Unified analytical treatment for calculation of the two-dimensional Franck-Condon factors using the duschinsky transformation

Including binomial expansion theorems, we present an analytical formula for calculating Franck–Condon (FC) factors of two‐dimensional (2D) harmonic oscillators including the Duschinsky effect. The FC principle has various practical applications in quantum modeling of electronic spectra of polyatomic...

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Bibliographic Details
Published in:International journal of quantum chemistry 2013-05, Vol.113 (9), p.1372-1375
Main Author: Mamedov, B. A.
Format: Article
Language:English
Subjects:
Chemistry
Duschinsky effect
harmonic oscillator
multidimensional Franck-Condon factor
photoelectron spectra
Physical chemistry
Quantum physics
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Summary:Including binomial expansion theorems, we present an analytical formula for calculating Franck–Condon (FC) factors of two‐dimensional (2D) harmonic oscillators including the Duschinsky effect. The FC principle has various practical applications in quantum modeling of electronic spectra of polyatomic molecules. The 2D FC factors are expressed through the binomial coefficients. Use of the memory of the computer for the calculation of binomial coefficients may extend the limits to large arguments for users and result in speeder calculation, should such limits be required in practice. Accurate numerical results are provided to validate the proposed algorithm. © 2012 Wiley Periodicals, Inc. The Franck–Condon overlap integrals between the two electronic states determine the transition probabilities for various vibrational levels as well as intensities of various lines in the spectra of diatomic and polyatomic molecules. Using the Duschinsky effect, an efficient analytical calculation approach to compute the two‐dimensional Franck‐Condon factors, as the squares of the overlap intergrals are also known, is introduced in this work.
ISSN:0020-7608
1097-461X
DOI:10.1002/qua.24313