A Strategy for the Regional Characterization of Potential Energy Surfaces

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 H 2 O, H 2 S, and H 2 Se. Results are reported for the equilibrium geometries and force constants for these molecules. Results are comparable to those obtained by others for H 2 O and H 2 S. A full set of values is reported for H 2 Se.