A DUAL-LEVEL SHEPARD INTERPOLATION METHOD FOR GENERATING POTENTIAL-ENERGY SURFACES FOR DYNAMICS CALCULATIONS

We present a new dual-level approach to representing potential energy surfaces in which a very small number of high-level electronic structu re calculations are combined with a lower-level global surface, e.g., one defined implicitly by neglect-of-diatomic-differential-overlap cal culations with specific reaction parameters, to generate the potential at any geometry where it may be needed. We interpolate the potential energy surface with a small number of accurate data points (the higher level) that are placed along the reaction path by using information o n the global shape of the potential from less accurate calculations (t he lower level). We confirm the findings of Ischtwan and Collins on th e usefulness of single-level schemes including Hessians, and we deline ate the regime of usefulness of single-level schemes based on gradient s or even single-point energies. Furthermore we find that dual-level i nterpolation can offer cost savings over single-level schemes, and dua l-level methods employing Hessians, gradients, or even only simple ene rgy evaluations can yield reasonable potential energy surfaces with re latively low cost, with the potentials being more accurate along the r eaction path, For all methods considered in this paper the accuracy of the interpolation for our test cases is lower when the potentials at points significantly removed from the reaction path are predicted from data that he entirely on the reaction path. (C) 1995 American Institu te of Physics.