Multidimensional potential matrix elements for molecular vibration- and vibration-rotation calculations

Abstract

An elegant method for the calculation of the matrix elements of the Born-Oppenheimer potential energy surface for one dimensional systems has been given by Harris, Engerholm and Gwinn (HEG) [1]. The advantage of the method is that the potential can be given in any coordinate system and any analytical form or even numerically. In this work we extend this method to several dimensions. We first construct a special finite multidimensional basis set that creates a diagonal representation of all matrices of interest. This allows the use of factorized basis sets for the numerical calculation of the potential matrix. Subsequently we project this matrix to a smaller space by a transformation that can be factorized into one degree of freedom blocks involving each degree of freedom separately. We demonstrate the utility of the method by an explicit calculation on H₂O.