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


Guseinov I. I. , Mamedov B. A. , Ekenoglu A. S.

COMPUTER PHYSICS COMMUNICATIONS, vol.175, no.3, pp.226-231, 2006 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 175 Issue: 3
  • Publication Date: 2006
  • Doi Number: 10.1016/j.cpc.2006.04.002
  • Title of Journal : COMPUTER PHYSICS COMMUNICATIONS
  • Page Numbers: pp.226-231

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(-2cx)) and Gaussian (exp(-cx(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 valid for the arbitrary values of parameters and the computation results are in good agreement with the literature. The numerical results illustrate clearly a further reduction in calculation times.