On Franck-Condon Factor Calculations

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Abstract
The band strength SUv′ Lv′ is an average with respect to vibrational wavefunctions ϕv′, and ϕv″, of the electronic transition moment Re (r) where and In Eq. (2) we see that the electronic transition moment is an average with respect to electronic wavefunctions of (ϕu and ϕL) the electronic dipole moment. If Re (r) is independent of r, Eq. (1) becomes where is called the Franck-Condon factor and is the square of the overlap integral of vibrational wavefunctions. The Franck-Condon factor controls the intensity distribution from band to band across a system.