APPROXIMATE SOLUTION OF THE CLASSICAL LIOUVILLE EQUATION USING GAUSSIAN PHASE PACKET DYNAMICS - APPLICATION TO ENHANCED EQUILIBRIUM AVERAGING AND GLOBAL OPTIMIZATION

An approximate method for integrating the Liouville equation to obtain the classical phase space density distribution at constant energy or temperature is presented. The density distribution of each degree of f reedom is represented by a single Gaussian phase packet (GPP) whose ce nter and width obey variationally optimized equations of motion. The c onstant energy dynamics is applied to the calculation of equilibrium t hermodynamic averages for a Lennard-Jones cluster and fluid to demonst rate the feasibility and utility of this approximate method for the si mulation of many-body condensed phase systems. The rate of kinetic ene rgy equipartitioning is examined for GPP dynamics using a generalizati on of the ergodic measure and found to be significantly faster than fo r standard molecular dynamics simulation. A global optimization algori thm is developed based on simulated annealing of the phase space densi ty distribution. This method is applied to the global energy minimizat ion of Lennard-Jones clusters and found to be superior to simulated an nealing methods employing classical point particles.