Improved recursion formulas for the calculation of two-center central potential integrals

Abstract

A commutator algebra procedure is used to get improved recurrence relations for the calculation of any f(r) off-diagonal two-center matrix elements in the general case of displaced arbitrary central potential wave functions. As expected, the proposed formulas reduce properly to the generalized recursion equations for the calculation of one-center integrals. Besides, when f(r) = rk, one obtains the equivalent of the Kramer rule for two-center multipolar matrix elements for arbitrary potentials, and when f(r) is constant, the Wu formula (for the calculation of Franck–Condon factors) is ameliorated in the sense that the new relation not necessarily considers equal mass. Furthermore, all diagonal matrix elements as well as all off-diagonal integrals between nondisplaced potentials appear, in our treatment, as particular cases in good agreement with already published results. As a useful application, the corresponding recurrence relations for the calculation of one-center hydrogenic matrix elements and two-center Kratzer potential integrals are given as examples. However, our approach is general and can be easily extended to obtain recursion formulae for other potential wave functions. © 1995 John Wiley & Sons, Inc.