Approximate solution of the classical Liouville equation using Gaussian phase packet dynamics: Application to enhanced equilibrium averaging and global optimization

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Abstract
An approximate method for integrating the Liouville equation to obtain the time‐dependent classical phase space density distribution at constant energy or temperature is presented. The density distribution of each degree of freedom is represented by a single Gaussian phase packet (GPP) whose center and width obey variationally optimized equations of motion. The constant energy dynamics is applied to the calculation of equilibrium thermodynamic averages for a Lennard‐Jones cluster and fluid to demonstrate the feasibility and utility of this approximate method for the simulation of many‐body condensed phase systems. The rate of kinetic energy equipartitioning is examined for GPP dynamics using a generalization of the ergodic measure and found to be significantly faster than for standard molecular dynamics simulation. A global optimization algorithm is developed based on simulated annealing of the phase space density distribution. This method is applied to the global energy minimization of Lennard‐Jones clusters and found to be superior to simulated annealing methods employing classical point particles.