Monte Carlo sampling methods for determining potential energy surfaces using Shepard interpolation. The O(1D)+H2 system

Shepard interpolation provides an effective way to define global analytical potential energy surfaces using ab initio energies, gradients and hessians as input. We examine Monte Carlo techniques for sampling geometries for the ab initio calculations, including the iterative determination of points which are used with the Shepard approach to optimize selected dynamical properties. Applications are presented to the O(1D)+H2 surface which demonstrate the effectiveness of the method under circumstances where trajectory-based sampling gives poor results.