A Strategy for the Regional Characterization of Potential Energy Surfaces

Abstract

The problem of characterization of a region of an n-dimensional potential energy surface with maximization of the quality of representation for a given amount of computational effort is examined with the aid of well known theorems from numerical analysis. A choice of nonlinear grid and a representation of the potential expanded in Chebyshev polynomials is shown to be efficient. The strategy was applied to a two-dimensional analytical representation of a transition state and to the ground-state equilibrium geometry region of the Hartree-Fock potential energy surface obtained with split-valence basis sets for HzO, HzS, and H,Se. Results are reported for the equilibrium geometries and force constants for these molecules. Results are comparable to those obtained by others for HzO and H,S. A full set of values is reported for HzSe.