# Evaluating Franck-Condon factors

Franck-Condon overlap integrals are given by $\langle\psi^e_{v_e}|\psi^g_{v_g}\rangle$, where $\psi^e_{v_e}$ and $\psi^g_{v_g}$ are the vibrational functions for the $v^{th}$ vibrational states of the excited and ground electronic states, respectively.

• Why is it considered difficult to obtain Franck-Condon factors (judged by the fact that there is a lot of literature dedicated to their calculation) – is the problem only in obtaining high-accuracy vibrational wavefunctions for the two electronic states, or there something else at play?
• If you can obtain both $\psi^e_{v_e}$ and $\psi^g_{v_g}$, could you calculate the overlap integral in Cartesian coordinates?
• As FC factors are the integral of the product of two vibrational (wave) functions their calculation is not particularly hard if you have the functions in the first place and in cartesians, usually, as they are vibrational functions. Thus obtaining these is the hard part. – porphyrin Jul 7 '18 at 7:14