General formulation of rovibrational kinetic energy operators and matrix elements in internal bond-angle coordinates using factorized Jacobians.

Abstract

We show how inverse metric tensors and rovibrational kinetic energy operators in terms of internal bond-angle coordinates can be obtained analytically following a factorization of the Jacobian worked out by Frederick and Woywod. The structure of these Jacobians is exploited in two ways: On one hand, the elements of the metric tensor as well as its determinant all have the form ∑rmsin(αn)cos(βo). This form can be preserved by working with the adjugate metric tensor that can be obtained without divisions. On the other hand, the adjugate can be obtained with less effort by exploiting the lower triangular structure of the Jacobians. Together with a suitable choice of the wavefunction, we avoid singularities and show how to obtain analytical expressions for the rovibrational kinetic energy matrix elements.