Interpolating moving least-squares methods for fitting potential energy surfaces: The dependence on coordinate systems for six-dimensional applications

The basic formal and numerical aspects of different degree interpolated moving least-squares (IMLS) methods are studied using sixteen different combinations of coordinate system for fitting and weight functions. For the application we use six-dimensional potential energy surface (PES) of hydrogen peroxide, for which an analytic ("exact") potential is available in the literature. We systematically examine the effect of parameters in the weight function, the degree of the IMLS fit, and number of ab initio points. From these studies we discovered that the IMLS for almost all pairs of coordinate system show qualitatively similar behavior, however, the accuracy of the fits is noticeably different. We also found compact and accurate representations of potentials for presented degrees of IMLS.