Solutions of mixed quantum-classical dynamics in multiple dimensions using classical trajectories

Abstract

The multithreads algorithm for solving the mixed quantum-classical Liouville equation is extended to systems in which multiple classical degrees of freedom couple explicitly to a quantum subsystem. The method involves evolving a discrete set of matrices representing operators positioned at classical phase space coordinates according to precise dynamical rules dictated by evolution equations. The propagation scheme is based on the Trotter expansion of the time evolution operator and involves trajectory (thread) branching and pruning operations at each time step. The method is tested against exact numerical solution of the quantum dynamics for two models in which the nonadiabatic evolution of two heavy coordinates (nuclei) induces changes in population in two electronic states. It is demonstrated that the multithreads algorithm provides a good quantitative as well as qualitative description of the dynamics for branching ratios and populations as a function of time. Critical performance issues such as the computational demand of the method, energy conservation, and how the scheme scales with the number of classical degrees of freedom coupled to the quantum subsystem are discussed.