Exact and asymptotic solutions of the mixed quantum-classical Liouville equation

In this article, an exact surface-hopping procedure and an approximate asym ptotic method for performing molecular dynamics based on a mixed quantum-cl assical Liouville equation [J. Chem. Phys. 110, 8919 (1999)] for partially Wigner transformed dynamical variables of a coupled quantum subsystem and c lassical bath are elaborated. The methods are based upon writing the equati ons of motion in a basis set in which quantum transitions do not alter the classical trajectory, and therefore avoid ad-hoc momentum jump approximatio ns and are free of singular kernels associated with sampling momenta. Resul ts obtained utilizing the new trajectory methods are presented for a model two-level system bilinearly coupled to a classical harmonic oscillator. The se results are compared to results obtained from standard methods of perfor ming mixed quantum-classical dynamics. The new methods perform well for the model system over a wide range of initial kinetic energies. (C) 2000 Ameri can Institute of Physics. [S0021-9606(00)01109-0].