite general: they may be applied to any type of quantum or classical Monte Carlo simulation, to other many-body approaches such as the GW method, and to Hartree-Fock and d.-functional calcns.**71**Reta, D.; Chilton, N. F. Uncertainty Estimates for Magnetic Relaxation Times and Magnetic Relaxation Parameters.*Phys. Chem. Chem. Phys.*2019,*21*(42), 23567– 23575, DOI: 10.1039/C9CP04301BGoogle Scholar71https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhvFejtr7O&md5=b1f3f307c9cdba48e3249004efae1bcdUncertainty estimates for magnetic relaxation times and magnetic relaxation parametersReta, Daniel; Chilton, Nicholas F.Physical Chemistry Chemical Physics (2019), 21 (42), 23567-23575CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)The use of a.c. (AC) magnetometry to measure magnetic relaxation times is one of the most fundamental measurements for characterizing single-mol. magnets (SMMs). These measurements, performed as a function of frequency, temp. and magnetic field, give vital information on the underlying magnetic relaxation process(es) occurring in the material. The magnetic relaxation times are usually fitted to model functions derived from spin-phonon coupling theories that allow characterization of the mechanisms of magnetic relaxation. The parameters of these relaxation models are then often compared between different mols. in order to find trends with mol. structure that may guide the field to the next breakthrough. However, such meta-analyses of the model parameters are doomed to over-interpretation unless uncertainties in the model parameters can be quantified. Here we det. a method for obtaining uncertainty ests. in magnetic relaxation times from AC expts., and provide a program called CC-FIT2 for fitting exptl. AC data as well as the resulting relaxation times, to obtain relaxation parameters with accurate uncertainties. Applying our approach to three archetypal families of high-performance dysprosium(III) SMMs shows that accounting for uncertainties has a significant impact on the uncertainties of relaxation parameters, and that larger uncertainties appear to correlate with crystallog. disorder in the compds. studied. We suggest that this type of anal. should become routine in the community.

## Cited By

This article is cited by 3 publications.

- Jakob Staab, Nicholas Chilton. Correction to Analytic Linear Vibronic Coupling Method for First-Principles Spin-Dynamics Calculations in Single-Molecule Magnets. Journal of Chemical Theory and Computation
**2024**,*20*(7) , 2969-2970. https://doi.org/10.1021/acs.jctc.4c00239 - Elisa Rotondo, Maxime Aragon-Alberti, Jérôme Rouquette, Jérôme Long. Modulation of the Slow Relaxation of the Magnetization Dynamics through Second Coordination Sphere in Macrocyclic Dysprosium(III) Complexes. Crystal Growth & Design
**2024**,*24*(3) , 1458-1464. https://doi.org/10.1021/acs.cgd.3c01401 - Jack Emerson-King, Gemma K. Gransbury, George F. S. Whitehead, Iñigo J. Vitorica-Yrezabal, Mathieu Rouzières, Rodolphe Clérac, Nicholas F. Chilton, David P. Mills. Isolation of a Bent Dysprosium Bis(amide) Single-Molecule Magnet. Journal of the American Chemical Society
**2024**,*146*(5) , 3331-3342. https://doi.org/10.1021/jacs.3c12427

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Hierarchical mol. design and synthesis, from small mols. to supramol. assemblies, combined with new spectroscopic probes of quantum coherence and theor. modeling of complex systems, offer a broad range of possibilities to realize practical quantum information science applications. [graphic not available: see fulltext].**2**Caravan, P.; Ellison, J. J.; McMurry, T. J.; Lauffer, R. B. Gadolinium(III) Chelates as MRI Contrast Agents: Structure, Dynamics, and Applications.*Chem. Rev.*1999,*99*(9), 2293– 2352, DOI: 10.1021/cr980440x2https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXlt12rsrg%253D&md5=10b76764c56cadb0b2426c6bdf01506bGadolinium(III) Chelates as MRI Contrast Agents: Structure, Dynamics, and ApplicationsCaravan, Peter; Ellison, Jeffrey J.; McMurry, Thomas J.; Lauffer, Randall B.Chemical Reviews (Washington, D. C.) (1999), 99 (9), 2293-2352CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)A review with 343 refs. on gadolinium(III) chelates judged to be of sufficient stability for in vivo use. Topics covered include soln. and solid state structures, relaxation theory, phys. properties, and macromol. conjugates.**3**Weiss, L. R.; Bayliss, S. L.; Kraffert, F.; Thorley, K. J.; Anthony, J. E.; Bittl, R.; Friend, R. H.; Rao, A.; Greenham, N. C.; Behrends, J. Strongly Exchange-Coupled Triplet Pairs in an Organic Semiconductor.*Nat. Phys.*2017,*13*(2), 176– 181, DOI: 10.1038/nphys39083https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XhslShtr7I&md5=03e6e0ab3a5dff319fd0c3f38fdf6119Strongly exchange-coupled triplet pairs in an organic semiconductorWeiss, Leah R.; Bayliss, Sam L.; Kraffert, Felix; Thorley, Karl J.; Anthony, John E.; Bittl, Robert; Friend, Richard H.; Rao, Akshay; Greenham, Neil C.; Behrends, JanNature Physics (2017), 13 (2), 176-181CODEN: NPAHAX; ISSN:1745-2473. (Nature Publishing Group)From biol. complexes to devices based on org. semiconductors, spin interactions play a key role in the function of mol. systems. For instance, triplet-pair reactions impact operation of org. light-emitting diodes as well as photovoltaic devices. Conventional models for triplet pairs assume they interact only weakly. Here, using ESR, we observe long-lived, strongly interacting triplet pairs in an org. semiconductor, generated via singlet fission. Using coherent spin manipulation of these two-triplet states, we identify exchange-coupled (spin-2) quintet complexes coexisting with weakly coupled (spin-1) triplets. We measure strongly coupled pairs with a lifetime approaching 3 μs and a spin coherence time approaching 1 μs, at 10 K. Our results pave the way for the utilization of high-spin systems in org. semiconductors.**4**Paulus, B. C.; Adelman, S. L.; Jamula, L. L.; McCusker, J. K. Leveraging Excited-State Coherence for Synthetic Control of Ultrafast Dynamics.*Nature*2020,*582*(7811), 214– 218, DOI: 10.1038/s41586-020-2353-24https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtFCnu7rI&md5=b1e9d7af59c9e4b371e5ff9f49fd863aLeveraging excited-state coherence for synthetic control of ultrafast dynamicsPaulus, Bryan C.; Adelman, Sara L.; Jamula, Lindsey L.; McCusker, James K.Nature (London, United Kingdom) (2020), 582 (7811), 214-218CODEN: NATUAS; ISSN:0028-0836. (Nature Research)Design-specific control over excited-state dynamics is necessary for any application seeking to convert light into chem. potential. Such control is esp. desirable in iron(II)-based chromophores, which are an Earth-abundant option for a wide range of photo-induced electron-transfer applications including solar energy conversion1 and catalysis2. However, the sub-200-fs lifetimes of the redox-active metal-to-ligand charge transfer (MLCT) excited states typically encountered in these compds. have largely precluded their widespread use3. Here we show that the MLCT lifetime of an iron(II) complex can be manipulated using information from excited-state quantum coherences as a guide to implementing synthetic modifications that can disrupt the reaction coordinate assocd. with MLCT decay. We developed a structurally tunable mol. platform in which vibronic coherences-i.e., coherences reflecting a coupling of vibrational and electronic degrees of freedom-were obsd. in ultrafast time-resolved absorption measurements after MLCT excitation of the mol. Following visualization of the vibrational modes assocd. with these coherences, we synthetically modified an iron(II) chromophore to interfere with these specific at. motions. The redesigned compd. exhibits a MLCT lifetime that is more than a factor of 20 longer than that of the parent compd., indicating that the structural modification at least partially decoupled these degrees of freedom from the population dynamics assocd. with the electronic-state evolution of the system. These results demonstrate that using excited-state coherence data may be used to tailor ultrafast excited-state dynamics through targeted synthetic design.**5**Liedy, F.; Eng, J.; McNab, R.; Inglis, R.; Penfold, T. J.; Brechin, E. K.; Johansson, J. O. Vibrational Coherences in Manganese Single-Molecule Magnets after Ultrafast Photoexcitation.*Nat. Chem.*2020,*12*(5), 452– 458, DOI: 10.1038/s41557-020-0431-65https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXkt1Ohuro%253D&md5=80edc7d4d5332427f86fbbaf3930ee13Vibrational coherences in manganese single-molecule magnets after ultrafast photoexcitationLiedy, Florian; Eng, Julien; McNab, Robbie; Inglis, Ross; Penfold, Thomas J.; Brechin, Euan K.; Johansson, J. OlofNature Chemistry (2020), 12 (5), 452-458CODEN: NCAHBB; ISSN:1755-4330. (Nature Research)Single-mol. magnets (SMMs) are metal complexes with 2 degenerate magnetic ground states and are promising for increasing storage d., but remain unexplored using ultrafast techniques. The dynamics occurring after photoexcitation of a trinuclear μ3-oxo-bridged Mn(III)-based SMM, whose magnetic anisotropy is closely related to the Jahn-Teller distortion, was explored. Ultrafast transient absorption spectroscopy in soln. reveals oscillations superimposed on the decay traces due to a vibrational wavepacket. Based on complementary measurements and calcns. on the monomer Mn(acac)3, the wavepacket motion in the trinuclear SMM is constrained along the Jahn-Teller axis due to the μ3-oxo and μ-oxime bridges. The results provide new possibilities for optical control of the magnetization in SMMs on fs timescales and open up new mol.-design challenges to control the wavepacket motion in the excited state of polynuclear transition-metal complexes.**6**Serrano, D.; Kuppusamy, S. K.; Heinrich, B.; Fuhr, O.; Hunger, D.; Ruben, M.; Goldner, P. Ultra-Narrow Optical Linewidths in Rare-Earth Molecular Crystals.*Nature*2022,*603*(7900), 241– 246, DOI: 10.1038/s41586-021-04316-26https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XmsF2rtbc%253D&md5=4cd06e702fd5e80c6011c39c85d91edfUltra-narrow optical linewidths in rare-earth molecular crystalsSerrano, Diana; Kuppusamy, Senthil Kumar; Heinrich, Benoit; Fuhr, Olaf; Hunger, David; Ruben, Mario; Goldner, PhilippeNature (London, United Kingdom) (2022), 603 (7900), 241-246CODEN: NATUAS; ISSN:1476-4687. (Nature Portfolio)Rare-earth ions (REIs) are promising solid-state systems for building light-matter interfaces at the quantum level. This relies on their potential to show narrow optical and spin homogeneous linewidths, or, equivalently, long-lived quantum states. This enables the use of REIs for photonic quantum technologies such as memories for light, optical-microwave transduction and computing. However, so far, few cryst. materials have shown an environment quiet enough to fully exploit REI properties. This hinders further progress, in particular towards REI-contg. integrated nanophotonics devices. Mol. systems can provide such capability but generally lack spin states. If, however, mol. systems do have spin states, they show broad optical lines that severely limit optical-to-spin coherent interfacing. Here we report on europium mol. crystals that exhibit linewidths in the tens of kilohertz range, orders of magnitude narrower than those of other mol. systems. We harness this property to demonstrate efficient optical spin initialization, coherent storage of light using an at. frequency comb, and optical control of ion-ion interactions towards implementation of quantum gates. These results illustrate the utility of rare-earth mol. crystals as a new platform for photonic quantum technologies that combines highly coherent emitters with the unmatched versatility in compn., structure and integration capability of mol. materials.**7**Shiddiq, M.; Komijani, D.; Duan, Y.; Gaita-Ariño, A.; Coronado, E.; Hill, S. Enhancing Coherence in Molecular Spin Qubits via Atomic Clock Transitions.*Nature*2016,*531*(7594), 348– 351, DOI: 10.1038/nature169847https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XktlGjtbc%253D&md5=0e9730a46270daeb395bd3751776d06eEnhancing coherence in molecular spin qubits via atomic clock transitionsShiddiq, Muhandis; Komijani, Dorsa; Duan, Yan; Gaita-Arino, Alejandro; Coronado, Eugenio; Hill, StephenNature (London, United Kingdom) (2016), 531 (7594), 348-351CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)Quantum computing is an emerging area within the information sciences revolving around the concept of quantum bits (qubits). A major obstacle is the extreme fragility of these qubits due to interactions with their environment that destroy their quantumness. This phenomenon, known as decoherence, is of fundamental interest. There are many competing candidates for qubits, including superconducting circuits, quantum optical cavities, ultracold atoms and spin qubits, and each has its strengths and weaknesses. When dealing with spin qubits, the strongest source of decoherence is the magnetic dipolar interaction. To minimize it, spins are typically dild. in a diamagnetic matrix. For example, this diln. can be taken to the extreme of a single phosphorus atom in silicon, whereas in mol. matrixes a typical ratio is one magnetic mol. per 10,000 matrix mols. However, there is a fundamental contradiction between reducing decoherence by diln. and allowing quantum operations via the interaction between spin qubits. To resolve this contradiction, the design and engineering of quantum hardware can benefit from a 'bottom-up' approach whereby the electronic structure of magnetic mols. is chem. tailored to give the desired phys. behavior. Here we present a way of enhancing coherence in solid-state mol. spin qubits without resorting to extreme diln. It is based on the design of mol. structures with crystal field ground states possessing large tunnelling gaps that give rise to optimal operating points, or at. clock transitions, at which the quantum spin dynamics become protected against dipolar decoherence. This approach is illustrated with a holmium mol. nanomagnet in which long coherence times (up to 8.4 μs at 5 K) are obtained at unusually high concns. This finding opens new avenues for quantum computing based on mol. spin qubits.**8**Leuenberger, M. N.; Loss, D. Quantum Computing in Molecular Magnets.*Nature*2001,*410*(6830), 789– 793, DOI: 10.1038/350710248https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3MXjtVeltrY%253D&md5=022c5fb0488cb4515259100bd8b0e2c1Quantum computing in molecular magnetsLeuenberger, Michael N.; Loss, DanielNature (London, United Kingdom) (2001), 410 (6830), 789-793CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)Shor and Grover demonstrated that a quantum computer can outperform any classical computer in factoring nos. and in searching a database by exploiting the parallelism of quantum mechanics. Whereas Shor's algorithm requires both superposition and entanglement of a many-particle system, the superposition of single-particle quantum states is sufficient for Grover's algorithm. Recently, the latter has been successfully implemented using Rydberg atoms. Here we propose an implementation of Grover's algorithm that uses mol. magnets, which are solid-state systems with a large spin; their spin eigenstates make them natural candidates for single-particle systems. We show theor. that mol. magnets can be used to build dense and efficient memory devices based on the Grover algorithm. In particular, one single crystal can serve as a storage unit of a dynamic random access memory device. Fast ESR pulses can be used to decode and read out stored nos. of up to 10, with access times as short as 10 s. We show that our proposal should be feasible using the mol. magnets Fe8 and Mn12.**9**Bogani, L.; Wernsdorfer, W. Molecular Spintronics Using Single-Molecule Magnets.*Nat. Mater.*2008,*7*(3), 179– 186, DOI: 10.1038/nmat21339https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1cXisVSrsrk%253D&md5=bb273c3bb73ad278d09345f6213f1571Molecular spintronics using single-molecule magnetsBogani, Lapo; Wernsdorfer, WolfgangNature Materials (2008), 7 (3), 179-186CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)A review. A revolution in electronics is in view, with the contemporary evolution of the two novel disciplines of spintronics and mol. electronics. A fundamental link between these two fields can be established using mol. magnetic materials and, in particular, single-mol. magnets. Here, we review the first progress in the resulting field, mol. spintronics, which will enable the manipulation of spin and charges in electronic devices contg. one or more mols. We discuss the advantages over more conventional materials, and the potential applications in information storage and processing. We also outline current challenges in the field, and propose convenient schemes to overcome them.**10**Gaita-Ariño, A.; Luis, F.; Hill, S.; Coronado, E. Molecular Spins for Quantum Computation.*Nat. Chem.*2019,*11*(4), 301– 309, DOI: 10.1038/s41557-019-0232-y10https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXotFamsL4%253D&md5=9284f40e8343f6d4c76de6ba423617e3Molecular spins for quantum computationGaita-Arino, A.; Luis, F.; Hill, S.; Coronado, E.Nature Chemistry (2019), 11 (4), 301-309CODEN: NCAHBB; ISSN:1755-4330. (Nature Research)Spins in solids or in mols. possess discrete energy levels, and the assocd. quantum states can be tuned and coherently manipulated by means of external electromagnetic fields. Spins therefore provide one of the simplest platforms to encode a quantum bit (qubit), the elementary unit of future quantum computers. Performing any useful computation demands much more than realizing a robust qubit-one also needs a large no. of qubits and a reliable manner with which to integrate them into a complex circuitry that can store and process information and implement quantum algorithms. This 'scalability' is arguably one of the challenges for which a chem.-based bottom-up approach is best-suited. Mols., being much more versatile than atoms, and yet microscopic, are the quantum objects with the highest capacity to form non-trivial ordered states at the nanoscale and to be replicated in large nos. using chem. tools.**11**Gatteschi, D.; Sessoli, R.; Villain, J.*Molecular Nanomagnets*; Oxford University Press, 2006.There is no corresponding record for this reference.**12**Chilton, N. F. Molecular Magnetism.*Annu. Rev. Mater. Res.*2022,*52*(1), 79– 101, DOI: 10.1146/annurev-matsci-081420-04255312https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XnsFGksrg%253D&md5=1e113733f16aaff35d19e99e98291188Molecular MagnetismChilton, Nicholas F.Annual Review of Materials Research (2022), 52 (), 79-101CODEN: ARMRCU; ISSN:1531-7331. (Annual Reviews)A review. Mol. magnetism, though distinctly a field within chem., encompasses much more than synthesis and has strong links with other disciplines across the phys. sciences. Research goals in this area are currently dominated by magnetic memory and quantum information processing but extend in other directions toward medical diagnostics and catalysis. This review focuses on two popular subtopics, single-mol. magnetism and mol. spin qubits, outlining their design and study and some of the latest outstanding results in the field. The above topics are complemented by an overview of pertinent electronic structure methods and, in a look towards the future, an overview of the state of the art in measurement and modeling of mol. spin-phonon coupling.**13**Escalera-Moreno, L.; J Baldoví, J.; Gaita-Ariño, A.; Coronado, E. Spin States, Vibrations and Spin Relaxation in Molecular Nanomagnets and Spin Qubits: A Critical Perspective.*Chem. Sci.*2018,*9*(13), 3265– 3275, DOI: 10.1039/C7SC05464E13https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXjvFWqu78%253D&md5=0687f59f35f9c3cda5e476eaea5ed284Spin states, vibrations and spin relaxation in molecular nanomagnets and spin qubits: a critical perspectiveEscalera-Moreno, Luis; Baldovi, Jose J.; Gaita-Arino, Alejandro; Coronado, EugenioChemical Science (2018), 9 (13), 3265-3275CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)Very recently the closely related fields of mol. spin qubits, single ion magnets and single atom magnets have been shaken by unexpected results. We have witnessed a jump in the phase memory times of spin qubits from a few microseconds to almost a millisecond in a vanadium complex, magnetic hysteresis up to 60 K in a dysprosium-based magnetic mol. and magnetic memory up to 30 K in a holmium atom deposited on a surface. With single-mol. magnets being more than two decades old, this rapid improvement in the phys. properties is surprising and its explanation deserves urgent attention. The general assumption of focusing uniquely on the energy barrier is clearly insufficient to model magnetic relaxation. Other factors, such as vibrations that couple to spin states, need to be taken into account. In fact, this coupling is currently recognized to be the key factor that accounts for the slow relaxation of magnetization at higher temps. Herein we will present a crit. perspective of the recent advances in mol. nanomagnetism towards the goal of integrating spin-phonon interactions into the current computational methodologies of spin relaxation. This presentation will be placed in the context of the well-known models developed in solid state physics, which, as we will explain, are severely limited for mol. systems.**14**Lunghi, A.; Sanvito, S. The Limit of Spin Lifetime in Solid-State Electronic Spins.*J. Phys. Chem. Lett.*2020,*11*(15), 6273– 6278, DOI: 10.1021/acs.jpclett.0c0168114https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhtl2rsrfP&md5=3c6e646b3b537f46e159933629c0b465The Limit of Spin Lifetime in Solid-State Electronic SpinsLunghi, Alessandro; Sanvito, StefanoJournal of Physical Chemistry Letters (2020), 11 (15), 6273-6278CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)The development of spin qubits for quantum technologies requires their protection from the main source of finite-temp. decoherence: at. vibrations. Here the authors eliminate one of the main barriers to the progress in this field by providing a complete 1st-principles picture of spin relaxation that includes up to 2-phonon processes. Method is based on machine learning and electronic structure theory and makes the prediction of spin lifetime in realistic systems feasible. The authors study a prototypical V-based mol. qubit and reveal that the spin lifetime at high temp. is limited by Raman processes due to a small no. of THz intramol. vibrations. These findings effectively change the conventional understanding of spin relaxation in this class of materials and open new avenues for the rational design of long-living spin systems.**15**Goodwin, C. A. P.; Ortu, F.; Reta, D.; Chilton, N. F.; Mills, D. P. Molecular Magnetic Hysteresis at 60 K in Dysprosocenium.*Nature*2017,*548*(7668), 439– 442, DOI: 10.1038/nature2344715https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXhtlyisbfF&md5=8bc379889e7ac64db1802a4e14fed96eMolecular magnetic hysteresis at 60 kelvin in dysprosoceniumGoodwin, Conrad A. P.; Ortu, Fabrizio; Reta, Daniel; Chilton, Nicholas F.; Mills, David P.Nature (London, United Kingdom) (2017), 548 (7668), 439-442CODEN: NATUAS; ISSN:0028-0836. (Nature Publishing Group)Lanthanides were studied extensively for potential applications in quantum information processing and high-d. data storage at the mol. and at. scale. Exptl. achievements include reading and manipulating single nuclear spins, exploiting at. clock transitions for robust qubits and, most recently, magnetic data storage in single atoms. Single-mol. magnets exhibit magnetic hysteresis of mol. origin-a magnetic memory effect and a prerequisite of data storage-and so far lanthanide examples have exhibited this phenomenon at the highest temps. However, in the nearly 25 years since the discovery of single-mol. magnets, hysteresis temps. have increased from 4 K to only ∼14 K using a consistent magnetic field sweep rate of ∼20 Oe per s, although higher temps. were achieved by using very fast sweep rates (for example, 30 K with 200 Oe per s). Here the authors report a hexa-tert-butyldysprosocenium complex-[Dy(Cpttt)2][B(C6F5)4], with Cpttt = {C5H2tBu3-1,2,4} and tBu = CMe3-which exhibits magnetic hysteresis at temps. of up to 60 K at a sweep rate of 22 Oe per s. The authors observe a clear change in the relaxation dynamics at this temp., which persists in magnetically dild. samples, suggesting that the origin of the hysteresis is the localized metal-ligand vibrational modes that are unique to dysprosocenium. Ab initio calcns. of spin dynamics demonstrate that magnetic relaxation at high temps. is due to local mol. vibrations. With judicious mol. design, magnetic data storage in single mols. at temps. above liq. nitrogen should be possible.**16**Lunghi, A.; Totti, F.; Sanvito, S.; Sessoli, R. Intra-Molecular Origin of the Spin-Phonon Coupling in Slow-Relaxing Molecular Magnets.*Chem. Sci.*2017,*8*(9), 6051– 6059, DOI: 10.1039/C7SC02832F16https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXht1GrtrvP&md5=b72061032d53ce16e8f9869479e52355Intra-molecular origin of the spin-phonon coupling in slow-relaxing molecular magnetsLunghi, Alessandro; Totti, Federico; Sanvito, Stefano; Sessoli, RobertaChemical Science (2017), 8 (9), 6051-6059CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)We perform a systematic investigation of the spin-phonon coupling leading to spin relaxation in the prototypical mononuclear single mol. magnet [(tpaPh)Fe]-. In particular we analyze in detail the nature of the most relevant vibrational modes giving rise to the relaxation. Our fully ab initio calcns., where the phonon modes are evaluated at the level of d. functional theory and the spin-phonon coupling by mapping post-Hartree-Fock electronic structures onto an effective spin Hamiltonian, reveal that acoustic phonons are not active in the spin-phonon relaxation process of dil. SMMs crystals. Furthermore, we find that intra-mol. vibrational modes produce anisotropy tensor modulations orders of magnitude higher than those assocd. to rotations. In light of these results we are able to suggest new designing rules for spin-long-living SMMs which go beyond the tailoring of static mol. features but fully take into account dynamical features of the vibrational thermal bath evidencing those internal mol. distortions more relevant to the spin dynamics.**17**Abragam, A.; Bleaney, B.*Electron Paramagnetic Resonance of Transition Ions*; Oxford University Press, 1970.There is no corresponding record for this reference.**18**Guo, F.-S.; Day, B. M.; Chen, Y.-C.; Tong, M.-L.; Mansikkamäki, A.; Layfield, R. A. Magnetic Hysteresis up to 80 K in a Dysprosium Metallocene Single-Molecule Magnet.*Science*2018,*362*(6421), 1400– 1403, DOI: 10.1126/science.aav065218https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXisFeksL3F&md5=13d4c594df879bd5b507078447ab9af2Magnetic hysteresis up to 80 kelvin in a dysprosium metallocene single-molecule magnetGuo, Fu-Sheng; Day, Benjamin M.; Chen, Yan-Cong; Tong, Ming-Liang; Mansikkamaeki, Akseli; Layfield, Richard A.Science (Washington, DC, United States) (2018), 362 (6421), 1400-1403CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)Single-mol. magnets (SMMs) contg. only one metal center may represent the lower size limit for mol.-based magnetic information storage materials. Their current drawback is that all SMMs require liq.-helium cooling to show magnetic memory effects. We now report a chem. strategy to access the dysprosium metallocene cation [(CpiPr5)Dy(Cp*)]+ (CpiPr5, penta-iso-propylcyclopentadienyl; Cp*, pentamethylcyclopentadienyl), which displays magnetic hysteresis above liq.-nitrogen temps. An effective energy barrier to reversal of the magnetization of Ueff = 1541 wave no. is also measured. The magnetic blocking temp. of TB = 80 K for this cation overcomes an essential barrier toward the development of nanomagnet devices that function at practical temps.**19**Gould, C. A.; McClain, K. R.; Reta, D.; Kragskow, J. G. C.; Marchiori, D. A.; Lachman, E.; Choi, E.-S.; Analytis, J. G.; Britt, R. D.; Chilton, N. F.; Harvey, B. G.; Long, J. R. Ultrahard Magnetism from Mixed-Valence Dilanthanide Complexes with Metal-Metal Bonding.*Science*2022,*375*(6577), 198– 202, DOI: 10.1126/science.abl547019https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XhvV2lsbk%253D&md5=ebf15df0aa5b317333b45859719de25fUltrahard magnetism from mixed-valence dilanthanide complexes with metal-metal bondingGould, Colin A.; McClain, K. Randall; Reta, Daniel; Kragskow, Jon G. C.; Marchiori, David A.; Lachman, Ella; Choi, Eun-Sang; Analytis, James G.; Britt, R. David; Chilton, Nicholas F.; Harvey, Benjamin G.; Long, Jeffrey R.Science (Washington, DC, United States) (2022), 375 (6577), 198-202CODEN: SCIEAS; ISSN:1095-9203. (American Association for the Advancement of Science)Metal-metal bonding interactions can engender outstanding magnetic properties in bulk materials and mols., and examples abound for the transition metals. Extending this paradigm to the lanthanides, herein we report mixed-valence dilanth anide complexes (CpiPr5)2Ln2I3 (Ln is Gd, Tb, or Dy; CpiPr5, pentaisopropylcyclopentadienyl), which feature a singly occupied lanthanide-lanthanide σ-bonding orbital of 5dz2 parentage, as detd. by structural, spectroscopic, and computational analyses. Valence delocalization, wherein the d electron is equally shared by the two lanthanide centers, imparts strong parallel alignment of the σ-bonding and f electrons on both lanthanides according to Hund's rules. The combination of a well-isolated high-spin ground state and large magnetic anisotropy in (CpiPr5)2Dy2I3 gives rise to an enormous coercive magnetic field with a lower bound of 14 T at temps. as high as 60 K.**20**Chiesa, A.; Cugini, F.; Hussain, R.; Macaluso, E.; Allodi, G.; Garlatti, E.; Giansiracusa, M.; Goodwin, C. A. P.; Ortu, F.; Reta, D.; Skelton, J. M.; Guidi, T.; Santini, P.; Solzi, M.; De Renzi, R.; Mills, D. P.; Chilton, N. F.; Carretta, S. Understanding Magnetic Relaxation in Single-Ion Magnets with High Blocking Temperature.*Phys. Rev. B*2020,*101*(17), 174402 DOI: 10.1103/PhysRevB.101.17440220https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXhsFequrfK&md5=c8334ba3e94991645831b1b0a005de83Understanding magnetic relaxation in single-ion magnets with high blocking temperatureChiesa, A.; Cugini, F.; Hussain, R.; Macaluso, E.; Allodi, G.; Garlatti, E.; Giansiracusa, M.; Goodwin, C. A. P.; Ortu, F.; Reta, D.; Skelton, J. M.; Guidi, T.; Santini, P.; Solzi, M.; De Renzi, R.; Mills, D. P.; Chilton, N. F.; Carretta, S.Physical Review B (2020), 101 (17), 174402CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)The recent discovery of single-ion magnets with magnetic hysteresis above liq.-nitrogen temps. placed these compds. among the best candidates to realize high-d. storage devices. Starting from a prototypical dysprosocenium mol., showing hysteresis up to 60 K, we derive here a general recipe to design high-blocking-temp. rare-earth single-ion magnets. The complex magnetic relaxation is unraveled by combining magnetization and NMR measurements with inelastic neutron scattering expts. and ab initio calcns., thus disentangling the different mechanisms and identifying the key ingredients behind slow relaxation.**21**Randall McClain, K.; Gould, C. A.; Chakarawet, K.; Teat, S.; Groshens, T. J.; Long, J. R.; Harvey, B. G. High-Temperature Magnetic Blocking and Magneto-Structural Correlations in a Series of Dysprosium(III) Metallocenium Single-Molecule Magnets.*Chem. Sci.*2018,*9*, 8492– 8503, DOI: 10.1039/C8SC03907K21https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhvFCjsrjN&md5=1223684628a7d022399fa5a032335ba5High-temperature magnetic blocking and magneto-structural correlations in a series of dysprosium(III) metallocenium single-molecule magnetsRandall McClain, K.; Gould, Colin A.; Chakarawet, Khetpakorn; Teat, Simon J.; Groshens, Thomas J.; Long, Jeffrey R.; Harvey, Benjamin G.Chemical Science (2018), 9 (45), 8492-8503CODEN: CSHCCN; ISSN:2041-6520. (Royal Society of Chemistry)A series of dysprosium(III) metallocenium salts, [Dy(CpiPr4R)2][B(C6F5)4] (R = H (1), Me (2), Et (3), iPr (4)), was synthesized by reaction of DyI3 with the corresponding known NaCpiPr4R (R = H, iPr) and novel NaCpiPr4R (R = Me, Et) salts at high temp., followed by iodide abstraction with [H(SiEt3)2][B(C6F5)4]. Variation of the substituents in this series results in substantial changes in mol. structure, with more sterically-encumbering cyclopentadienyl ligands promoting longer Dy-C distances and larger Cp-Dy-Cp angles. Dc and ac magnetic susceptibility data reveal that these structural changes have a considerable impact on the magnetic relaxation behavior and operating temp. of each compd. In particular, the magnetic relaxation barrier increases as the Dy-C distance decreases and the Cp-Dy-Cp angle increases. An overall 45 K increase in the magnetic blocking temp. is obsd. across the series, with compds. 2-4 exhibiting the highest 100 s blocking temps. yet reported for a single-mol. magnet. Compd. 2 possesses the highest operating temp. of the series with a 100 s blocking temp. of 62 K. Concomitant increases in the effective relaxation barrier and the max. magnetic hysteresis temp. are obsd., with 2 displaying a barrier of 1468 cm-1 and open magnetic hysteresis as high as 72 K at a sweep rate of 3.1 mT s-1. Magneto-structural correlations are discussed with the goal of guiding the synthesis of future high operating temp. DyIII metallocenium single-mol. magnets.**22**Reta, D.; Kragskow, J. G. C.; Chilton, N. F. Ab Initio Prediction of High-Temperature Magnetic Relaxation Rates in Single-Molecule Magnets.*J. Am. Chem. Soc.*2021,*143*(15), 5943– 5950, DOI: 10.1021/jacs.1c0141022https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXnvF2gu7w%253D&md5=2f860e9ac222235f2792d230259e57fbAb Initio Prediction of High-Temperature Magnetic Relaxation Rates in Single-Molecule MagnetsReta, Daniel; Kragskow, Jon G. C.; Chilton, Nicholas F.Journal of the American Chemical Society (2021), 143 (15), 5943-5950CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)Organometallic mols. based on [Dy(CpR)2]+ cations (where CpR is a substituted cyclopentadienyl anion) have emerged as clear front-runners in the search for high-temp. single-mol. magnets. Within this family of structurally similar mols., significant variations in their magnetic properties are seen, demonstrating the importance of understanding magneto-structural relationships to develop more efficient design strategies. Here we develop an ab initio spin dynamics methodol. and show that it is capable of quant. prediction of relative relaxation rates in the Orbach region. Applying it to all reported [Dy(CpR)2]+ cations allows us understand differences in their relaxation dynamics, highlighting that the main discriminant is the magnitude of the crystal field splitting, rather than differences in spin-vibrational coupling. We subsequently employ the method to predict relaxation rates for a series of hypothetical organometallic sandwich compds., revealing an upper limit to the effective barrier to magnetic relaxation of around 2100-2200 K, which has been reached by existing compds. Our conclusion is that further improvements to monometallic single-mol. magnets require moving vibrational modes off-resonance with electronic excitations.**23**Lunghi, A.; Sanvito, S. Surfing Multiple Conformation-Property Landscapes via Machine Learning: Designing Single-Ion Magnetic Anisotropy.*J. Phys. Chem. C*2020,*124*(10), 5802– 5806, DOI: 10.1021/acs.jpcc.0c0118723https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3cXivVaktLw%253D&md5=22d2b08703e9a20cb543a12f1d1cc041Surfing Multiple Conformation-Property Landscapes via Machine Learning: Designing Single-Ion Magnetic AnisotropyLunghi, Alessandro; Sanvito, StefanoJournal of Physical Chemistry C (2020), 124 (10), 5802-5806CODEN: JPCCCK; ISSN:1932-7447. (American Chemical Society)Computational statistical disciplines, such as machine learning, are leading to a paradigm shift in the way the authors conceive the design of new compds., offering a way to directly design the best compd. for specific applications. This approach, known as reverse engineering, requires the construction of models able to efficiently predict continuous structure-property maps. Here, the authors show that machine learning offers such a possibility by designing a model that predicts both the energy and magnetic properties as a function of the mol. structure of a single-ion magnet. This model is then used to explore the mol. conformational landscapes in search of structures that maximize magnetic anisotropy. The authors find that a 5% change in one of the coordination angles leads to a ∼50% increase in the anisotropy. This approach can be applied to any structure-property relation and paves the way for a machine-learning-driven optimization of chem. compds.**24**Escalera-Moreno, L.; Suaud, N.; Gaita-Ariño, A.; Coronado, E. Determining Key Local Vibrations in the Relaxation of Molecular Spin Qubits and Single-Molecule Magnets.*J. Phys. Chem. Lett.*2017,*8*, 1695– 1700, DOI: 10.1021/acs.jpclett.7b0047924https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXltVSqtrw%253D&md5=efae85248b706be0d5e6897009782538Determining Key Local Vibrations in the Relaxation of Molecular Spin Qubits and Single-Molecule MagnetsEscalera-Moreno, L.; Suaud, N.; Gaita-Arino, A.; Coronado, E.Journal of Physical Chemistry Letters (2017), 8 (7), 1695-1700CODEN: JPCLCD; ISSN:1948-7185. (American Chemical Society)To design mol. spin qubits and nanomagnets operating at high temps., there is an urgent need to understand the relationship between vibrations and spin relaxation processes. Herein we develop a simple first-principles methodol. to det. the modulation that vibrations exert on spin energy levels. This methodol. is applied to [Cu(mnt)2]2- (mnt2- = 1,2-dicyanoethylene-1,2-dithiolate), a highly coherent complex. By theor. identifying the most relevant vibrational modes, we are able to offer general strategies to chem. design more resilient magnetic mols., where the energy of the spin states is not coupled to vibrations.**25**Lunghi, A.; Totti, F.; Sessoli, R.; Sanvito, S. The Role of Anharmonic Phonons in Under-Barrier Spin Relaxation of Single Molecule Magnets.*Nat. Commun.*2017,*8*, 14620 DOI: 10.1038/ncomms1462025https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC1czjtFahug%253D%253D&md5=af55f4e5f2641e56670ec5651e0d608aThe role of anharmonic phonons in under-barrier spin relaxation of single molecule magnetsLunghi Alessandro; Totti Federico; Sessoli Roberta; Lunghi Alessandro; Sanvito StefanoNature communications (2017), 8 (), 14620 ISSN:.The use of single molecule magnets in mainstream electronics requires their magnetic moment to be stable over long times. One can achieve such a goal by designing compounds with spin-reversal barriers exceeding room temperature, namely with large uniaxial anisotropies. Such strategy, however, has been defeated by several recent experiments demonstrating under-barrier relaxation at high temperature, a behaviour today unexplained. Here we propose spin-phonon coupling to be responsible for such anomaly. With a combination of electronic structure theory and master equations we show that, in the presence of phonon dissipation, the relevant energy scale for the spin relaxation is given by the lower-lying phonon modes interacting with the local spins. These open a channel for spin reversal at energies lower than that set by the magnetic anisotropy, producing fast under-barrier spin relaxation. Our findings rationalize a significant body of experimental work and suggest a possible strategy for engineering room temperature single molecule magnets.**26**Lunghi, A. Toward Exact Predictions of Spin-Phonon Relaxation Times: An Ab Initio Implementation of Open Quantum Systems Theory.*Sci. Adv.*2022,*8*(31), eabn7880 DOI: 10.1126/sciadv.abn7880There is no corresponding record for this reference.**27**Albino, A.; Benci, S.; Tesi, L.; Atzori, M.; Torre, R.; Sanvito, S.; Sessoli, R.; Lunghi, A. First-Principles Investigation of Spin–Phonon Coupling in Vanadium-Based Molecular Spin Quantum Bits.*Inorg. Chem.*2019,*58*(15), 10260– 10268, DOI: 10.1021/acs.inorgchem.9b0140727https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhsVaqtL3E&md5=ecf53e227cb269283c657c52364625dcFirst-Principles Investigation of Spin-Phonon Coupling in Vanadium-Based Molecular Spin Quantum BitsAlbino, Andrea; Benci, Stefano; Tesi, Lorenzo; Atzori, Matteo; Torre, Renato; Sanvito, Stefano; Sessoli, Roberta; Lunghi, AlessandroInorganic Chemistry (2019), 58 (15), 10260-10268CODEN: INOCAJ; ISSN:0020-1669. (American Chemical Society)Paramagnetic mols. can show long spin-coherence times, which make them good candidates as quantum bits (qubits). Reducing the efficiency of the spin-phonon interaction is the primary challenge toward achieving long coherence times over a wide temp. range in soft mol. lattices. The lack of a microscopic understanding about the role of vibrations in spin relaxation strongly undermines the possibility of chem. designing better-performing mol. qubits. Here we report a first-principles characterization of the main mechanism contributing to the spin-phonon coupling for a class of vanadium(IV) mol. qubits. Post-Hartree-Fock and d. functional theory methods are used to det. the effect of both intermol. and intramol. vibrations on modulation of the Zeeman energy for four mols. showing different coordination geometries and ligands. This comparative study provides the first insight into the role played by coordination geometry and ligand-field strength in detg. the spin-lattice relaxation time of mol. qubits, opening an avenue to the rational design of new compds.**28**Shevlin, S.; Castro, B.; Li, X. Computational Materials Design.*Nat. Mater.*2021,*20*(6), 727, DOI: 10.1038/s41563-021-01038-828https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BB2c7gtVeluw%253D%253D&md5=6e7825cd82f936741e7b83ce17404140Computational materials designShevlin Stephen; Castro Bruno; Li XinNature materials (2021), 20 (6), 727 ISSN:.There is no expanded citation for this reference.**29**Butler, K. T.; Frost, J. M.; Skelton, J. M.; Svane, K. L.; Walsh, A. Computational Materials Design of Crystalline Solids.*Chem. Soc. Rev.*2016,*45*(22), 6138– 6146, DOI: 10.1039/C5CS00841G29https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28XksVajt7c%253D&md5=f9695a25b788f726dc66ed4ac4ae65fbComputational materials design of crystalline solidsButler, Keith T.; Frost, Jarvist M.; Skelton, Jonathan M.; Svane, Katrine L.; Walsh, AronChemical Society Reviews (2016), 45 (22), 6138-6146CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)The modeling of materials properties and processes from first principles is becoming sufficiently accurate as to facilitate the design and testing of new systems in silico. Computational materials science is both valuable and increasingly necessary for developing novel functional materials and composites that meet the requirements of next-generation technol. A range of simulation techniques are being developed and applied to problems related to materials for energy generation, storage and conversion including solar cells, nuclear reactors, batteries, fuel cells, and catalytic systems. Such techniques may combine crystal-structure prediction (global optimization), data mining (materials informatics) and high-throughput screening with elements of machine learning. We explore the development process assocd. with computational materials design, from setting the requirements and descriptors to the development and testing of new materials. As a case study, we critically review progress in the fields of thermoelecs. and photovoltaics, including the simulation of lattice thermal cond. and the search for Pb-free hybrid halide perovskites. Finally, a no. of universal chem.-design principles are advanced.**30**Nolan, A. M.; Zhu, Y.; He, X.; Bai, Q.; Mo, Y. Computation-Accelerated Design of Materials and Interfaces for All-Solid-State Lithium-Ion Batteries.*Joule*2018,*2*(10), 2016– 2046, DOI: 10.1016/j.joule.2018.08.01730https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1cXhvFOrsb%252FI&md5=c4feeea90a614cdda2f06b973a5492afComputation-Accelerated Design of Materials and Interfaces for All-Solid-State Lithium-Ion BatteriesNolan, Adelaide M.; Zhu, Yizhou; He, Xingfeng; Bai, Qiang; Mo, YifeiJoule (2018), 2 (10), 2016-2046CODEN: JOULBR; ISSN:2542-4351. (Cell Press)A review. The all-solid-state lithium-ion battery is a promising next-generation battery technol. However, the realization of all-solid-state batteries is impeded by limited understanding of solid electrolyte materials and solid electrolyte-electrode interfaces. In this review, we present an overview of recently developed computation techniques and their applications in understanding and advancing materials and interfaces in all-solid-state batteries. We review the role of ab initio mol. dynamics simulations in studying fast ion conductors and discuss the capabilities of thermodn. calcns. powered by materials databases for identifying the chem. and electrochem. stability of solid electrolyte materials and solid electrolyte-electrode interfaces. We highlight the computational studies in the design and discovery of new solid electrolyte materials and outline design guidelines for solid electrolytes and their interfaces. We conclude with discussion of future directions in computation techniques, materials development, and interface engineering for all-solid-state lithium-ion batteries.**31**Briganti, M.; Santanni, F.; Tesi, L.; Totti, F.; Sessoli, R.; Lunghi, A. A Complete Ab Initio View of Orbach and Raman Spin–Lattice Relaxation in a Dysprosium Coordination Compound.*J. Am. Chem. Soc.*2021,*143*(34), 13633– 13645, DOI: 10.1021/jacs.1c0506831https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXhvVSqs7%252FL&md5=ae99249136f2543532fc8fbdfdcc288fA Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination CompoundBriganti, Matteo; Santanni, Fabio; Tesi, Lorenzo; Totti, Federico; Sessoli, Roberta; Lunghi, AlessandroJournal of the American Chemical Society (2021), 143 (34), 13633-13645CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)The unique electronic and magnetic properties of lanthanide mol. complexes place them at the forefront of the race toward high-temp. single-mol. magnets and magnetic quantum bits. The design of compds. of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its max. potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chem. beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-mol. magnet. Computational predictions are in agreement with the exptl. detn. of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temp., is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive anal. of spin-phonon coupling mechanism reveals that mol. vibrations beyond the ion's first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chem. sound design rules tackling every aspect of spin relaxation at any temp.**32**Liu, J.; Chen, Y.-C.; Liu, J.-L.; Vieru, V.; Ungur, L.; Jia, J.-H.; Chibotaru, L. F.; Lan, Y.; Wernsdorfer, W.; Gao, S.; Chen, X.-M.; Tong, M.-L. A Stable Pentagonal Bipyramidal Dy(III) Single-Ion Magnet with a Record Magnetization Reversal Barrier over 1000 K.*J. Am. Chem. Soc.*2016,*138*(16), 5441– 5450, DOI: 10.1021/jacs.6b0263832https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC28Xls1Gru7s%253D&md5=913ebcfdd033b556209ebcccdfb268e0A Stable Pentagonal Bipyramidal Dy(III) Single-Ion Magnet with a Record Magnetization Reversal Barrier over 1000 KLiu, Jiang; Chen, Yan-Cong; Liu, Jun-Liang; Vieru, Veacheslav; Ungur, Liviu; Jia, Jian-Hua; Chibotaru, Liviu F.; Lan, Yanhua; Wernsdorfer, Wolfgang; Gao, Song; Chen, Xiao-Ming; Tong, Ming-LiangJournal of the American Chemical Society (2016), 138 (16), 5441-5450CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)Single-mol. magnets (SMMs) with a large spin reversal barrier were recognized to exhibit slow magnetic relaxation that can lead to a magnetic hysteresis loop. Synthesis of highly stable SMMs with both large energy barriers and significantly slow relaxation times is challenging. Here, the authors report two highly stable and neutral Dy(III) classical coordination compds. with pentagonal bipyramidal local geometry that exhibit SMM behavior. Weak intermol. interactions in the undiluted single crystals are 1st obsd. for mononuclear lanthanide SMMs by micro-SQUID measurements. The study of magnetic relaxation reveals the thermally activated quantum tunneling of magnetization through the 3rd excited Kramers doublet, owing to the increased axial magnetic anisotropy and weaker transverse magnetic anisotropy. As a result, pronounced magnetic hysteresis loops up to 14 K are obsd., and the effective energy barrier (Ueff = 1025 K) for relaxation of magnetization reached a breakthrough among the SMMs.**33**Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; Nakatsuji, H.; Caricato, M.; Li, X.; Hratchian, H. P.; Izmaylov, A. F.; Bloino, J.; Zheng, G.; Sonnenberg, J. L.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Vreven, T.; Montgomery, J. A., Jr.; Peralta, J. E.; Ogliaro, F.; Bearpark, M.; Heyd, J. J.; Brothers, E.; Kudin, K. N.; Staroverov, V. N.; Keith, T.; Kobayashi, R.; Normand, J.; Raghavachari, K.; Rendell, A.; Burant, J. C.; Iyengar, S. S.; Tomasi, J.; Cossi, M.; Rega, N.; Millam, J. M.; Klene, M.; Knox, J. E.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Martin, R. L.; Morokuma, K.; Zakrzewski, V. G.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Dapprich, S.; Daniels, A. D.; Farkas, Ö.; Foresman, J. B.; Ortiz, J. V.; Cioslowski, J.; Fox, D. J.*Gaussian 09*, revision D.01; Gaussian, Inc.: Wallingford CT, 2013.There is no corresponding record for this reference.**34**Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple.*Phys. Rev. Lett.*1996,*77*(18), 3865– 3868, DOI: 10.1103/PhysRevLett.77.386534https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XmsVCgsbs%253D&md5=55943538406ee74f93aabdf882cd4630Generalized gradient approximation made simplePerdew, John P.; Burke, Kieron; Ernzerhof, MatthiasPhysical Review Letters (1996), 77 (18), 3865-3868CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)Generalized gradient approxns. (GGA's) for the exchange-correlation energy improve upon the local spin d. (LSD) description of atoms, mols., and solids. We present a simple derivation of a simple GGA, in which all parameters (other than those in LSD) are fundamental consts. Only general features of the detailed construction underlying the Perdew-Wang 1991 (PW91) GGA are invoked. Improvements over PW91 include an accurate description of the linear response of the uniform electron gas, correct behavior under uniform scaling, and a smoother potential.**35**Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu.*J. Chem. Phys.*2010,*132*(15), 154104 DOI: 10.1063/1.338234435https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3cXkvVyks7o%253D&md5=2bca89d904579d5565537a0820dc2ae8A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-PuGrimme, Stefan; Antony, Jens; Ehrlich, Stephan; Krieg, HelgeJournal of Chemical Physics (2010), 132 (15), 154104/1-154104/19CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)The method of dispersion correction as an add-on to std. Kohn-Sham d. functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coeffs. and cutoff radii that are both computed from first principles. The coeffs. for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination nos. (CN). They are used to interpolate between dispersion coeffs. of atoms in different chem. environments. The method only requires adjustment of two global parameters for each d. functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of at. forces. Three-body nonadditivity terms are considered. The method has been assessed on std. benchmark sets for inter- and intramol. noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean abs. deviations for the S22 benchmark set of noncovalent interactions for 11 std. d. functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C6 coeffs. also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in mols. and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems. (c) 2010 American Institute of Physics.**36**Dunning, T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen.*J. Chem. Phys.*1989,*90*(2), 1007– 1023, DOI: 10.1063/1.45615336https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL1MXksVGmtrk%253D&md5=c6cd67a3748dc61692a9cb622d2694a0Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogenDunning, Thom H., Jr.Journal of Chemical Physics (1989), 90 (2), 1007-23CODEN: JCPSA6; ISSN:0021-9606.Guided by the calcns. on oxygen in the literature, basis sets for use in correlated at. and mol. calcns. were developed for all of the first row atoms from boron through neon, and for hydrogen. As in the oxygen atom calcns., the incremental energy lowerings, due to the addn. of correlating functions, fall into distinct groups. This leads to the concept of correlation-consistent basis sets, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation-consistent sets are given for all of the atoms considered. The most accurate sets detd. in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding at.-natural-orbital sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estd. that this set yields 94-97% of the total (HF + 1 + 2) correlation energy for the atoms neon through boron.**37**Kresse, G.; Hafner, J. Ab Initio Molecular Dynamics for Liquid Metals.*Phys. Rev. B*1993,*47*(1), 558– 561, DOI: 10.1103/PhysRevB.47.55837https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3sXlt1Gnsr0%253D&md5=c9074f6e1afc534b260d29dd1846e350Ab initio molecular dynamics of liquid metalsKresse, G.; Hafner, J.Physical Review B: Condensed Matter and Materials Physics (1993), 47 (1), 558-61CODEN: PRBMDO; ISSN:0163-1829.The authors present ab initio quantum-mech. mol.-dynamics calcns. based on the calcn. of the electronic ground state and of the Hellmann-Feynman forces in the local-d. approxn. at each mol.-dynamics step. This is possible using conjugate-gradient techniques for energy minimization, and predicting the wave functions for new ionic positions using sub-space alignment. This approach avoids the instabilities inherent in quantum-mech. mol.-dynamics calcns. for metals based on the use of a factitious Newtonian dynamics for the electronic degrees of freedom. This method gives perfect control of the adiabaticity and allows one to perform simulations over several picoseconds.**38**Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal--Amorphous-Semiconductor Transition in Germanium.*Phys. Rev. B*1994,*49*(20), 14251– 14269, DOI: 10.1103/PhysRevB.49.1425138https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2cXkvFKrtL4%253D&md5=c5dddfd01394e53720fb4c3a3ccfd6c0Ab initio molecular-dynamics simulation of the liquid-metal-amorphous-semiconductor transition in germaniumKresse, G.; Hafner, J.Physical Review B: Condensed Matter and Materials Physics (1994), 49 (20), 14251-69CODEN: PRBMDO; ISSN:0163-1829.The authors present ab initio quantum-mech. mol.-dynamics simulations of the liq.-metal-amorphous-semiconductor transition in Ge. The simulations are based on (a) finite-temp. d.-functional theory of the 1-electron states, (b) exact energy minimization and hence calcn. of the exact Hellmann-Feynman forces after each mol.-dynamics step using preconditioned conjugate-gradient techniques, (c) accurate nonlocal pseudopotentials, and (d) Nose' dynamics for generating a canonical ensemble. This method gives perfect control of the adiabaticity of the electron-ion ensemble and allows the authors to perform simulations over >30 ps. The computer-generated ensemble describes the structural, dynamic, and electronic properties of liq. and amorphous Ge in very good agreement with expt.. The simulation allows the authors to study in detail the changes in the structure-property relation through the metal-semiconductor transition. The authors report a detailed anal. of the local structural properties and their changes induced by an annealing process. The geometrical, bounding, and spectral properties of defects in the disordered tetrahedral network are studied and compared with expt.**39**Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set.*Comput. Mater. Sci.*1996,*6*(1), 15– 50, DOI: 10.1016/0927-0256(96)00008-039https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XmtFWgsrk%253D&md5=779b9a71bbd32904f968e39f39946190Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis setKresse, G.; Furthmuller, J.Computational Materials Science (1996), 6 (1), 15-50CODEN: CMMSEM; ISSN:0927-0256. (Elsevier)The authors present a detailed description and comparison of algorithms for performing ab-initio quantum-mech. calcns. using pseudopotentials and a plane-wave basis set. The authors will discuss: (a) partial occupancies within the framework of the linear tetrahedron method and the finite temp. d.-functional theory, (b) iterative methods for the diagonalization of the Kohn-Sham Hamiltonian and a discussion of an efficient iterative method based on the ideas of Pulay's residual minimization, which is close to an order N2atoms scaling even for relatively large systems, (c) efficient Broyden-like and Pulay-like mixing methods for the charge d. including a new special preconditioning optimized for a plane-wave basis set, (d) conjugate gradient methods for minimizing the electronic free energy with respect to all degrees of freedom simultaneously. The authors have implemented these algorithms within a powerful package called VAMP (Vienna ab-initio mol.-dynamics package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semi-conducting surfaces, phonons in simple metals, transition metals and semiconductors) and turned out to be very reliable.**40**Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set.*Phys. Rev. B*1996,*54*(16), 11169– 11186, DOI: 10.1103/PhysRevB.54.1116940https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28Xms1Whu7Y%253D&md5=9c8f6f298fe5ffe37c2589d3f970a697Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis setKresse, G.; Furthmueller, J.Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.**41**Kresse, G.; Hafner, J. Norm-Conserving and Ultrasoft Pseudopotentials for First-Row and Transition Elements.*J. Phys.: Condens. Matter*1994,*6*(40), 8245– 8257, DOI: 10.1088/0953-8984/6/40/01541https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK2cXms1Cjsr4%253D&md5=401c0f2ca351bb8484b70bc9bcaed11eNorm-conserving and ultrasoft pseudopotentials for first-row and transition elementsKresse, G.; Hafner, J.Journal of Physics: Condensed Matter (1994), 6 (40), 8245-57CODEN: JCOMEL; ISSN:0953-8984.The construction of accurate pseudopotentials with good convergence properties for the first-row and transition elements is discussed. By combining an improved description of the pseudo-wavefunction inside the cut-off radius with the concept of ultrasoft pseudopotentials introduced by Vanderbilt optimal compromise between transferability and plane-wave convergence can be achieved. With the new pseudopotentials, basis sets with no more than 75-100 plane waves per atom are sufficient to reproduce the results obtained with the most accurate norm-conserving pseudopotentials.**42**Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method.*Phys. Rev. B*1999,*59*(3), 1758– 1775, DOI: 10.1103/PhysRevB.59.175842https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXkt12nug%253D%253D&md5=78a73e92a93f995982fc481715729b14From ultrasoft pseudopotentials to the projector augmented-wave methodKresse, G.; Joubert, D.Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.**43**Togo, A.; Tanaka, I. First Principles Phonon Calculations in Materials Science.*Scr. Mater.*2015,*108*, 1– 5, DOI: 10.1016/j.scriptamat.2015.07.02143https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXht1GltLbE&md5=5b0b051b706cef43bfbb682a583fd4adFirst principles phonon calculations in materials scienceTogo, Atsushi; Tanaka, IsaoScripta Materialia (2015), 108 (), 1-5CODEN: SCMAF7; ISSN:1359-6462. (Elsevier Ltd.)Phonon plays essential roles in dynamical behaviors and thermal properties, which are central topics in fundamental issues of materials science. The importance of first principles phonon calcns. cannot be overly emphasized. Phonopy is an open source code for such calcns. launched by the present authors, which has been world-widely used. Here we demonstrate phonon properties with fundamental equations and show examples how the phonon calcns. are applied in materials science.**44**Togo, A.; Chaput, L.; Tanaka, I. Distributions of Phonon Lifetimes in Brillouin Zones.*Phys. Rev. B*2015,*91*(9), 094306 DOI: 10.1103/PhysRevB.91.09430644https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXovVyrtLg%253D&md5=d9b81b8d71595c2cc5a1aef413b113caDistributions of phonon lifetimes in Brillouin zonesTogo, Atsushi; Chaput, Laurent; Tanaka, IsaoPhysical Review B: Condensed Matter and Materials Physics (2015), 91 (9), 094306/1-094306/31CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)Lattice thermal conductivities of zincblende- and wurtzite-type compds. with 33 combinations of elements are calcd. with the single-mode relaxation-time approxn. and a full soln. of the linearized phonon Boltzmann equation from first-principles anharmonic lattice dynamics calcns. In nine zincblende-type compds., distributions of phonon linewidths (inverse phonon lifetimes) are discussed in detail. The phonon linewidths vary nonsmoothly with respect to wave vector, which is explained from the imaginary parts of the self-energies. It is presented that detailed combination of phonon-phonon interaction strength and three-phonon selection rule is critically important to det. phonon lifetime for these compds. This indicates difficulty to predict phonon lifetime quant. without anharmonic force consts. However, it is shown that joint d. of states weighted by phonon nos., which is calcd. only from harmonic force consts., can be potentially used for a screening of the lattice thermal cond. of materials.**45**Kragskow, J. G. C.; Mattioni, A.; Staab, J. K.; Reta, D.; Skelton, J. M.; Chilton, N. F. Spin–Phonon Coupling and Magnetic Relaxation in Single-Molecule Magnets.*Chem. Soc. Rev.*2023,*52*(14), 4567– 4585, DOI: 10.1039/D2CS00705C45https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXhtlCjsL7I&md5=0b1b2a3e3e75b276e82836775e0b37beSpin-phonon coupling and magnetic relaxation in single-molecule magnetsKragskow, Jon G. C.; Mattioni, Andrea; Staab, Jakob K.; Reta, Daniel; Skelton, Jonathan M.; Chilton, Nicholas F.Chemical Society Reviews (2023), 52 (14), 4567-4585CODEN: CSRVBR; ISSN:0306-0012. (Royal Society of Chemistry)A review. Electron-phonon coupling is important in many phys. phenomena, e.g. photosynthesis, catalysis and quantum information processing, but its impacts are difficult to grasp on the microscopic level. One area attracting wide interest is that of single-mol. magnets, which is motivated by searching for the ultimate limit in the miniaturization of binary data storage media. The utility of a mol. to store magnetic information is quantified by the timescale of its magnetic reversal processes, also known as magnetic relaxation, which is limited by spin-phonon coupling. Several recent accomplishments of synthetic organometallic chem. have led to the observation of mol. magnetic memory effects at temps. above that of liq. nitrogen. These discoveries have highlighted how far chem. design strategies for maximising magnetic anisotropy have come, but have also highlighted the need to characterize the complex interplay between phonons and mol. spin states. The crucial step is to make a link between magnetic relaxation and chem. motifs, and so be able to produce design criteria to extend mol. magnetic memory. The basic physics assocd. with spin-phonon coupling and magnetic relaxation was outlined in the early 20th century using perturbation theory, and has more recently been recast in the form of a general open quantum systems formalism and tackled with different levels of approxns. It is the purpose of this Tutorial Review to introduce the topics of phonons, mol. spin-phonon coupling, and magnetic relaxation, and to outline the relevant theories in connection with both the traditional perturbative texts and the more modern open quantum systems methods.**46**Breneman, C. M.; Wiberg, K. B. Determining Atom-Centered Monopoles from Molecular Electrostatic Potentials. The Need for High Sampling Density in Formamide Conformational Analysis.*J. Comput. Chem.*1990,*11*(3), 361– 373, DOI: 10.1002/jcc.54011031146https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3cXitFGrtr4%253D&md5=459ad3de5200b9d914d2cd8c896f387aDetermining atom-centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysisBreneman, Curt M.; Wiberg, Kenneth B.Journal of Computational Chemistry (1990), 11 (3), 361-73CODEN: JCCHDD; ISSN:0192-8651.An improved method for computing potential-derived charges is described which is based upon the CHELP program available from QCPE. This approach (CHELPG) is shown to be considerably less dependent upon mol. orientation than the original CHELP program. In the second part of this work, the CHELPG point selection algorithm was used to analyze the changes in the potential-derived charges in formamide during rotation about the C-N bond. In order to achieve a level of rotational invariance less than 10% of the magnitude of the electronic effects studied, an equally-spaced array of points 0.3 Å apart was required. Points found to be greater than 2.8 Å from any nucleus were eliminated, along with all points contained within the defined VDW distances from each of the atoms. The results are compared to those obtained by using CHELP. Even when large nos. of points (ca. 3000) were sampled using the CHELP selection routine, the results did not indicate a satisfactory level of rotational invariance. On the basis of these results, the original CHELP program was inadequate for analyzing internal rotations.**47**Chan, W.-T.; Fournier, R. Binding of Ammonia to Small Copper and Silver Clusters.*Chem. Phys. Lett.*1999,*315*(3), 257– 265, DOI: 10.1016/S0009-2614(99)01195-147https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK1MXotVKrsr8%253D&md5=979ba9910e96eb8552412eb2060e6d58Binding of ammonia to small copper and silver clustersChan, W.-T.; Fournier, R.Chemical Physics Letters (1999), 315 (3,4), 257-265CODEN: CHPLBC; ISSN:0009-2614. (Elsevier Science B.V.)Equil. geometries, harmonic frequencies, and thermochem. data are reported for the metal cluster-NH3 complexes Agn(NH3) and Cun(NH3) (n=1,2,3,4), Ag4(NH3)2, and Cu4(NH3)2 calcd. by a d. functional method. The calcd. shifts in NH3 umbrella mode frequency correlate with the obsd. shifts and the calcd. enthalpies of complexation. The preferred site for NH3 adsorption and the calcd. bond enthalpies can be rationalized by considering at. charges obtained from a natural population anal. and polarization of the metal electron d.**48**Valdés, Á.; Prosmiti, R.; Villarreal, P.; Delgado-Barrio, G. HeBr2 Complex: Ground-State Potential and Vibrational Dynamics from Ab Initio Calculations.*Mol. Phys.*2004,*102*(21–22), 2277– 2283, DOI: 10.1080/0026897041233129063448https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2cXhtFGmu73N&md5=87238d42143bcb3255cfed8b55f9be47HeBr2 complex: Ground-state potential and vibrational dynamics from ab initio calculationsValdes, Alvaro; Prosmiti, Rita; Villarreal, Pablo; Delgado-Barrio, GerardoMolecular Physics (2004), 102 (21-22), 2277-2283CODEN: MOPHAM; ISSN:0026-8976. (Taylor & Francis Ltd.)The three-dimensional interaction potential for HeBr2 was studied using a coupled-cluster (CCSD(T)) method. In our calcns., the Stuttgart group (SDD) effective-core potentials, augmented with diffusion (sp) and polarization (3df) functions (denoted SDD + G(3df)), basis sets are employed for the bromine atoms. For the He atom, the augmented correlation-consistent aug-cc-pV5Z basis set, supplemented with a set of bond functions, is used. The potential energy surface is constructed by fitting the CCSD(T) calcd. ab initio data to an anal. expression. The present ground-state potential for HeBr2 shows a double-min. topol., with wells for both linear and T-shaped configurations. Bound-state calcns. are carried out and the lowest vibrational levels are assigned to linear and T-shaped isomers. Dissocn. energies and vibrationally averaged structures for both species are detd. and found to be in very good agreement with the available exptl. data.**49**Lei, M.; Wang, N.; Zhu, L.; Tang, H. Peculiar and Rapid Photocatalytic Degradation of Tetrabromodiphenyl Ethers over Ag/TiO2 Induced by Interaction between Silver Nanoparticles and Bromine Atoms in the Target.*Chemosphere*2016,*150*, 536– 544, DOI: 10.1016/j.chemosphere.2015.10.04849https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2MXhslKktLfN&md5=74176daf90d1056376d066d2a0be5c4ePeculiar and rapid photocatalytic degradation of tetrabromodiphenyl ethers over Ag/TiO2 induced by interaction between silver nanoparticles and bromine atoms in the targetLei, Ming; Wang, Nan; Zhu, Lihua; Tang, HeqingChemosphere (2016), 150 (), 536-544CODEN: CMSHAF; ISSN:0045-6535. (Elsevier Ltd.)As a typical moderately-brominated diphenylethers, 2,2,4,4-tetrabromodiphenyl ether (BDE47) is hardly debrominated by a conventional TiO2-mediated photocatalysis. However, its reductive debromination was rapid achieved over silver nanoparticle-loaded TiO2 (Ag/TiO2) in UV-irradiated anoxic acetonitrile-water within 13 min. An "Ag-promoted electron transfer and C-Br cleavage" concept was proposed based on exptl. results and d. functional theory calcns. Ag0 exerted affinity interaction with bromine atoms, and the storing of electrons on Ag0 increased the binding interaction, which elongated the C-Br bond of BDE47 and facilitated its cleavage. The initiating of the BDE47 debromination on Ag0 required an induction period to enrich a crit. amt. of electrons, leading to a stronger driving force for both injecting electron to BDE47 and stretching the C-Br bond. Stronger photo-excitation, higher polar solvent, and a moderate Ag0 load strengthened the interfacial electron transfer over Ag/TiO2, and thereby shortening the induction time and accelerating the BDE47 degrdn.**50**Ungur, L.; Chibotaru, L. F. Ab Initio Crystal Field for Lanthanides.*Chem. – Eur. J.*2017,*23*(15), 3708– 3718, DOI: 10.1002/chem.20160510250https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC2sXjtVehsLg%253D&md5=7449a485b779634f64c774721976ed5fAb Initio Crystal Field for LanthanidesUngur, Liviu; Chibotaru, Liviu F.Chemistry - A European Journal (2017), 23 (15), 3708-3718CODEN: CEUJED; ISSN:0947-6539. (Wiley-VCH Verlag GmbH & Co. KGaA)An ab initio methodol. for the first-principle derivation of crystal-field (CF) parameters for lanthanides is described. The methodol. is applied to the anal. of CF parameters in [Tb(Pc)2]- (Pc = phthalocyanine) and Dy4K2 ([Dy4K2O(OtBu)12]) complexes, and compared with often used approx. and model descriptions. It is found that the application of geometry symmetrization, and the use of electrostatic point-charge and phenomenol. CF models, lead to unacceptably large deviations from predictions based on ab initio calcns. for exptl. geometry. It is shown how the predictions of std. CASSCF (Complete Active Space SCF) calcns. (with 4f orbitals in the active space) can be systematically improved by including effects of dynamical electronic correlation (CASPT2 step) and by admixing electronic configurations of the 5d shell. This is exemplified for the well-studied Er-trensal complex (H3trensal = 2,2',2"-tris(salicylideneimido)trimethylamine). The electrostatic contributions to CF parameters in this complex, calcd. with true charge distributions in the ligands, yield less than half of the total CF splitting, thus pointing to the dominant role of covalent effects. This anal. allows the conclusion that ab initio crystal field is an essential tool for the decent description of lanthanides.**51**spin_phonon_suite. https://gitlab.com/chilton-group/spin_phonon_suite (accessed Aug 21, 2023).There is no corresponding record for this reference.**52**Karlstroem, G. New Approach to the Modeling of Dielectric Media Effects in Ab Initio Quantum Chemical Calculations.*J. Phys. Chem. A*1988,*92*(5), 1315– 1318, DOI: 10.1021/j100316a060There is no corresponding record for this reference.**53**Li Manni, G.; Fdez Galván, I.; Alavi, A.; Aleotti, F.; Aquilante, F.; Autschbach, J.; Avagliano, D.; Baiardi, A.; Bao, J. J.; Battaglia, S.; Birnoschi, L.; Blanco-González, A.; Bokarev, S. I.; Broer, R.; Cacciari, R.; Calio, P. B.; Carlson, R. K.; Carvalho Couto, R.; Cerdán, L.; Chibotaru, L. F.; Chilton, N. F.; Church, J. R.; Conti, I.; Coriani, S.; Cuéllar-Zuquin, J.; Daoud, R. E.; Dattani, N.; Decleva, P.; de Graaf, C.; Delcey, M. G.; De Vico, L.; Dobrautz, W.; Dong, S. S.; Feng, R.; Ferré, N.; Filatov Gulak, M.; Gagliardi, L.; Garavelli, M.; González, L.; Guan, Y.; Guo, M.; Hennefarth, M. R.; Hermes, M. R.; Hoyer, C. E.; Huix-Rotllant, M.; Jaiswal, V. K.; Kaiser, A.; Kaliakin, D. S.; Khamesian, M.; King, D. S.; Kochetov, V.; Krośnicki, M.; Kumaar, A. A.; Larsson, E. D.; Lehtola, S.; Lepetit, M.-B.; Lischka, H.; López Ríos, P.; Lundberg, M.; Ma, D.; Mai, S.; Marquetand, P.; Merritt, I. C. D.; Montorsi, F.; Mörchen, M.; Nenov, A.; Nguyen, V. H. A.; Nishimoto, Y.; Oakley, M. S.; Olivucci, M.; Oppel, M.; Padula, D.; Pandharkar, R.; Phung, Q. M.; Plasser, F.; Raggi, G.; Rebolini, E.; Reiher, M.; Rivalta, I.; Roca-Sanjuán, D.; Romig, T.; Safari, A. A.; Sánchez-Mansilla, A.; Sand, A. M.; Schapiro, I.; Scott, T. R.; Segarra-Martí, J.; Segatta, F.; Sergentu, D.-C.; Sharma, P.; Shepard, R.; Shu, Y.; Staab, J. K.; Straatsma, T. P.; Sørensen, L. K.; Tenorio, B. N. C.; Truhlar, D. G.; Ungur, L.; Vacher, M.; Veryazov, V.; Voß, T. A.; Weser, O.; Wu, D.; Yang, X.; Yarkony, D.; Zhou, C.; Zobel, J. P.; Lindh, R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry.*J. Chem. Theory Comput.*2023,*19*, 6933– 6991, DOI: 10.1021/acs.jctc.3c0018253https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3sXhtVert7zL&md5=9c537979f7071e510b139e143620f3aaThe OpenMolcas Web: A Community-Driven Approach to Advancing Computational ChemistryLi Manni, Giovanni; Fdez. Galvan, Ignacio; Alavi, Ali; Aleotti, Flavia; Aquilante, Francesco; Autschbach, Jochen; Avagliano, Davide; Baiardi, Alberto; Bao, Jie J.; Battaglia, Stefano; Birnoschi, Letitia; Blanco-Gonzalez, Alejandro; Bokarev, Sergey I.; Broer, Ria; Cacciari, Roberto; Calio, Paul B.; Carlson, Rebecca K.; Carvalho Couto, Rafael; Cerdan, Luis; Chibotaru, Liviu F.; Chilton, Nicholas F.; Church, Jonathan Richard; Conti, Irene; Coriani, Sonia; Cuellar-Zuquin, Juliana; Daoud, Razan E.; Dattani, Nike; Decleva, Piero; de Graaf, Coen; Delcey, Mickael G.; De Vico, Luca; Dobrautz, Werner; Dong, Sijia S.; Feng, Rulin; Ferre, Nicolas; Filatov, Michael; Gagliardi, Laura; Garavelli, Marco; Gonzalez, Leticia; Guan, Yafu; Guo, Meiyuan; Hennefarth, Matthew R.; Hermes, Matthew R.; Hoyer, Chad E.; Huix-Rotllant, Miquel; Jaiswal, Vishal Kumar; Kaiser, Andy; Kaliakin, Danil S.; Khamesian, Marjan; King, Daniel S.; Kochetov, Vladislav; Krosnicki, Marek; Kumaar, Arpit Arun; Larsson, Ernst D.; Lehtola, Susi; Lepetit, Marie-Bernadette; Lischka, Hans; Lopez Rios, Pablo; Lundberg, Marcus; Ma, Dongxia; Mai, Sebastian; Marquetand, Philipp; Merritt, Isabella C. D.; Montorsi, Francesco; Moerchen, Maximilian; Nenov, Artur; Nguyen, Vu Ha Anh; Nishimoto, Yoshio; Oakley, Meagan S.; Olivucci, Massimo; Oppel, Markus; Padula, Daniele; Pandharkar, Riddhish; Phung, Quan Manh; Plasser, Felix; Raggi, Gerardo; Rebolini, Elisa; Reiher, Markus; Rivalta, Ivan; Roca-Sanjuan, Daniel; Romig, Thies; Safari, Arta Anushirwan; Sanchez-Mansilla, Aitor; Sand, Andrew M.; Schapiro, Igor; Scott, Thais R.; Segarra-Marti, Javier; Segatta, Francesco; Sergentu, Dumitru-Claudiu; Sharma, Prachi; Shepard, Ron; Shu, Yinan; Staab, Jakob K.; Straatsma, Tjerk P.; Soerensen, Lasse Kragh; Tenorio, Bruno Nunes Cabral; Truhlar, Donald G.; Ungur, Liviu; Vacher, Morgane; Veryazov, Valera; Voss, Torben Arne; Weser, Oskar; Wu, Dihua; Yang, Xuchun; Yarkony, David; Zhou, Chen; Zobel, J. Patrick; Lindh, RolandJournal of Chemical Theory and Computation (2023), 19 (20), 6933-6991CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)A review. In this article the recent developments of the open-source OpenMolcas chem. software environment, since spring 2020, are described, with the main focus on novel functionalities that are accessible in the stable branch of the package and/or via interfaces with other packages. These community developments span a wide range of topics in computational chem., and are presented in thematic sections assocd. with electronic structure theory, electronic spectroscopy simulations, analytic gradients and mol. structure optimizations, ab initio mol. dynamics, and other new features. This report represents a useful summary of these developments, and it offers a solid overview of the chem. phenomena and processes that OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.**54**Reiher, M. Douglas–Kroll–Hess Theory: A Relativistic Electrons-Only Theory for Chemistry.*Theor. Chem. Acc.*2006,*116*(1–3), 241– 252, DOI: 10.1007/s00214-005-0003-254https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD28Xns1Sqs7Y%253D&md5=32bd8fff4b0c49e80dcd3c97af2f34f4Douglas-Kroll-Hess Theory: A relativistic electrons-only theory for chemistryReiher, MarkusTheoretical Chemistry Accounts (2006), 116 (1-3), 241-252CODEN: TCACFW; ISSN:1432-881X. (Springer GmbH)A review. A unitary transformation allows to sep. (block-diagonalize) the Dirac Hamiltonian into two parts one part: solely describes electrons, while the other gives rise to neg.-energy states, which are the so-called positronic states. The block-diagonal form of the Hamiltonian no longer accounts for the coupling of both kinds of states. The pos.-energy ('electrons-only') part can serve as a 'fully' relativistic electrons-only theory, which can be understood as a rigorous basis for chem. Recent developments of the Douglas-Kroll-Hess (DKH) method allowed to derive a sequence of expressions, which approx. this electrons-only Hamiltonian up to arbitrary-order. While all previous work focused on the numerical stability and accuracy of these arbitrary-order DKH Hamiltonians, conceptual issues and paradoxa of the method were mostly left aside. In this work, the conceptual side of DKH theory is revisited in order to identify essential aspects of the theory to be distinguished from purely computational consideration.**55**Aquilante, F.; Gagliardi, L.; Pedersen, T. B.; Lindh, R. Atomic Cholesky Decompositions: A Route to Unbiased Auxiliary Basis Sets for Density Fitting Approximation with Tunable Accuracy and Efficiency.*J. Chem. Phys.*2009,*130*(15), 154107 DOI: 10.1063/1.311678455https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD1MXkslaqsbY%253D&md5=42b21986fd7324f3540f96521dd6e62cAtomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiencyAquilante, Francesco; Gagliardi, Laura; Pedersen, Thomas Bondo; Lindh, RolandJournal of Chemical Physics (2009), 130 (15), 154107/1-154107/9CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)Cholesky decompn. of the at. two-electron integral matrix has recently been proposed as a procedure for automated generation of auxiliary basis sets for the d. fitting approxn. In order to increase computational performance while maintaining accuracy, we propose here to reduce the no. of primitive Gaussian functions of the contracted auxiliary basis functions by means of a second Cholesky decompn. Test calcns. show that this procedure is most beneficial in conjunction with highly contracted AO basis sets such as at. natural orbitals, and that the error resulting from the second decompn. is negligible. We also demonstrate theor. as well as computationally that the locality of the fitting coeffs. can be controlled by means of the decompn. threshold even with the long-ranged Coulomb metric. Cholesky decompn.-based auxiliary basis sets are thus ideally suited for local d. fitting approxns. (c) 2009 American Institute of Physics.**56**Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.; Widmark, P.-O. New Relativistic ANO Basis Sets for Transition Metal Atoms.*J. Phys. Chem. A*2005,*109*(29), 6575– 6579, DOI: 10.1021/jp058112656https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD2MXls1Ohsbo%253D&md5=b8f2a0bb7b0edaed9b6e4580224001daNew Relativistic ANO Basis Sets for Transition Metal AtomsRoos, Bjoern O.; Lindh, Roland; Malmqvist, Per-Aake; Veryazov, Valera; Widmark, Per-OlofJournal of Physical Chemistry A (2005), 109 (29), 6575-6579CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)New basis sets of the at. natural orbital (ANO) type have been developed for the first, second, and third row transition metal atoms. The ANOs have been obtained from the av. d. matrix of the ground and lowest excited states of the atom, the pos. and neg. ions, and the atom in an elec. field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calcns. of ionization energies, electron affinities, and excitation energies for all atoms and polarizabilities for spherically sym. atoms. These calcns. include spin-orbit coupling using a variation-perturbation approach. Computed ionization energies have an accuracy better than 0.2 eV in most cases. The accuracy of computed electron affinities is the same except in cases where the exptl. values are smaller than 0.5 eV. Accurate results are obtained for the polarizabilities of atoms with spherical symmetry. Multiplet levels are presented for some of the third row transition metals.**57**Roos, B. O.; Lindh, R.; Malmqvist, P.-Å.; Veryazov, V.; Widmark, P.-O. Main Group Atoms and Dimers Studied with a New Relativistic ANO Basis Set.*J. Phys. Chem. A*2004,*108*(15), 2851– 2858, DOI: 10.1021/jp031064+57https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3sXpvFGksLs%253D&md5=0376f88ebbc6bd69daee46c198d463eeMain Group Atoms and Dimers Studied with a New Relativistic ANO Basis SetRoos, Bjoern O.; Lindh, Roland; Malmqvist, Per-Aake; Veryazov, Valera; Widmark, Per-OlofJournal of Physical Chemistry A (2004), 108 (15), 2851-2858CODEN: JPCAFH; ISSN:1089-5639. (American Chemical Society)New basis sets of the at. natural orbital (ANO) type have been developed for the main group and rare gas atoms. The ANO's have been obtained from the av. d. matrix of the ground and lowest excited states of the atom, the pos. and neg. ions, and the dimer at its equil. geometry. Scalar relativistic effects are included through the use of a Douglas-Kroll Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calcns. of ionization energies, electron affinities, and excitation energies for all atoms and the ground-state potentials for the dimers. These calcns. include spin-orbit coupling using the RASSCF State Interaction (RASSI-SO) method. The spin-orbit splitting for the lowest at. term is reproduced with an accuracy of better than 0.05 eV, except for row 5, where it is 0.15 eV. Ionization energies and electron affinities have an accuracy better than 0.2 eV, and at. polarizabilities for the spherical atoms are computed with errors smaller than 2.5%. Computed bond energies for the dimers are accurate to better than 0.15 eV in most cases (the dimers for row 5 excluded).**58**angmom_suite. https://gitlab.com/chilton-group/angmom_suite (accessed Aug 21, 2023).There is no corresponding record for this reference.**59**Kragskow, J. G. C.; Marbey, J.; Buch, C. D.; Nehrkorn, J.; Ozerov, M.; Piligkos, S.; Hill, S.; Chilton, N. F. Analysis of Vibronic Coupling in a 4f Molecular Magnet with FIRMS.*Nat. Commun.*2022,*13*(1), 825 DOI: 10.1038/s41467-022-28352-259https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XjsVGrtr8%253D&md5=dbe8805fe522125b8c05fa3420cac0cdAnalysis of vibronic coupling in a 4f molecular magnet with FIRMSKragskow, Jon G. C.; Marbey, Jonathan; Buch, Christian D.; Nehrkorn, Joscha; Ozerov, Mykhaylo; Piligkos, Stergios; Hill, Stephen; Chilton, Nicholas F.Nature Communications (2022), 13 (1), 825CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)Vibronic coupling, the interaction between mol. vibrations and electronic states, is a fundamental effect that profoundly affects chem. processes. In the case of mol. magnetic materials, vibronic, or spin-phonon, coupling leads to magnetic relaxation, which equates to loss of magnetic memory and loss of phase coherence in mol. magnets and qubits, resp. The study of vibronic coupling is challenging, and most exptl. evidence is indirect. Here we employ far-IR magnetospectroscopy to directly probe vibronic transitions in [Yb(trensal)] (where H3trensal = 2,2,2-tris(salicylideneimino)trimethylamine). We find intense signals near electronic states, which we show arise due to an ''envelope effect'' in the vibronic coupling Hamiltonian, which we calc. fully ab initio to simulate the spectra. We subsequently show that vibronic coupling is strongest for vibrational modes that simultaneously distort the first coordination sphere and break the C3 symmetry of the mol. With this knowledge, vibrational modes could be identified and engineered to shift their energy towards or away from particular electronic states to alter their impact. Hence, these findings provide new insights towards developing general guidelines for the control of vibronic coupling in mols.**60**Staab, J. K.; Chilton, N. F. Analytic Linear Vibronic Coupling Method for First-Principles Spin-Dynamics Calculations in Single-Molecule Magnets.*J. Chem. Theory Comput.*2022,*18*(11), 6588– 6599, DOI: 10.1021/acs.jctc.2c0061160https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38Xis1Ohur3J&md5=e423b88538384f7e0384d827cee433dcAnalytic Linear Vibronic Coupling Method for First-Principles Spin-Dynamics Calculations in Single-Molecule MagnetsStaab, Jakob K.; Chilton, Nicholas F.Journal of Chemical Theory and Computation (2022), 18 (11), 6588-6599CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)Accurate modeling of vibronically driven magnetic relaxation from ab initio calcns. is of paramount importance to the design of next-generation single-mol. magnets (SMMs). Previous theor. studies have been relying on numerical differentiation to obtain spin-phonon couplings in the form of derivs. of spin Hamiltonian parameters. In this work, we introduce a novel approach to obtain these derivs. fully anal. by combining the linear vibronic coupling (LVC) approach with analytic complete active space SCF derivs. and nonadiabatic couplings computed at the equil. geometry with a single electronic structure calcn. We apply our analytic approach to the computation of Orbach and Raman relaxation rates for a bis-cyclobutadienyl Dy(III) sandwich complex in the frozen-soln. phase, where the soln. environment is modeled by electrostatic multipole expansions, and benchmark our findings against results obtained using conventional numerical derivs. and a fully electronic description of the whole system. We demonstrate that our LVC approach exhibits high accuracy over a wide range of coupling strengths and enables significant computational savings due to its analytic, "single-shot" nature. Evidently, this offers great potential for advancing the simulation of a wide range of vibronic coupling phenomena in magnetism and spectroscopy, ultimately aiding the design of high-performance SMMs. Considering different environmental representations, we find that a point charge model shows the best agreement with the ref. calcn., including the full electronic environment, but note that the main source of discrepancies obsd. in the magnetic relaxation rates originates from the approx. equil. electronic structure computed using the electrostatic environment models rather than from the couplings.**61**tau. https://gitlab.com/chilton-group/tau (accessed Aug 21, 2023).There is no corresponding record for this reference.**62**Shrivastava, K. N. Theory of Spin–Lattice Relaxation.*Phys. Status Solidi B*1983,*117*(2), 437– 458, DOI: 10.1002/pssb.222117020262https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaL3sXktFGisrY%253D&md5=9f186f6be6ed2a4dfb360fcdfcb952d5Theory of spin-lattice relaxationShrivastava, K. N.Physica Status Solidi B: Basic Research (1983), 117 (2), 437-58CODEN: PSSBBD; ISSN:0370-1972.A review with 46 refs. Topics include: the spin-lattice interaction, the direct process, the Raman process, the sum process, the Orbach process, the 3-phonon process, the local mode process, and the collision process.**63**Ho, L. T. A.; Chibotaru, L. F. Spin-Lattice Relaxation of Magnetic Centers in Molecular Crystals at Low Temperature.*Phys. Rev. B*2018,*97*(2), 024427 DOI: 10.1103/PhysRevB.97.02442763https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXltVCqu7g%253D&md5=0a3742a91ac20c5e5e7304e842f8a44aSpin-lattice relaxation of magnetic centers in molecular crystals at low temperatureHo, Le Tuan Anh; Chibotaru, Liviu F.Physical Review B (2018), 97 (2), 024427CODEN: PRBHB7; ISSN:2469-9969. (American Physical Society)We study the spin-phonon relaxation rate of both Kramers and non-Kramers mol. magnets in strongly dild. samples at low temp. Using the "rotational" contribution to the spin-phonon Hamiltonian, universal formulas for the relaxation rate are obtained. Intriguingly, these formulas are all entirely expressed via measurable or ab initio computable phys. quantities. Moreover, they are also independent of the energy gaps to excited states involved in the relaxation process. These obtained expressions for direct and Raman processes offer an easy way to det. the lowest limit of the spin-phonon relaxation of any spin system based on magnetic properties of the ground doublet only. In addn., some intriguing properties of Raman process are also found. Particularly, Raman process in Kramers system is found dependent on the magnetic field's orientation but independent of its magnitude, meanwhile, the same process in non-Kramers system is significantly reduced out of resonance, i.e., for an applied external field. Interestingly, Raman process is demonstrated to vary as T9 for both systems. Application of the theory to a recently investigated cobalt(II) complex shows that it can provide a reasonably good description for the relaxation. Based on these findings, a strategy in developing efficient single-mol. magnets by enhancing the mech. rigidity of the mol. unit is proposed.**64**Dove, M. T.*Introduction to Lattice Dynamics*; Cambridge topics in mineral physics and chemistry; Cambridge University Press: Cambridge ; New York, 1993.There is no corresponding record for this reference.**65**Evans, P.; Reta, D.; Whitehead, G. F. S.; Chilton, N. F.; Mills, D. P. Bis-Monophospholyl Dysprosium Cation Showing Magnetic Hysteresis at 48 K.*J. Am. Chem. Soc.*2019,*141*(50), 19935– 19940, DOI: 10.1021/jacs.9b1151565https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXit1SnsbzL&md5=bdae8e6b829adb3cb921ae07805875c4Bis-Monophospholyl Dysprosium Cation Showing Magnetic Hysteresis at 48 KEvans, Peter; Reta, Daniel; Whitehead, George F. S.; Chilton, Nicholas F.; Mills, David P.Journal of the American Chemical Society (2019), 141 (50), 19935-19940CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)Single-mol. magnets (SMMs) have potential applications in high-d. data storage, but magnetic relaxation times at elevated temps. must be increased to make them practically useful. Bis-cyclopentadienyl lanthanide sandwich complexes have emerged as the leading candidates for SMMs that show magnetic memory at liq. nitrogen temps., but the relaxation mechanisms mediated by arom. C5 rings have not been fully established. Here we synthesize a bis-monophospholyl dysprosium SMM [Dy(Dtp)2][Al{OC(CF3)3}4] (1, Dtp = {P(CtBuCMe)2}) by the treatment of in situ-prepd. "[Dy(Dtp)2(C3H5)]" with [HNEt3][Al{OC(CF3)3}4]. SQUID magnetometry reveals that 1 has an effective barrier to magnetization reversal of 1,760 K (1,223 cm-1) and magnetic hysteresis up to 48 K. Ab initio calcn. of the spin dynamics reveal that transitions out of the ground state are slower in 1 than in the first reported dysprosocenium SMM, [Dy(Cpttt)2][B(C6F5)4] (Cpttt = C5H2tBu3-1,2,4), however relaxation is faster in 1 overall due to the compression of electronic energies and to vibrational modes being brought on-resonance by the chem. and structural changes introduced by the bis-Dtp framework. With the prepn. and anal. of 1 we are thus able to further refine our understanding of relaxation processes operating in bis-C5/C4P sandwich lanthanide SMMs, which is the necessary first step towards rationally achieving higher magnetic blocking temps. in these systems in future.**66**Smith, E. R.; Rowlinson, J. S. Electrostatic Energy in Ionic Crystals.*Proc. R. Soc. London, Ser. A*1997,*375*(1763), 475– 505, DOI: 10.1098/rspa.1981.0064There is no corresponding record for this reference.**67**Ewald, P. P. Die Berechnung Optischer Und Elektrostatischer Gitterpotentiale.*Ann. Phys.*1921,*369*(3), 253– 287, DOI: 10.1002/andp.19213690304There is no corresponding record for this reference.**68**Derenzo, S. E.; Klintenberg, M. K.; Weber, M. J. Determining Point Charge Arrays That Produce Accurate Ionic Crystal Fields for Atomic Cluster Calculations.*J. Chem. Phys.*2000,*112*(5), 2074– 2081, DOI: 10.1063/1.48077668https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BD3cXnsFWqtg%253D%253D&md5=7892892b36bc1eb18234d1c5780ee01cDetermining point charge arrays that produce accurate ionic crystal fields for atomic cluster calculationsDerenzo, Stephen E.; Klintenberg, Mattias K.; Weber, Marvin J.Journal of Chemical Physics (2000), 112 (5), 2074-2081CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)In performing at. cluster calcns. of local electronic structure defects in ionic crystals, the crystal is often modeled as a central cluster of 5-50 ions embedded in an array of point charges. For most crystals, however, a finite three-dimensional repeated array of unit cells generates electrostatic potentials that are in significant disagreement with the Madelung (infinite crystal) potentials computed by the Ewald method. This is illustrated for the cubic crystal CaF2. We present a novel algorithm for solving this problem for any crystal whose unit cell information is known: (1) the unit cell is used to generate a neutral array contg. typically 10 000 point charges at their normal crystallog. positions; (2) the array is divided into zone 1 (a vol. defined by the at. cluster of interest), zone 2 (several hundred addnl. point charges that together with zone 1 fill a spherical vol.), and zone 3 (all other point charges); (3) the Ewald formula is used to compute the site potentials at all point charges in zones 1 and 2; (4) a system of simultaneous linear equations is solved to find the zone 3 charge values that make the zone 1 and zone 2 site potentials exactly equal to their Ewald values and the total charge and dipole moments equal to zero, and (5) the soln. is checked at 1000 addnl. points randomly chosen in zone 1. The method is applied to 33 different crystal types with 50-71 ions in zone 1. In all cases the accuracy detd. in step 5 steadily improves as the sizes of zones 2 and 3 are increased, reaching a typical rms error of 1 μV in zone 1 for 500 point charges in zone 2 and 10 000 in zone 3.**69**Rivera, M.; Dommett, M.; Crespo-Otero, R. ONIOM(QM:QM′) Electrostatic Embedding Schemes for Photochemistry in Molecular Crystals.*J. Chem. Theory Comput.*2019,*15*(4), 2504– 2516, DOI: 10.1021/acs.jctc.8b0118069https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXkslaitrk%253D&md5=46534739fc9ceab577f97a0f4e4580dbONIOM(QM:QM') electrostatic embedding schemes for photochemistry in molecular crystalsRivera, Miguel; Dommett, Michael; Crespo-Otero, RachelJournal of Chemical Theory and Computation (2019), 15 (4), 2504-2516CODEN: JCTCCE; ISSN:1549-9618. (American Chemical Society)Understanding photoinduced processes in mol. crystals is central to the design of highly emissive materials such as org. lasers and org. light-emitting diodes. The modeling of such processes is, however, hindered by the lack of excited state methodologies tailored for these systems. Embedding approaches based on the Ewald sum can be used in conjunction with excited state electronic structure methods to model the localized excitations which characterize these materials. In this article, we describe the implementation of a two-level ONIOM(QM:QM') point charge embedding approach based on the Ewald method, the ONIOM Ewald embedded cluster (OEEC) model. An alternative self-consistent method is also considered to simulate the response of the environment to the excitation. Two mol. crystals with opposing photochem. behavior were used to benchmark the results with single ref. and multireference methods. We obsd. that the inclusion of an explicit ground state cluster surrounding the QM region was imperative for the exploration of the excited state potential energy surfaces. Using OEEC, accurate absorption and emission energies as well as S1-S0 conical intersections were obtained for both crystals. We discuss the implications of the use of these embedding schemes considering the degree of localization of the excitation. The methods discussed herein are implemented in an open source platform (fromage, https://github.com/Crespo-Otero-group/fromage) which acts as an interface between popular electronic structure codes (Gaussian, Turbomole, and Molcas).**70**Fraser, L. M.; Foulkes, W. M. C.; Rajagopal, G.; Needs, R. J.; Kenny, S. D.; Williamson, A. J. Finite-Size Effects and Coulomb Interactions in Quantum Monte Carlo Calculations for Homogeneous Systems with Periodic Boundary Conditions.*Phys. Rev. B*1996,*53*(4), 1814– 1832, DOI: 10.1103/PhysRevB.53.181470https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK28XptV2jsw%253D%253D&md5=8766705cf1df20e8f6a3bed60aa04bcdFinite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditionsFraser, Louisa M.; Foulkes, W. M. C.; Rajagopal, G.; Needs, R. J.; Kenny, S. D.; Williamson, A. J.Physical Review B: Condensed Matter (1996), 53 (4), 1814-32CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)Quantum Monte Carlo (QMC) calcns. are only possible in finite systems and so solids and liqs. must be modeled using small simulation cells subject to periodic boundary conditions. The resulting finite-size errors are often cor. using data from the local-d. functional or Hartree-Fock calcns., but systematic errors remain after these corrections have been applied. The results of the authors' jellium QMC calcns. for simulation cells contg. more than 600 electrons conform that the residual errors are significant and decay very slowly as the system size increases. They are sensitive to the form of the model Coulomb interaction used in the simulation cell Hamiltonian; the usual choice, exemplified by the Ewald summation technique, is not the best. The finite-size errors can be greatly reduced and the speed of the calcns. increased by a factor of 20 if a better choice is made. Finite-size effects plague most methods used for extended Coulomb systems and many of the ideas in this paper are quite general: they may be applied to any type of quantum or classical Monte Carlo simulation, to other many-body approaches such as the GW method, and to Hartree-Fock and d.-functional calcns.**71**Reta, D.; Chilton, N. F. Uncertainty Estimates for Magnetic Relaxation Times and Magnetic Relaxation Parameters.*Phys. Chem. Chem. Phys.*2019,*21*(42), 23567– 23575, DOI: 10.1039/C9CP04301B71https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhvFejtr7O&md5=b1f3f307c9cdba48e3249004efae1bcdUncertainty estimates for magnetic relaxation times and magnetic relaxation parametersReta, Daniel; Chilton, Nicholas F.Physical Chemistry Chemical Physics (2019), 21 (42), 23567-23575CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)The use of a.c. (AC) magnetometry to measure magnetic relaxation times is one of the most fundamental measurements for characterizing single-mol. magnets (SMMs). These measurements, performed as a function of frequency, temp. and magnetic field, give vital information on the underlying magnetic relaxation process(es) occurring in the material. The magnetic relaxation times are usually fitted to model functions derived from spin-phonon coupling theories that allow characterization of the mechanisms of magnetic relaxation. The parameters of these relaxation models are then often compared between different mols. in order to find trends with mol. structure that may guide the field to the next breakthrough. However, such meta-analyses of the model parameters are doomed to over-interpretation unless uncertainties in the model parameters can be quantified. Here we det. a method for obtaining uncertainty ests. in magnetic relaxation times from AC expts., and provide a program called CC-FIT2 for fitting exptl. AC data as well as the resulting relaxation times, to obtain relaxation parameters with accurate uncertainties. Applying our approach to three archetypal families of high-performance dysprosium(III) SMMs shows that accounting for uncertainties has a significant impact on the uncertainties of relaxation parameters, and that larger uncertainties appear to correlate with crystallog. disorder in the compds. studied. We suggest that this type of anal. should become routine in the community.

## Supporting Information

## Supporting Information

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.3c06015.

Convergence testing, optimized unit cell parameters,

*ab initio*calculated line widths, DoS plots, magnetic relaxation rates under different approximations, and contributions to Raman relaxation (PDF)

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