An algebraic approach to calculate Franck–Condon factors

Abstract

An algebraic approach based on unitary algebras to calculate Franck-Condon factors (FCF's) is presented. The method is based on the unitary group approach, which consists in adding a scalar boson to the ν-D harmonic oscillator space, taking advantage of the transformation brackets connecting the energy, coordinate and momentum representations. In this scheme the solutions are given in terms of an expansion of harmonic oscillator functions. In this way the overlaps are expressed in terms of simple scalar product of the eigenvectors. As a benchmark to illustrate our approach the case of two 1D-Morse potentials is presented. Discussions concerned with both non-Condon contributions and the harmonic limit are included. FCF's involving the 1D-Morse and asymmetric double Morse potentials are also considered. As an application, the FCF's involving the S-S stretching in the S 2 O molecule are described in terms of two Morse potentials.

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

“…The selection of the method is based on the symmetry of the potential to be described. Another aspect of our approach is that it can easly extended to incorporate the non-Condon factors, as explained in [39].…”

“…Taking advantage of this fact, an analytic formula for FCFs involving the Morse potential has been obtained in terms of binomial series containing polygamma function [31]. Because of the sums involved, also approximate approaches have been proposed, some of them can be found in [32][33][34][35][36][37][38][39][40][41]. The Morse and other anharmonic potentials have been used in molecular physics but also in condensed matter [42,43].…”

Empirical quality criteria for the approximation of the electronic term of a diatomic molecule by the Morse formula

“…The Morse model potential [1], despite a very rough approximation, is widely used in molecular spectroscopy and in other areas of optics and chemical physics. According to the Chemical Abstracts Service, over 6,000 references are given on the request " Morse Formula" Ȧs an example, we present random selections of recent studies in the field of spectroscopy [2][3][4][5][6][7][8][9][10][11][12][13], the influence of an external field, laser dissociation of moleculescool [14][15][16][17][18][19][20][21][22][23][24], thermodynamics, kinetics [25][26][27][28][29][30][31][32][33][34], solid and liquid physicssti [35][36][37][38][39][40][41][42][43][44], intermolecular interactions [45][46][47]…”

Эмпирические Критерии Качества Аппроксимации Электронного Терма Двухатомногой Молекулы Формулой Морза

“…По данным химической реферативной службы (Chemical Abstracts Service) на запрос " Формула Морза" выдаётся более 6000 ссылок. Как пример, приведём случайные выборки работ последнего времени в области спектроскопии [2][3][4][5][6][7][8][9][10][11][12][13], влияния внешнего поля, лазерной диссоциации молекул [14][15][16][17][18][19][20][21][22][23][24], термодинамики, кинетики [25][26][27][28][29][30][31][32][33][34], физики твёрдого тела и жидкости [35][36][37][38][39][40][41][42][43][44], межмолекулярных взаимодействий [45][46][47][48][49][50]…”