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Unified analytical treatment for calculation of the two‐dimensional Franck–Condon factors using the duschinsky transformation
Author(s) -
Mamedov B. A.
Publication year - 2012
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.24313
Subject(s) - transformation (genetics) , polyatomic ion , binomial coefficient , binomial (polynomial) , harmonic , statistical physics , mathematics , computer science , physics , quantum mechanics , molecule , chemistry , statistics , discrete mathematics , biochemistry , gene
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.