Classical trajectory-based approaches to solving the quantum Liouville equation



The time-dependent quantum mechanics of heavy particles moving on a single potential energy surface can often be represented surprisingly well by the evolution of classical trajectory ensembles. However, manifestly quantum mechanical phenomena—such as transitions between coupled electronic states, electronic coherence and its decay, or quantum mechanical tunneling—require fundamental modification of the purely classical motion. We introduced and developed an approach to this problem that is based on solving the quantum Liouville equation using ensembles of classical trajectories. In this article, we describe the general approach and its application to the problems of nonadiabatic dynamics, coherent multistate electronic–nuclear dynamics, and tunneling through potential barriers. When viewed from the trajectory ensemble perspective, quantum effects arise as a breakdown of the statistical independence of the trajectories in the ensemble and a nonlocal entanglement of their collective evolution. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002