Test of Trajectory Surface Hopping Against Accurate Quantum Dynamics for an Electronically Nonadiabatic Chemical Reaction

Abstract

This paper presents the first test of the popular trajectory surface-hopping (TSH) method against accurate three-dimensional quantum mechanics for a reactive system. The system considered is a model system in which an excited atom with an excitation energy of 0.76 eV reacts with or is quenched by the H 2 molecule. The electronically nonadiabatic collisions occur primarily near a conical intersection of an exciplex with a repulsive ground state. The accurate quantal results are calculated using the outgoing wave variational principle in an electronically diabatic representation. Four variants of the TSH method are tested, differing in the criteria for hopping and the component of momentum that is adjusted in order to conserve energy when a hop occurs. Coupling between the ground and excited surface occurs primarily in the vicinity of a conical intersection and is mediated by an exciplex found on the upper surface. We find that the overall TSH quenching probabilities are in good agreement with quantum mechanical results, but the branching ratios between reactive and nonreactive trajectories and many of the state-selected results are poorly reproduced by trajectory calculations. The agreement between trajectory surface hopping and quantal results is on average worse for the relatively more "quantum mechanical" j ) 0 initial state and M + H 2 quenching process and better for the relatively more "classical" j ) 2 initial state and MH + H′ reactive process. We also perform a statistical calculation of overall quenching probability and unimolecular rate of the nonadiabatic decay of the exciplex. We find that only about 10 % of trajectories can be described as "statistical" and that statistical calculation overestimates the total quenching rate significantly.

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

“…Each trajectory in the ensemble, denoted by index i, finishes the simulation with some weight W i that is the product of the weights assigned to it at every decision point along the propagation of the trajectory. By using the histogram method, 3,27 each electronically nonadiabatic trajectory is also assigned values ri for three of the applicable final quantum number r , where 2 ϭЈ, 3 ϭ jЈ, 4 ϭЉ, 5 ϭ jЉ, and 1 is the final electronic-arrangement quantum number ␣, which is assigned as 1 for Y*ϩRH, 2 for RϩYH, and 3 for YϩRH. Note that 1i , 2i , and 3i are assigned if ␣ϭ2, and 1i , 4i , and 5i are assigned if ␣ϭ3.…”

“…The final quantum states of the diatomic products are calculated according to the following equations using the energy nonconserving histogram method, as discussed elsewhere. 27 The first moments of the final vibrational and rotational quantum numbers r are given by…”

“…25,27,[32][33][34]36,[41][42][43][44]46,53 Because it has been impractical to study dynamics for systems with very small semiclassical transition probabilities, these tests have been carried out for systems with nonadiabatic probabilities of 3ϫ10 Ϫ4 and larger. The army ants algorithm allows us to extend these tests down to much lower probabilities; for example, in the present paper we present well-converged calculations for a system with a nonadiabatic transition probability of 1ϫ10…”

Introductory lecture: Nonadiabatic effects in chemical dynamics

“…68 OWVP calculations have been performed more recently on a variety of model systems, including three qualitatively different types of chemical systems: (1) systems with conical intersections, [69][70][71][72][73] (2) systems with diabatic surfaces that cross and adiabatic surfaces that do not intersect, 74 and (3) systems with wide regions of weak coupling where neither the diabatic nor the adiabatic surfaces cross. 75,76 This set of calculations includes reactive 69,72,[74][75][76] and nonreactive 71,72 scattering collisions as well as unimolecular excited-state decay processes. 70,73 The availability of accurate quantum mechanical results for realistic full-dimensional non-BO systems allows for the systematic study of the accuracy of more approximate methods, and we have identified a subset of the calculations discussed above to serve as benchmark test cases.…”

Communication: Standard surface hopping predicts incorrect scaling for Marcus’ golden-rule rate: The decoherence problem cannot be ignored

“…While most publications have so far focused on calculating detailed balance properties or inelastic scattering cross sections, [8][9][10][11] we will instead address the question of rates, 6,12,13 which is crucial for modeling photo-induced experiments. In so doing, we can critically evaluate the long-time behavior of surfacehopping algorithms, where nuclei visit regions of nonadiabatic coupling repeatedly and any failures of FSSH should be obvious.…”