GLOBAL ENERGY MINIMUM SEARCHES USING AN APPROXIMATE SOLUTION OF THE IMAGINARY TIME SCHRODINGER-EQUATION

We present a method for finding the global energy minimum of a multidimensional potential energy surface through an approximate solution of the Schrodinger equation in imaginary time. The wave function of each particle is represented as a single Gaussian wave packet, while that for the n-body system is expressed as a Hartree product of single particle wave functions. Equations of motion are derived for each Gaussian wave packet's center and width. While evolving in time the wave packet tunnels through barriers seeking out the global minimum of the potential energy surface. The classical minimum is then found by setting Planck's constant equal to zero. We apply our method first to the pedagogically interesting case of an asymmetric double-well potential and then use it to find the correct global energy minima for a series of Lennard-Jones n-mer clusters ranging from n = 2 to 19.