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

Abstract

In this contribution a discrete variable representation (DVR) approach to calculate Franck-Condon factors (FCFs) is presented. The method is illustrated using a harmonic oscillator basis. The advantage of this approach is that it is possible to calculate FCFs 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 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 ${X}^{1}{{\rm{\Sigma }}}_{g}^{+}$ and the excited state a ^1 Π _g of the diatomic molecule ^14 N _2 both modelled with Morse potentials.

Keywords

• discrete variable representation
• vibronic transitions
• morse potential
• diatomic molecule
• molecular spectroscopy