How to calculate the rate constants for nonradiative transitions between the
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            components of spin multiplets?

Rooein, Mitra; Varganov, Sergey A.

doi:10.1080/00268976.2022.2116364

Cited by 4 publications

(5 citation statements)

References 42 publications

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“…Due to the spin–orbit selection rule | M S – M S′ | = 0, 1, each row contains only three non-zero SOCMEs: two complex and one imaginary. As the spin multiplicities of the crossing states increase, the size of the Hamiltonian matrix also increases; however, there are always only three diagonals with non-zero SOCMEs …”

Section: Nonadiabatic Statistical Theorymentioning

confidence: 99%

“…As the spin multiplicities of the crossing states increase, the size of the Hamiltonian matrix also increases; however, there are always only three diagonals with non-zero SOCMEs. 31 There are three approaches for obtaining the SOC constants for calculating the transition probabilities (eq 1 and 2) from the individual SOCMEs (Table 1). 1,31 In the M S -specific approach, each SOCME is treated as a separate coupling constant, which allows calculations of the transition probabilities and rates between each pair of the M S components of the states with the different quantum numbers S. In the intermediate approach, the spin−orbit coupling constants SOC |±Md S | are calculated for each M S component of the low-spin state as a root-mean-square of the SOCMEs between this component and all M S components of the high-spin state.…”

Section: ■ Nonadiabatic Statistical Theorymentioning

confidence: 99%

“…31 There are three approaches for obtaining the SOC constants for calculating the transition probabilities (eq 1 and 2) from the individual SOCMEs (Table 1). 1,31 In the M S -specific approach, each SOCME is treated as a separate coupling constant, which allows calculations of the transition probabilities and rates between each pair of the M S components of the states with the different quantum numbers S. In the intermediate approach, the spin−orbit coupling constants SOC |±Md S | are calculated for each M S component of the low-spin state as a root-mean-square of the SOCMEs between this component and all M S components of the high-spin state. Here, the low-and high-spin states are defined based on the value of the spin quantum number S. The SOC |±Md S | values are equal to half of the energy gaps between a pair of the spin-adiabatic states obtained by diagonalizing the spin-diabatic Hamiltonian, assuming the linear dependence of spin-diabatic energies on a reaction coordinate.…”

Section: ■ Nonadiabatic Statistical Theorymentioning

confidence: 99%

“…Here, the low-and high-spin states are defined based on the value of the spin quantum number S. The SOC |±Md S | values are equal to half of the energy gaps between a pair of the spin-adiabatic states obtained by diagonalizing the spin-diabatic Hamiltonian, assuming the linear dependence of spin-diabatic energies on a reaction coordinate. 31 In the third approach, the effective spin−orbit coupling constant SOC eff is calculated as the root-mean-square of all SOCMEs. This is the simplest, and arguably the most common way to calculate the SOC constant between electronic states of different spin multiplicities.…”

Section: ■ Nonadiabatic Statistical Theorymentioning

confidence: 99%

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Predicting Kinetics and Dynamics of Spin-Dependent Processes

Dergachev

Rooein

et al. 2023

Acc. Chem. Res.

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Metrics & MoreArticle Recommendations CONSPECTUS: Predicting mechanisms and rates of nonadiabatic spin-dependent processes including photoinduced intersystem crossings, thermally activated spin-forbidden reactions, and spin crossovers in metal centers is a very active field of research. These processes play critical roles in transition-metal-based and metalloenzymatic catalysis, molecular magnets, lightharvesting materials, organic light-emitting diodes, photosensitizers for photodynamic therapy, and many other applications. Therefore, accurate modeling of spin-dependent processes in complex systems and on different time scales is important for many problems in chemistry, biochemistry, and materials sciences. Nonadiabatic statistical theory (NAST) and nonadiabatic molecular dynamics (NAMD) are two complementary approaches to modeling the kinetics and dynamics of spin-dependent processes. NAST predicts the probabilities and rate constants of nonradiative transitions between electronic states with different spin multiplicities using molecular properties at only few critical points on the potential energy surfaces (PESs), including the reactant minimum and the minimum energy crossing point (MECP) between two spin states. This makes it possible to obtain molecular properties for NAST calculations using accurate but often computationally expensive electronic structure methods, which is critical for predicting the rate constants of spin-dependent processes. Alternatively, NAST can be used to study spindependent processes in very large complex molecular systems using less computationally expensive electronic structure methods.The nuclear quantum effects, such as zero-point vibrational energy, tunneling, and interference between reaction paths can be easily incorporated. However, the statistical and local nature of NAST makes it more suitable for large systems and slow kinetics. In contrast, NAMD explores entire PESs of interacting electronic states, making it ideal for modeling fast barrierless spin-dependent processes. Because the knowledge of large portions of PESs is often needed, the simulations require a very large number of electronic structure calculations, which limits the NAMD applicability to relatively small molecular systems and ultrafast kinetics.In this Account, we discuss our contribution to the development of the NAST and NAMD approaches for predicting the rates and mechanism of spin-dependent processes. First, we briefly describe our NAST and NAMD implementations. The NAST implementation is an extension of the transition state theory to the processes involving two crossing potential energy surfaces of different spin multiplicities. The NAMD approach includes the trajectory surface hopping (TSH) and ab initio multiple spawning (AIMS) methods. Second, we discuss several applications of NAST and NAMD to model spin-dependent processes in different systems. The NAST applicability to large complex systems is demonstrated by the studies of the spin-forbidden isomerization of the active sites of metal−sulfur pr...

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Section: Nonadiabatic Statistical Theorymentioning

confidence: 99%

Section: ■ Nonadiabatic Statistical Theorymentioning

confidence: 99%

Section: ■ Nonadiabatic Statistical Theorymentioning

confidence: 99%

Section: ■ Nonadiabatic Statistical Theorymentioning

confidence: 99%

See 2 more Smart Citations

Predicting Kinetics and Dynamics of Spin-Dependent Processes

Dergachev

Rooein

et al. 2023

Acc. Chem. Res.

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“…Recent studies have suggested a correlation between the value of SOC and the energy difference between the two

orbitals for complexes involving O

[ 43 ]. On top of the importance of the SOC value, according to the Landau-Zenner equation [ 39 , 44 ], the hopping probability also depends on the reduced mass associated with the vibrational coordinate parallel to the crossing seam, and the difference of the gradient between the two PESs involved [ 45 ].…”

Section: Introductionmentioning

confidence: 99%

Spin-Forbidden Addition of Molecular Oxygen to Stable Enol Intermediates—Decarboxylation of 2-Methyl-1-tetralone-2-carboxylic Acid

Ortega

Gil‐Guerrero

González-Sánchez

et al. 2023

IJMS

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The deprotonation of an organic substrate is a common preactivation step for the enzymatic cofactorless addition of O2 to this substrate, as it promotes charge-transfer between the two partners, inducing intersystem crossing between the triplet and singlet states involved in the process. Nevertheless, the spin-forbidden addition of O2 to uncharged ligands has also been observed in the laboratory, and the detailed mechanism of how the system circumvents the spin-forbiddenness of the reaction is still unknown. One of these examples is the cofactorless peroxidation of 2-methyl-3,4-dihydro-1-naphthol, which will be studied computationally using single and multi-reference electronic structure calculations. Our results show that the preferred mechanism is that in which O2 picks a proton from the substrate in the triplet state, and subsequently hops to the singlet state in which the product is stable. For this reaction, the formation of the radical pair is associated with a higher barrier than that associated with the intersystem crossing, even though the absence of the negative charge leads to relatively small values of the spin-orbit coupling.

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Analytical nonadiabatic coupling and state-specific energy gradient for the crystal field Hamiltonian describing lanthanide single-ion magnets

Dergachev,

Nakritskaia,

Alexeev

et al. 2023

The Journal of Chemical Physics

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Paramagnetic molecules with a metal ion as an electron spin center are promising building blocks for molecular qubits and high-density memory arrays. However, fast spin relaxation and decoherence in these molecules lead to a rapid loss of magnetization and quantum information. Nonadiabatic coupling (NAC), closely related to spin-vibrational coupling, is the main source of spin relaxation and decoherence in paramagnetic molecules at higher temperatures. Predicting these couplings using numerical differentiation requires a large number of computationally intensive ab initio or crystal field electronic structure calculations. To reduce computational cost and improve accuracy, we derive and implement analytical NAC and state-specific energy gradient for the ab initio parametrized crystal field Hamiltonian describing single-ion molecular magnets. Our implementation requires only a single crystal field calculation. In addition, the accurate NACs and state-specific energy gradients can be used to model spin relaxation using sophisticated nonadiabatic molecular dynamics, which avoids the harmonic approximation for molecular vibrations. To test our implementation, we calculate the NAC values for three lanthanide complexes. The predicted values support the relaxation mechanisms reported in previous studies.

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How to calculate the rate constants for nonradiative transitions between the M _S components of spin multiplets?

Cited by 4 publications

References 42 publications

Predicting Kinetics and Dynamics of Spin-Dependent Processes

Predicting Kinetics and Dynamics of Spin-Dependent Processes

Spin-Forbidden Addition of Molecular Oxygen to Stable Enol Intermediates—Decarboxylation of 2-Methyl-1-tetralone-2-carboxylic Acid

Analytical nonadiabatic coupling and state-specific energy gradient for the crystal field Hamiltonian describing lanthanide single-ion magnets

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How to calculate the rate constants for nonradiative transitions between the M S components of spin multiplets?

Cited by 4 publications

References 42 publications

Predicting Kinetics and Dynamics of Spin-Dependent Processes

Predicting Kinetics and Dynamics of Spin-Dependent Processes

Spin-Forbidden Addition of Molecular Oxygen to Stable Enol Intermediates—Decarboxylation of 2-Methyl-1-tetralone-2-carboxylic Acid

Analytical nonadiabatic coupling and state-specific energy gradient for the crystal field Hamiltonian describing lanthanide single-ion magnets

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How to calculate the rate constants for nonradiative transitions between the M _S components of spin multiplets?