Representation of potential energy surfaces by discrete polynomials: proton transfer in malonaldehyde

Abstract

A new method for the expansion of potential energy surfaces has been developed exploiting the peculiar properties of Hahn polynomials, a class of orthogonal polynomials of a discrete variable which generalize 3j vector coupling coefficients of angular momentum algebra. The method has been tested for the Hénon–Heiles potential, a typical model for coupled oscillators, and applied to the representation of the potential energy surface of malonaldehyde, a prototype system for intramolecular proton transfer in polyatomic molecules. The representation is obtained by fitting the polynomial expansion to a set of points calculated by the density functional theory method on a hyperspherical effective three-center coordinate system, in view of perspective quantum dynamical calculations of the proton transfer process.