# Exact analytical expressions and numerical analysis of two-center Franck–Condon factors and matrix elements over displaced harmonic oscillator wave functions

## Description

Abstract A detailed study is undertaken, using various techniques, in deriving analytical formula of Franck-Condon overlap integrals and matrix elements of various functions of power (x^l ), exponential (exp (- 2 c x)) and Gaussian (exp (- c x^2 )) over displaced harmonic oscillator wave functions with arbitrary frequencies. The results suggested by previous experience with various algorithms are presented in mathematically compact form and consist of generalization. The relationships obtained are val... Title of program: FRANCK (Franck-Condon factors and matrix elements programs) Catalogue Id: ADXX_v1_0 Nature of problem The programs calculate the Franck-Condon factors and matrix elements over displaced harmonic oscillator wave functions with arbitrary quantum numbers (n, n1), frequencies (a, a1) and displacement (d) for the various functions of power (x l ), exponential (exp(-2cx)) and Gaussian (exp(-cx 2 )). Versions of this program held in the CPC repository in Mendeley Data ADXX_v1_0; FRANCK (Franck-Condon factors and matrix elements programs); 10.1016/j.cpc.2006.04.002 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)