Smoothing techniques of global optimization: Distance scaling method in searches for most stable Lennard-Jones atomic clusters

Spatial averaging of the potential energy function facilitates the search for the most stable configuration of a molecular system Recently some global optimization methods of this kind. have been designed in the literature that rely on physical phenomena such as diffusion, wave function evolution in quantum mechanics, Smoluchowski dynamics, evolution in temperature of canonical ensembles, etc. In the present article we highlight the fact that all these methods, when applied to the Gaussian distributions of an ensemble, represent special cases of a set of differential equations involving the spatially averaged potential energy. Their structure suggests that the nature's strategy to cope with the global optimization is robust and differs only in the details in particular applications. The strategy consists of going downhill of the averaged potential energy, removing the barriers, and hunting for low energy regions by a selective increasing of the spatial averaging. In this study we explore the deformation of the potential rather than its averaging. The deformation comes from scaling of atomic distances and reduces the barriers even more effectively than the Gaussian averaging. The position and widths of the Gaussian distribution evolve similarly to the Gaussian density annealing (GDA), but we allow elliptical instead of spherical Gaussians as well as branching of the single trajectory of the system into multiple ones. When the temperature reaches 0 K, one has a number of independent Gaussian distributions, each corresponding to a structure and (usually low) energy of the system. The multiple elliptic-Gaussian distance scaling method has been applied to clusters of argon atoms (N = 5,...,31), a system serving usually as a benchmark domain. The method found the global minima for all but three clusters (of very low energy). The procedure is 20 or more times less expensive than the GDA one. (C) 1997 John Wiley & Sons, Inc.