An accurate analytic method for the calculation of the Franck–Condon factors: Its application to the study of rotational dependence

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Abstract
We incorporated the perturbed Morse oscillator function and Manneback’s formulas into the matrix method to calculate the Franck–Condon factors. The method is exact in the context of the variational principle and is presented as a viable alternative to the numerical integration method where computational facilities are limited. Its accuracy is demonstrated by computing the eigenvalues of CO and Franck–Condon factors of the (B–X) band system of Na2. It is then applied to the study of rotational dependence of the Franck–Condon factors in the (A–X) band system of MgH.