Fitting Potential Energy Surfaces

This paper reviews several methods for determining analytical representations of potential energy surfaces for small molecule systems which are involved in unimolecular dissociation and/or bimolecular reaction. These methods may be categorized as “global” or “local” and they may involve either “fitting” or “interpolation” of ab initio data. The methods may be applied either directly to the full potential energy surface, or to individual terms in a many-body expansion of the full potential surface. In addition, most of the methods may be applied to the description of multiple coupled potential energy surfaces (typically using a diabatic representation) as well as to Born-Oppenheimer surfaces. Included in the global methods are least squares fitting and spline, Morse-spline, rotated Morse-spline, and reproducing kernel Hilbert space interpolation methods. The local methods include Shepard and moving least squares interpolation. Examples of the application of these methods to several triatomic reactive surfaces are discussed.