Our previously described diffusion equation method for global optimization was applied here to find minimum-energy structures of several clusters of identical atoms. In this method, the potential energy surface of the system, which contains a large number of minima, is deformed (the deformation parameter being analogous to "time") in such a way that the number of minima is decreased dramatically. The deformation is carried out by finding a solution F of the diffusion equation for some time t, with the original potential function f as the boundary condition. In the present calculations, the atoms are assumed to interact by means of a Lennard-Jones potential, with parameters pertaining to argon; however, the results can easily be rescaled to any other Lennard-Jones parameters. The Lennard-Jones potential was fitted by a linear combination of Gaussians, so chosen to reproduce the potential accurately at physically relevant distances in clusters. The choice of Gaussians as fitting functions allowed F to be determined analytically. Further, by enforcing certain constraints on the Gaussian approximation of f, the following desirable behavior of F was guaranteed: at sufficiently large (known) time, the interaction potential is purely attractive so that the minimum of F can easily be recognized as the only existing one; it corresponds to a collapsed configuration (i.e., one with all atoms occupying the same position in space). Subsequent local minimizations for gradually decreasing times (the so-called time-reversing procedure) led rapidly to the global minimum of the original function. The resulting cluster configuration did not depend on the number of reversing time steps when this number was sufficiently large (approximately 100). The method was applied to several systems of up to m = 55 atoms and successfully found the global minimum, even in the largest of these (the 55-atom system, which involves minimization in the space of dimension 3m - 6 = 159 for a function having about 10(45) local minima).
