Analytical Evaluation for Calculation of Two-Center Franck–Condon Factor and Matrix Elements

Author:

Koç Hüseyin1ORCID

Affiliation:

1. Department of Electrical and Electronics Engineering, Faculty of Engineering, Muş Alparslan University, Muş, Turkey

Abstract

The Franck–Condon (FC) factor is defined as squares of the Franck–Condon (FC) overlap integral and represents one of the principle fundamental factors of molecular physics. The FC factor is used to determine the transition probabilities in different vibrational levels of the two electronic states and the spectral line intensities of diatomic and polyatomic molecules. In this study, new analytical formulas were derived to calculate Franck–Condon integral (FCI) of harmonic oscillators and matrix elements (xη, e2cx, and ecx2) including simple finite summations of binomial coefficients. These formulas are valid for arbitrary values. The results of formulas are in agreement with the results in the literature.

Publisher

Hindawi Limited

Subject

General Chemistry

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