CHAPTER 17: Putting Together the Pieces: A Global Description of Valence and Long-Range Forces via Combined Hyperbolic Inverse Power Representation of the Potential Energy Surface

This review focuses on a recently suggested scheme to fit a smooth function of the many-body expansion type to a multidimensional large data set using an optimized basis. Named as combined hyperbolic iInverse power representation (CHIPR) after the chosen basis, the method has so far been tested only for up to triatomic systems, which include trihydrogen and the hydroperoxyl radical. Although the former is the best known prototype of a Jahn–Teller system, thus requiring an electronic Hilbert space of at least dimension two for an accurate representation, its use may provide a tool for estimating the errors that arise when forcefully fitting the data to a single-sheeted form since cusp-like features pervade most reactive systems with practical interest. This issue is further illustrated for the paradigmatic hyproperoxyl radical, with two fits examined: one, to data generated from a popular single-sheeted form; the other to energies calculated by solving the electronic Schrödinger equation with a high-level ab initio method. Focusing on such a scheme, also applicable to potential energy curves, its relationship to other methods is also pointed out. Although the focal point here is on the potential energy surface, a brief reference to dynamics calculations is also made.