Time-dependent studies of reaction dynamics: a test of mixed quantum/classical time-dependent self-consistent field approximations

Abstract

Two approaches for applying the quantum/classical time-dependent self-consistent field approximation to collinear reaction dynamics are investigated for a generic heavy plus light–heavy (A+HB) reaction. In the first, a single quantum/classical trajectory is run, and in the second a small ensemble of quantum/classical trajectories are used. In the latter case, we derive a multiple trajectory extension to the quantum/classical TDSCF approximation starting from the Liouville–Von Neumann equation. In our formulation, the initial conditions for the classical degree of freedom are chosen from the phase space probability distribution given by the Wigner transform of the wave function that was used in the quantum simulation. Both approaches yield reaction probabilities that are in good agreement with the results of a two-dimensional quantum simulation, but the detailed dynamics are more accurately described by an ensemble average over several quantum/classical trajectories than by a single trajectory. The reasons for the relative successes of the two quantum/classical approaches will be discussed.