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

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

doi:10.1016/j.cpc.2006.04.002

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

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

COMPUTER PHYSICS COMMUNICATIONS, vol.175, no.3, pp.226-231, 2006 (SCI-Expanded)

Publication Type: Article / Article
Volume: 175 Issue: 3
Publication Date: 2006
Doi Number: 10.1016/j.cpc.2006.04.002
Journal Name: COMPUTER PHYSICS COMMUNICATIONS
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Page Numbers: pp.226-231
Çanakkale Onsekiz Mart University Affiliated: No

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.