SIMULTANEOUS INTEGRATION OF MIXED QUANTUM-CLASSICAL SYSTEMS BY DENSITY-MATRIX EVOLUTION-EQUATIONS USING INTERACTION REPRESENTATION AND ADAPTIVE TIME-STEP INTEGRATOR

A density matrix evolution method [H. J. C. Berendsen and J. Mavri, J. Phys. Chem., 97, 13464 (1993)] to simulate the dynamics of quantum sy stems embedded in a classical environment is applied to study the inel astic collisions of a classical particle with a five-level quantum har monic oscillator. We improved the numerical performance by rewriting t he Liouville-von Neumann equation in the interaction representation an d so eliminated the frequencies of the unperturbed oscillator. Further more, replacement of the fixed time step fourth-order Runge-Kutta inte grator with an adaptive step size control fourth-order Runge-Kutta res ulted in significantly lower computational effort at the same desired accuracy. (C) 1996 by John Wiley & Sons, Inc.