Nonadiabatic scattering of NO off Au3 clusters: A simple and robust diabatic state manifold generation method for multiconfigurational wavefunctions

The presence of nonadiabatic effects during the interaction of small molecules with metals has been observed experimentally for the last decades. Specially remarkable are the effects found for NO/Au, where experiments have suggested the presence of very strong vibronic coupling during the molecular scattering. However, the accurate inclusion of the nonadiabatic effects in periodic boundary conditions (PBC) theoretical methods remain an unapproachable challenge. Here, aiming to give some theoretical insight to the strong vibronic coupling, we have adopted a pragmatic point of view, taking use of an auxiliary simplified system, NO/Au₃. We show the importance of nonadiabatic coupling, during the scattering of NO from a Au₃ cluster, using a diabatic representation of 12 electronic states of the system, including a few charge-transfer states. Our diabatic representation is obtained by rotating the orbital and configuration interaction (CI) vectors of a restricted active space (RAS) wavefunction. We present a strategy for extracting the best effective manifold of states relevant to the system, below some prescribed energy, directly from the RAS CI vectors. This scheme is able to disentangle a large dense manifold of adiabatic states with strong coupling and crossings. This approach is also shown to work for multireference configuration interaction (MRCI). By performing quantum propagations, we observed an increase in vibrational redistribution with increasing initial vibrational or translational energies. We suggest that these nonadiabatic effects should also be present at smaller energies in larger clusters. © 2018 Wiley Periodicals, Inc.     

Quantized time correlation function approach to nonadiabatic decay rates in condensed phase: application to solvated electrons in water and methanol

A new, alternative form of the golden rule formula defining the nonadiabatic transition rate between two quantum states in condensed phase is presented. The formula involves the quantum time correlation function of the energy gap, of the nonadiabatic coupling, and their cross terms. Those quantities can be inferred from their classical counterparts, determined via molecular dynamics simulations. The formalism is applied to the problem of the nonadiabatic p-->s relaxation of an equilibrated p-electron in water and methanol. We find that, in both solvents, the relaxation is induced by the coupling to the vibrational modes and the quantum effects modify the rate by a factor of 2-10 depending on the quantization procedure applied. The resulting p-state lifetime for a hypothetical equilibrium excited state appears extremely short, in the sub-100 fs regime. Although this result is in contrast with all previous theoretical predictions, we also illustrate that the lifetimes computed here are very sensitive to the simulated electronic quantum gap and to the strongly correlated nonadiabatic coupling.     

An unusually large nonadiabatic error in the BNB molecule

The vibronic coupling model of Ko?uppel, Domcke, and Cederbaum in one dimension is introduced as a means to estimate the effects of electronic nonadiabaticity on the vibrational energy levels of molecules that exhibit vibronic coupling. For the BNB molecule, the nonadiabatic contribution to the nominal fundamental vibrational energy of the antisymmetric stretching mode is approximately -80?cm(-1). The surprisingly large effect for this mode, which corresponds to an adiabatic potential that is essentially flat near the minimum due to the vibronic interaction, is contrasted with another model system that also exhibits a flat potential (precisely, a vanishing quadratic force constant) but has a significantly larger gap between interacting electronic states. For the latter case, the nonadiabatic contribution to the level energies is about two orders of magnitude smaller even though the effect on the potential is qualitatively identical. A simple analysis shows that significant nonadiabatic corrections to energy levels should occur only when the affected vibrational frequency is large enough to be of comparable magnitude to the energy gap involved in the coupling. The results provide evidence that nonadiabatic corrections should be given as much weight as issues such as high-level electron correlation, relativistic corrections, etc., in quantum chemical calculations of energy levels for radicals with close-lying and strongly coupled electronic states even in cases where conical intersections are not obviously involved. The same can be said for high-accuracy thermochemical studies, as the zero-point vibrational energy of the BNB example contains a nonadiabatic contribution of approximately -70?cm(-1) (-0.9?kJ mol(-1)).     

Significant nonadiabatic effects in the S(1D) + HD reaction

A nonadiabatic quantum dynamics calculation involving four coupled potential energy surfaces (two degenerate 3A' ', one 3A', and one 1A') and the spin-orbit coupling matrix for these states is reported for the title reaction. The results show that the important discrepancy between theoretically calculated and experimentally measured intramolecular isotope effects can at least in part be attributed to significant nonadiabatic effects.     

Coriolis coupling and nonadiabaticity in chemical reaction dynamics

The nonadiabatic quantum dynamics and Coriolis coupling effect in chemical reaction have been reviewed, with emphasis on recent progress in using the time-dependent wave packet approach to study the Coriolis coupling and nonadiabatic effects, which was done by K. L. Han and his group. Several typical chemical reactions, for example, H+D(2), F+H(2)/D(2)/HD, D(+)+H(2), O+H(2), and He+H(2)(+), have been discussed. One can find that there is a significant role of Coriolis coupling in reaction dynamics for the ion-molecule collisions of D(+)+H(2), Ne+H(2)(+), and He+H(2)(+) in both adiabatic and nonadiabatic context.     

Quantum nonadiabatic dynamics of hydrogen exchange reactions

In continuation of our earlier effort to understand the nonadiabatic coupling effects in the prototypical H + H₂ exchange reaction [Jayachander Rao et al. Chem. Phys. 333 (2007) 135], we present here further quantum dynamical investigations on its isotopic variants. The present work also corrects a technical scaling error occurred in our previous studies on the H + HD reaction. Initial state-selected total reaction cross sections and Boltzmann averaged thermal rate constants are calculated with the aid of a time-dependent wave packet approach employing the double many body expansion potential energy surfaces of the system. The theoretical results are compared with the experimental and other theoretical data whenever available. The results re-establish our earlier conclusion, on a more general perspective, that the electronic nonadiabatic effects are negligible on the important quantum dynamical observables of these reactive systems reported here.     

Nonadiabatic quantum dynamics in O(3P)+H2→OH+H: a revisited study

To investigate the extent of nonadiabatic effects in the title reaction, quasi-classical trajectory and nonadiabatic quantum scattering as well as the nonadiabatic quantum-classical trajectory calculations were performed on the accurate ab initio benchmark potential energy surfaces of the lowest (3)A' and (3)A" electronic states [Rogers et al., J Phys Chem A 2000, 104, 2308], together with the spin-orbit coupling matrix [Maiti and Schatz, J Chem Phys 2003, 119, 12360] and the lowest singlet (1) A' potential energy surface [Dobby and Knowles, Faraday Discuss 1998, 110, 247]. Comparison of the calculated total cross sections from both adiabatic and nonadiabatic calculations has demonstrated that for adiabatic channels including (3)A'→(3)A' and (3)A"→(3)A", difference does exist between the two kinds of adiabatic and nonadiabatic calculations, showing nonadiabatic effects to some extent. Such nonadiabatic effects tend to become more conspicuous at high collision energies and are found to be more pronounced with trajectories/quantum wave packet initiated on (3)A' than on (3)A". Furthermore, the present study also showed that nonadiabatic effects can bring the component of forward-scattering in the product angular distributions.     

Reactive chemical dynamics through conical intersections

Reaction dynamics of prototypical, D + H₂ and Cl (²P) + H₂, chemical reactions occurring through the conical intersections of the respective coupled multi-sheeted potential energy surfaces is examined here. In addition to the electronic coupling, nonadiabatic effects due to relativistic spin-orbit coupling are also considered for the latter reaction. A time-dependent wave packet propagation approach is undertaken and the quantum dynamical observables viz., energy resolved reaction probabilities, integral reaction cross-sections and thermal rate constants are reported.     

Semiclassical treatment of thermally activated electron transfer in the intermediate to strong electronic coupling regime under the fast dielectric relaxation

The generalized nonadiabatic transition-state theory (NA-TST) (Zhao, Y.; et al. J. Chem. Phys. 2004, 121, 8854) is used to study electron transfer with use of the Zhu-Nakamura (ZN) formulas of nonadiabatic transition in the case of fast dielectric relaxation. The rate constant is expressed as a product of the well-known Marcus formula and a coefficient which represents the correction due to the strong electronic coupling. In the case of general multidimensional systems, the Monte Carlo approach is utilized to evaluate the rate by taking into account the multidimensionality of the crossing seam surface. Numerical demonstration is made by using a model system of a collection of harmonic oscillators in the Marcus normal region. The results are naturally coincident with the perturbation theory in the weak electronic coupling limit; while in the intermediate to strong electronic coupling regime where the perturbation theory breaks down the present results are in good agreement with those from the quantum mechanical flux-flux correlation function within the model of effective one-dimensional mode.     

Nonadiabatic quantum-classical reaction rates with quantum equilibrium structure

Time correlation function expressions for quantum reaction-rate coefficients are computed in a quantum-classical limit. This form for the correlation function retains the full quantum equilibrium structure of the system in the spectral density function but approximates the time evolution of the operator by quantum-classical Liouville dynamics. Approximate analytical expressions for the spectral density function, which incorporate quantum effects in the many-body environment and reaction coordinate, are derived. The results of numerical simulations of the reaction rate are presented for a reaction model in which a two-level system is coupled to a bistable oscillator which is, in turn, coupled to a bath of harmonic oscillators. The nonadiabatic quantum-classical dynamics is simulated in terms of an ensemble of surface-hopping trajectories and the effects of the quantum equilibrium structure on the reaction rate are discussed.     

离子速度成像方法研究碘代正戊烷的紫外光解动力学

利用离子速度成像方法对n-C5H11I分子在266和277 nm下的光解动力学进行了研究. 实验分析了I*(5p 2P1/2)和I(5p 2P3/2)的离子影像, 得到其相应速度、角度分布和相对量子产率, 并根据相对量子产率和角度分布计算了不同解离通道的比例. 实验发现n-C5H11I的3Q0和1Q1态之间存在较强的耦合效应, 并且随着波长的减小, 这种非绝热耦合作用有递增的趋势. 由离子影像(I*和I)的角度分布结果发现, 在同一解离激光波长下I*的各向异性参数β值比I的β值小, 其中I*主要由3Q0直接解离产生, 而I绝大多数是由分子先跃迁到3Q0再经过3Q0→1Q1的非绝热耦合产生.     

Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions

An ab initio electronic wave-packet dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the off-diagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematic-coupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between H(2) and B(+) shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematic-coupling terms cannot be neglected in the CSF-basis representation. The present applications also demonstrate that the nonadiabatic electronic wave-packet dynamics within ab initio quantum chemical calculation is feasible.     

Full six-dimensional nonadiabatic quantum dynamics calculation for the energy pooling reaction O(2)(a (1)Delta)+O(2)(a (1)Delta)-->O(2)(b (1)Sigma)+O(2)(X (3)Sigma)

Six new potential energy surfaces of four singlet states and two triplet states for the title oxygen molecule reaction along with the spin-orbit coupling among them have been constructed from the complete active space second-order perturbation theory with a 6-311+G(d) basis. Accurate integral cross sections are calculated with a full six-dimensional nonadiabatic time-dependent quantum wave packet method. The thermal rate constant based on the integral cross sections agrees well with the result of the experimental measurements, and the intersystem crossing effects are also discussed in this electronic energy-transfer process.     

Nonadiabatic proton-coupled electron transfer reactions: impact of donor-acceptor vibrations, reorganization energies, and couplings on dynamics and rates

Fundamental aspects of proton-coupled electron transfer (PCET) reactions in solution are analyzed with molecular dynamics simulations for a series of model systems. The analysis addresses the impact of the solvent reorganization energy, the proton donor-acceptor mode vibrational frequency, and the distance dependence of the nonadiabatic coupling on the dynamics of the reaction and the magnitude of the rate. The rate for nonadiabatic PCET is expressed in terms of a time-dependent probability flux correlation function. The time dependence of the probability flux correlation function is determined mainly by the solvent reorganization energy and is not significantly influenced by the proton donor-acceptor frequency or the distance dependence of the nonadiabatic coupling. The magnitude of the PCET rate becomes greater as the solvent reorganization energy decreases, the proton donor-acceptor frequency decreases, and the distance dependence of the nonadiabatic coupling increases. The approximations underlying a previously derived analytical PCET rate expression are also investigated. The short-time approximation for the solvent is valid for these types of systems. In addition, solvent damping effects on the proton donor-acceptor motion are not significant on the time scale of the probability flux. The rates calculated from the molecular dynamics simulations agree well with those calculated from the analytical rate expression.     

Quantum equations for vibrational dynamics on metal surfaces

A first principles treatment of the vibrational dynamics of molecular chemisorbates on metal surfaces is presented. It is shown that the mean field quantum evolution of the vibrational position operator is determined by a quantum Langevin equation with an electronic friction. In the mean field limit, the quantum noise and friction are related by the quantum fluctuation-dissipation theorem. The classical limit of this model is shown to agree with previously proposed models. A criterion is presented to describe the validity of the weak-coupling approximation and equations of motion for the dynamics in the presence of strong nonadiabatic coupling to electron-hole pairs are presented.     

The effect of spin-orbit coupling on fast neutral chemical reaction O(3P)+CH3-->CH3O

The effect of nonadiabatic transitions through the spin-orbit couplings has been investigated on the fast neutral reaction, O((3)P)+CH(3)-->CH(3)O. Adiabatic potential energies and the spin-orbit coupling terms have been evaluated for the four electronic states of CH(3)O ((2)E, (2)A(2), (4)E, and (4)A(2)) that correlate with the O((3)P)+CH(3) asymptote, as a function of CO distance and OCH angle under the C(3v) symmetry, by ab initio electronic structure calculations using multireference internally contracted single and double excitation configuration interaction method with the 6-311G(2df,2pd) basis sets. Multistate quantum reactive scattering calculations have been carried out with the use of thus obtained potential energies and spin-orbit coupling matrices, based on the generalized R-matrix propagation method. The calculated thermal rate constants show a slight positive dependence on temperature in a range between 50 and 2000 K, supporting the previous experimental results. It is shown that the spin-orbit coupled excited states give rise to reflections over the centrifugal barrier due to the quantum interference. Classical capture calculations yield larger rate constants due to the neglect of quantum reflections. It is concluded that the effect of nonadiabatic transitions is of minor importance on the overall reactivity in this reaction.     

On the properties of a primitive semiclassical surface hopping propagator for nonadiabatic quantum dynamics

A previously developed nonadiabatic semiclassical surface hopping propagator [M. F. Herman J. Chem. Phys. 103, 8081 (1995)] is further studied. The propagator has been shown to satisfy the time-dependent Schrodinger equation (TDSE) through order h, and the O(h2) terms are treated as small errors, consistent with standard semiclassical analysis. Energy is conserved at each hopping point and the change in momentum accompanying each hop is parallel to the direction of the nonadiabatic coupling vector resulting in both transmission and reflection types of hops. Quantum mechanical analysis and numerical calculations presented in this paper show that the h2 terms involving the interstate coupling functions have significant effects on the quantum transition probabilities. Motivated by these data, the h2 terms are analyzed for the nonadiabatic semiclassical propagator. It is shown that the propagator can satisfy the TDSE for multidimensional systems by including another type of nonclassical trajectories that reflect on the same surfaces. This h2 analysis gives three conditions for these three types of trajectories so that their coefficients are uniquely determined. Besides the nonadiabatic semiclassical propagator, a numerically useful quantum propagator in the adiabatic representation is developed to describe nonadiabatic transitions.