Aw. Jasper et al., The treatment of classically forbidden electronic transitions in semiclassical trajectory surface hopping calculations, J CHEM PHYS, 115(4), 2001, pp. 1804-1816
A family of four weakly coupled electronically nonadiabatic bimolecular mod
el photochemical systems is presented. Fully converged quantum mechanical c
alculations with up to 25 269 basis functions were performed for full-dimen
sional atom-diatom collisions to determine the accurate scattering dynamics
for each of the four systems. The quantum mechanical probabilities for ele
ctronically nonadiabatic reaction and for nonreactive electronic deexcitati
on vary from 10(-1) to 10(-5). Tully's fewest-switches (TFS) semiclassical
trajectory surface-hopping method (also called molecular dynamics with quan
tum transitions or MDQT) is tested against the accurate quantal results. Th
e nonadiabatic reaction and nonreactive deexcitation events are found to be
highly classically forbidden for these systems, which were specifically de
signed to model classically forbidden electronic transitions (also called f
rustrated hops). The TFS method is shown to systematically overestimate the
nonadiabatic transition probabilities due to the high occurrence of frustr
ated hops. In order to better understand this problem and learn how to best
minimize the errors, we test several variants of the TFS method on the fou
r new weakly coupled systems and also on a set of three more strongly coupl
ed model systems that have been presented previously. The methods tested he
re differ from one another in their treatment of the classical trajectory d
uring and after a frustrated hopping event. During the hopping event we fin
d that using a rotated hopping vector results in the best agreement of semi
classical and quantal results for the nonadiabatic transition probabilities
. After the hopping event, we find that ignoring frustrated hops instead of
reversing the momentum along the nonadiabatic coupling vector results in t
he best agreement with the accurate quantum results for the final vibration
al and rotational moments. We also test the use of symmetrized probabilitie
s in the equations for the TFS hopping probabilities. These methods systema
tically lead to increased error for systems with weakly coupled electronic
states unless the hopping probabilities are symmetrized according to the el
ectronic state populations. (C) 2001 American Institute of Physics.