Calculation of the Franck–Condon Factors: Single-α Approximation Method

Abstract

It is shown that when the vibrational wave function is expanded in a set of harmonic oscillator eigenfunctions [Formula: see text], where α is the conventional nonlinear parameter, the energy eigenvalue remains very stationary over a wide range of α. The reason for this weak functional dependence is analyzed in some detail.The single-α approximation method is introduced, which gives the Franck–Condon factor in the closed form. Using three band systems of contrasting nature as test cases, these factors are also shown to change only weakly as a function of α. Comparison with the numerical integration method and the experiment clearly establishes the validity of this approximation. Various other advantages of the method are also briefly mentioned.