Relation between classical and quantum formulations of the FranckCondon principle: The generalized rcentroid approximation
Abstract
The classical transition point r _{v'v″}^{∗} for the ( v', v″) band is introduced as the point where the kinetic energy does not change during the transition (classical statement of the FranckCondon principle). It is shown that when the rcentroid approximation is valid, it implies that the r centroid overliner_{v'v″} equals r _{v'v″}^{∗}, allowing a new connection to be made between the classical and quantum statements of the FranckCondon principle. The rcentroid approximation fails for some classically allowed bands having large FranckCondon factors. This occurs when the ( v', v″) band has more than one classical transition point. A generalization of the rcentroid approximation permits such bands to be used in determining the variation of the electronic transition moment with internuclear distance.
 Publication:

Journal of Molecular Spectroscopy
 Pub Date:
 October 1982
 DOI:
 10.1016/00222852(82)901266
 Bibcode:
 1982JMoSp..95..254N