G. G. Maisuradze, A. Kawano, D. L. Thompson, A. F. Wagner, and M. Minkoff, "Interpolating Moving Least-Squares Methods for Fitting Potential Energy Surfaces: Analysis of an Application to a Six-Dimensional System," Preprint ANL/MCS-P1187-0704, July 2004. [pdf]
The basic formal and numerical aspects of different degree interpolated moving least-squares (IMLS) methods are applied to a six-dimensional potential energy surface (PES) of the HOOH molecule, for which an analytic (“exact”) potential is available in the literature. The results of systematic investigations of the effects of weight function parameters, the degree and partial degree of IMLS, the number of data points allowed, and the optimal automatic point selection of data points up to full third-degree IMLS (TD-IMLS) fits are reported. With partial reduction of cross terms and automatic point selection the full 6D HOOH PES can be fit over a range of 100 kcal/mol to an accuracy of less than 1 kcal/mol with ~1350 ab initio points.