A Diabatic Representation Including Both Valence Nonadiabatic Interactions and Spin−Orbit Effects for Reaction Dynamics

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

Direct coherent switching with decay of mixing for intersystem crossing dynamics of thioformaldehyde: The effect of decoherence

We evaluate the effect of electronic decoherence on intersystem crossing in the photodynamics of thioformaldehyde. First, we show that the state-averaged complete-active-space self-consistent field electronic structure calculations with a properly chosen active space of 12 active electrons in 10 active orbitals can predict the potential energy surfaces and the singlet-triplet spin-orbit couplings quite well for CH₂S, and we use this method for direct dynamics by coherent switching with decay of mixing (CSDM). We obtain similar dynamical results with CSDM or by adding energy-based decoherence to trajectory surface hopping, with the population of triplet states tending to a small steady-state value over 500 fs. Without decoherence, the state populations calculated by the conventional trajectory surface hopping method or the semiclassical Ehrenfest method gradually increase. This difference shows that decoherence changes the nature of the results not just quantitatively but qualitatively.

Internal Conversion and Intersystem Crossing with the Exact Factorization

We present a detailed derivation of the generalized coupled-trajectory mixed quantum-classical (G-CT-MQC) algorithm based on the exact-factorization equations. The ultimate goal is to propose an algorithm that can be employed for molecular dynamics simulations of nonradiative phenomena, as the spin-allowed internal conversions and the spin-forbidden intersystem crossings. Internal conversions are nonadiabatic processes driven by the kinetic coupling between electronic states, whereas intersystem crossings are mediated by the spin-orbit coupling. In this paper, we discuss computational issues related to the suitable representation for electronic dynamics and the different natures of kinetic and spin-orbit coupling. Numerical studies on model systems allow us to test the performance of the G-CT-MQC algorithm in different situations.

Spin-Orbit Interactions in Ultrafast Molecular Processes

We investigate spin-orbit interactions in ultrafast molecular processes employing the exact factorization of the electron-nuclear wave function. We revisit the original derivation by including spin-orbit coupling, and show how the dynamics driven by the time-dependent potential energy surface alleviates inconsistencies arising from different electronic representations. We propose a novel trajectory-based scheme to simulate spin-forbidden non-radiative processes, and we show its performance in the treatment of excited-state dynamics where spin-orbit effects couple different spin multiplets.

Automated reaction path searches for spin-forbidden reactions

Many catalytic and biomolecular reactions containing transition metals involve changes in the electronic spin state. These processes are referred to as "spin-forbidden" reactions within nonrelativistic quantum mechanics framework. To understand detailed reaction mechanisms of spin-forbidden reactions, one must characterize reaction pathways on potential energy surfaces with different spin states and then identify crossing points. Here we propose a practical computational scheme, where only the lowest mixed-spin eigenstate obtained from the diagonalization of the spin-coupled Hamiltonian matrix is used in reaction path search calculations. We applied this method to the ^6,4 FeO⁺  + H₂ → ^6,4 Fe⁺  + H₂ O, ^6,4 FeO⁺  + CH₄ → ^6,4 Fe⁺  + CH₃ OH, and ⁷ Mn⁺  + OCS → ⁵ MnS⁺  + CO reactions, for which crossings between the different spin states are known to play essential roles in the overall reaction kinetics. © 2018 Wiley Periodicals, Inc.

Spin crossover dynamics studies on the thermally activated molecular oxygen binding mechanism on a model copper complex

The theoretical description of the primary dioxygen (O₂) binding and activation step in many copper or iron enzymes, suffers from the instrinsically electronic non-adiabaticity of the spin flip events of the triplet dioxygen molecule (³O₂), mediated by spin–orbit couplings.

Comment on "Fe2: As simple as a Herculean labour. Neutral (Fe2), cationic (Fe2(+)), and anionic (Fe2(-)) species" [J. Chem. Phys. 142, 244304 (2015)]

A recent paper on Fe2 [A. Kalemos, J. Chem. Phys. 142, 244304 (2015)] critiqued our previous work on the system [Hoyer et al., J. Chem. Phys. 141, 204309 (2014)]. In this comment, we explain the nature of our previously reported potential energy curve for Fe2 and we discuss our computed properties for Fe2. Additionally, we fix a labeling error that was present in our previous work, although this error is unrelated to the main point of discussion.

Internal conversion and intersystem crossing in α,β-enones: a combination of electronic structure calculations and dynamics simulations

The geometrical constraint of the ring gives rise to a smaller spin–orbital coupling in the singlet–triplet crossing region, resulting in a lower intersystem crossing rate.

Generalized trajectory surface-hopping method for internal conversion and intersystem crossing

Trajectory-based fewest-switches surface-hopping (FSSH) dynamics simulations have become a popular and reliable theoretical tool to simulate nonadiabatic photophysical and photochemical processes. Most available FSSH methods model internal conversion. We present a generalized trajectory surface-hopping (GTSH) method for simulating both internal conversion and intersystem crossing processes on an equal footing. We consider hops between adiabatic eigenstates of the non-relativistic electronic Hamiltonian (pure spin states), which is appropriate for sufficiently small spin-orbit coupling. This choice allows us to make maximum use of existing electronic structure programs and to minimize the changes to available implementations of the traditional FSSH method. The GTSH method is formulated within the quantum mechanics (QM)/molecular mechanics framework, but can of course also be applied at the pure QM level. The algorithm implemented in the GTSH code is specified step by step. As an initial GTSH application, we report simulations of the nonadiabatic processes in the lowest four electronic states (S0, S1, T1, and T2) of acrolein both in vacuo and in acetonitrile solution, in which the acrolein molecule is treated at the ab initio complete-active-space self-consistent-field level. These dynamics simulations provide detailed mechanistic insight by identifying and characterizing two nonadiabatic routes to the lowest triplet state, namely, direct S1 → T1 hopping as major pathway and sequential S1 → T2 → T1 hopping as minor pathway, with the T2 state acting as a relay state. They illustrate the potential of the GTSH approach to explore photoinduced processes in complex systems, in which intersystem crossing plays an important role.

Toward spin-orbit coupled diabatic potential energy surfaces for methyl iodide using effective relativistic coupling by asymptotic representation

The theoretical treatment of state-state interactions and the development of coupled multidimensional potential energy surfaces (PESs) is of fundamental importance for the theoretical investigation of nonadiabatic processes. Usually, only derivative or vibronic coupling is considered, but the presence of heavy atoms in a system can render spin-orbit (SO) coupling important as well. In the present study, we apply a new method recently developed by us (J. Chem. Phys. 2012, 136, 034103, and J. Chem. Phys. 2012, 137, 064101) to generate SO coupled diabatic PESs along the C-I dissociation coordinate for methyl iodide (CH3I). This is the first and mandatory step toward the development of fully coupled full-dimensional PESs to describe the multistate photodynamics of this benchmark system. The method we use here is based on the diabatic asymptotic representation of the molecular fine structure states and an effective relativistic coupling operator. It therefore is called effective relativistic coupling by asymptotic representation (ERCAR). This approach allows the efficient and accurate generation of fully coupled PESs including derivative and SO coupling based on high-level ab initio calculations. In this study we develop a specific ERCAR model for CH3I that so far accounts only for the C-I bond cleavage. Details of the diabatization and the accuracy of the results are investigated in comparison to reference ab initio calculations and experiments. The energies of the adiabatic fine structure states are reproduced in excellent agreement with ab initio SO-CI data. The model is also compared to available literature data, and its performance is evaluated critically. This shows that the new method is very promising for the construction of fully coupled full-dimensional PESs for CH3I to be used in future quantum dynamics studies.

Perspective on Diabatic Models of Chemical Reactivity as Illustrated by the Gas-Phase S(N)2 Reaction of Acetate Ion with 1,2-Dichloroethane

Diabatic models are widely employed for studying chemical reactivity in condensed phases and enzymes, but there has been little discussion of the pros and cons of various diabatic representations for this purpose. Here we discuss and contrast six different schemes for computing diabatic potentials for a charge rearrangement reaction. They include (i) the variational diabatic configurations (VDC) constructed by variationally optimizing individual valence bond structures and (ii) the consistent diabatic configurations (CDC) obtained by variationally optimizing the ground-state adiabatic energy, both in the nonorthogonal molecular orbital valence bond (MOVB) method, along with the orthogonalized (iii) VDC-MOVB and (iv) CDC-MOVB models. In addition, we consider (v) the fourfold way (based on diabatic molecular orbitals and configuration uniformity), and (vi) empirical valence bond (EVB) theory. To make the considerations concrete, we calculate diabatic electronic states and diabatic potential energies along the reaction path that connects the reactant and the product ion-molecule complexes of the gas-phase bimolecular nucleophilic substitution (S(N)2) reaction of 1,2-dichloethane (DCE) with acetate ion, which is a model reaction corresponding to the reaction catalyzed by haloalkane dehalogenase. We utilize ab initio block-localized molecular orbital theory to construct the MOVB diabatic states and ab initio multi-configuration quasidegenerate perturbation theory to construct the fourfold-way diabatic states; the latter are calculated at reaction path geometries obtained with the M06-2X density functional. The EVB diabatic states are computed with parameters taken from the literature. The MOVB and fourfold-way adiabatic and diabatic potential energy profiles along the reaction path are in qualitative but not quantitative agreement with each other. In order to validate that these wave-function-based diabatic states are qualitatively correct, we show that the reaction energy and barrier for the adiabatic ground state, obtained with these methods, agree reasonably well with the results of high-level calculations using the composite G3SX and G3SX(MP3) methods and the BMC-CCSD multi-coefficient correlation method. However, a comparison of the EVB gas-phase adiabatic ground-state reaction path with those obtained from MOVB and with the fourfold way reveals that the EVB reaction path geometries show a systematic shift towards the products region, and that the EVB lowest-energy path has a much lower barrier. The free energies of solvation and activation energy in water reported from dynamical calculations based on EVB also imply a low activation barrier in the gas phase. In addition, calculations of the free energy of solvation using the recently proposed SM8 continuum solvation model with CM4M partial atomic charges lead to an activation barrier in reasonable agreement with experiment only when the geometries and the gas-phase barrier are those obtained from electronic structure calculations, i.e., methods i-v. These comparisons show the danger of basing the diabatic states on molecular mechanics without the explicit calculation of electronic wave functions. Furthermore, comparison of schemes i-v with one another shows that significantly different quantitative results can be obtained by using different methods for extracting diabatic states from wave function calculations, and it is important for each user to justify the choice of diabatization method in the context of its intended use.