The Journal of Biological Physics and Chemistry


Volume 8, Number 1, p.p. 17–21

Interpolated moving least-squares methods for fitting potential energy surfaces: analysis of an application to a five-atom molecule

Akio Kawano,1 and Gia G. Maisuradze,2*

1The Earth Simulator Centre, Japan Agency for Marine-Earth Science and Technology (JAMSTEC), 3173-25 Showa-machi, Kanazawa-ku, Yokohama, 236-0001, Japan
2DBaker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New Y ork, USA

The basic formal and numerical aspects of interpolated moving least-squares (IMLS) methods of different degrees are applied to a potential energy surface (PES) of a five-atom molecule (NH4). We present a general approach to solve the hitherto still remaining important technical problem related to the interatomic distance coördinate system, encountered in the PES of systems bigger than four atoms. The accurate representations of potentials and derivatives of IMLS for a nine-dimensional curved manifold are presented. With one of these potentials we can fit the PES of NH4 over a range of 60 kcal/mol to an accuracy of 1 kcal/mol with ~ 6000 ab initio points.

Keywords: interatomic distance coördinates, nine-dimensional curved manifold, valence internal coordinates

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