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Explicit expression of the franck–condon factors in terms of the potentials of the two states
Author(s) -
Kobeissi Hafez,
Dagher Mounzer,
Alameddine Mohamad Adel
Publication year - 1981
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.560200306
Subject(s) - expression (computer science) , coupling (piping) , interval (graph theory) , simple (philosophy) , wave function , chemistry , mathematical analysis , physics , quantum mechanics , mathematics , combinatorics , materials science , computer science , philosophy , epistemology , metallurgy , programming language
The calculus of the overlap integral for two states represented by the vibrational wave functions ψ ν′ aand ψ ν″ bis reduced to that of the Franck–Condon integral ℒ(0, x ) = ∫ 0 xψ ν′ a ψ ν″ b( t ) dt . It is proved that for “numerical potentials” (as well as for a Dunham potential), this integral is given on each interval by a simple analytic expression in terms of the two potentials. The Franck–Condon factors are well determined by “coupling constants” related uniquely to the coordinates of the turning points of the potentials. An application to the band system BIIXΣ of Nα 2 is compared with the usual numerical methods.