An approach to calculate Franck-Condon factors involving anharmonic potentials using harmonic oscillator bases

In this contribution an approach to calculate Franck-Condon factors (FCFs) is presented. The method is based on the knowledge of the quantum harmonic oscillator system, a familiar system included in any course of quantum mechanics. The advantage of this approach is that it is possible to calculate Franck-Condon factors associated with general potentials based on the knowledge of the harmonic oscillator theory. First the coordinate and momentum representations are introduced. Based on this concept, the discrete variable representation (DVR) is proposed, which allows the Franck-Condon factors to be calculated in a simple form. This method takes advantage of the momentum as generator of translations to include the displacement of the potentials. The calculation of the FCFs is exemplified for transitions involving the ground state X 1Σ+ g and the excited state a 1Πg of the diatomic molecule 14N2.