The routine location of the global minimum energy structures of a molecular system remains a challenging problem in chemical physics. Recently Straub and co-workers [J. Ma et al., J. Chem. Phys. 99, 4024 (1993) and 101, 533. (1994)] have introduced a number of novel dynamic simulated annealing algorithms for global optimization. Instead of using Newton’s equations, they are based on Liouville’s equation and the particles are described with phase space distributions. The methods were shown to have significantly enhanced effectiveness over traditional methods when used to locate the global minima of Lennard-Jones clusters. In this paper the extensions necessary to use these methods with ab initio quantum mechanical potentials are presented and their application is illustrated by the simulated annealing of a small lithium atom cluster.