The Journal of Biological Physics and Chemistry


Volume 6, Number 1, p.p. 37-44

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

Akio Kawano1 and Gia G. Maisuradze2

1 Holistic Simulation Research Program, the Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 3173-25 Showa-machi, Kanazawa-ku, Yokohama, 236-0001, Japan
2 Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, NV 89557, USA

The basic formal and numerical aspects of interpolated moving least-squares (IMLS) methods of different degrees are studied using sixteen different combinations of coordinate system for fitting and weight functions. As an illustrative application we use a 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 the number of ab initio points. From these studies we discovered that the IMLS for almost all pairs of coordinate systems show qualitatively similar behaviour, however, the accuracy of the fits is noticeably different. We also found compact and accurate representations of potentials for the presented degrees of the IMLS.

Keywords: hydrogen peroxide, interatomic distance coordinates, valence internal coordinates

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