A new trajectory branching approximation to propagate the mixed quantum-classical Liouville equation

Abstract

Starting from the mixed quantum-classical Liouville (MQCL) equation, we derive a new trajectory branching method as a modification to the conventional mean field approximation. In the new method, the mean field approximation is used to propagate the mixed quantum-classical dynamics for short times. When the mean field description becomes invalid, new trajectories are added in the simulation by branching the single trajectory into multiple ones. To achieve this, a new set of variables are defined to monitor the deviations of the dynamics on different potential energy surfaces from the reference mean field trajectory, and their equations of motion are derived from the MQCL equation based on the method of first moment expansion. The new method is tested on several one-dimensional two surface problems and is shown to correctly solve the problem of the mean field approximation in several cases.