Configuration Space Sampling Methods

Abstract

In order to achieve the maximum accuracy in characterizing the PES and the associated force fields for an MD investigation, careful preparation of the database is an essential step in the process. The points that must be addressed include the following: 1. The total volume of configuration space is extremely large, and its size increases as the internal energy of the system rises. For example, consider a four-atom system. For this system, at least six internal coordinates must be specified to determine the spatial configuration of the molecular system. At a given internal energy, each of these six coordinates can span a continuous range of values from some minimum to some maximum. If each variable range is divided into 100 equal increments and the potential energy of the system computed by some ab initio method for all possible configurations of the system, a total of 1006or 1012 electronic structure calculations would need to be executed. This is clearly beyond the computational capabilities of any computational system currently in existence. Grid sampling methods can and have been used effectively for three atom systems. However, for more complex systems, it is essential that procedures be developed that permit the regions of configuration space that are important in the reaction dynamics to be identified. 2. Sampling methods usually should be optimized to produce a reasonably uniform density of data points in those regions of configuration space that are important in the dynamics. If this is not done and there are regions of very high point density and others with low point density, no fitting technique will function well. The parameters of the method will adjust themselves to fit regions of high density preferentially over those with low density even when the low-density regions may be more important in the dynamics. An exception to the need to have an approximately uniform density of points in the database occurs in regions where the potential gradient is large. In such regions, the density of points in the database will need to be larger than in regions in which the gradient is small.