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Algebraic approximation to the Franck–Condon factors for the Morse oscillator
Author(s) -
Palma A.,
RivasSilva J. F.,
Durand J. S.,
Sandoval L.
Publication year - 1992
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.560410606
Subject(s) - anharmonicity , diatomic molecule , harmonic oscillator , morse potential , hamiltonian (control theory) , formalism (music) , algebraic number , quantum mechanics , physics , molecule , mathematics , mathematical analysis , art , mathematical optimization , musical , visual arts
An algebraic approach is proposed to calculate the Franck–Condon factors for the Morse potential of diatomic molecules. The Morse oscillator is approximated by means of a fourth‐order anharmonic oscillator. In the second‐quantized formalism, this anharmonic Hamiltonian is diagonalized by way of the Bogoliubov–Tyablikov transformation. The Franck–Condon factors are estimated using the harmonic frequency equivalent and the recurrence relations for the Franck–Condon factors of the harmonic oscillator. Overlap integrals are shown for three band systems and compared with values calculated with an RKR potential. Excellent agreement is achieved.