Automatic potential energy surface generation directly from ab initio calculations using Shepard interpolation: A test calculation for the H₂+H system

A modified version of the Shepard interpolation scheme proposed recently by Collins et al. is used to determine a potential energy surface for the H₂-H reaction. Our modifications are based on preliminary calculations in which the Liu-Siegbahn-Truhlar-Horowitz surface for H₃ is used to study convergence of the Shepard procedure. Included in the modifications are changes to the form of the weight functions, the coordinate sets used in the zeroth-order surface, and the transformation of the Cartesian first and second derivatives to internal coordinates. The new ab initio potential energy surface is based on calculations using the basis set of Siegbahn and Liu and second order Møller-Plesset (MP2) perturbation calculations. We have not experienced convergence problems with the self-consistent-field iteration while "growing" the surface. Furthermore, a converged fit can be obtained using only 85 ab initio calculations. This demonstrates that the Shepard interpolation scheme is a powerful candidate for automatic determination of medium quality potential surfaces for dynamical calculations.