A Study of the Franck-Condon Principle

Abstract

The validity of the Franck-Condon principle has been investigated in connection with its application to the calculation of spectral intensities in the continuous radiation due to the transitions between the 1sσ2sσ 3Σg and the 1sσ2pσ 3Σu states of H2. For the latter state, a potential curve was constructed on the basis of the authors' theoretical calculations. For the former state, a curve was computed from spectral data by Dunham's method. Accurate wave functions for both states were determined by mechanical integration with the differential analyzer. Transition probabilities from the first four vibrational levels of the stable state were determined by mechanical integration, both for the case that the electric moment matrix element is constant (as assumed in the Franck-Condon method) and for the case that it is a linear function of the nuclear separation. In addition integrals were determined which permitted the calculation of the probability of excitation of the several vibrational levels by electron impact from the ground state, upon the basis of an extension of the Franck-Condon method. The spectral intensities so obtained are compared with those given by several forms of approximate calculation, and the discrepancies critically discussed. Comparisons are also made with the experimental work of Smith and of Finkelnburg and Weizel. It is concluded that the Franck-Condon principle leads to results definitely incompatible with their observations. Indications are found that other transitions than the one treated in this work are contributing appreciably to the radiation observed by Smith. An analysis of the spectrum observed by Finkelnburg and Weizel leads to a critical discussion of the method used by them in deducing the potential curve of the repulsive state, from which is drawn the conclusion that this curve is without quantitative significance.

Dissociative Charge Exchange of HeH+: An Experimental Study of the HeH Molecule

“…15 The continuous part of the spectrum has been calculated in a standard way. 16 The comparison with the experiment [see Fig. 3(b)] provides support to the first hypothesis.…”

Ground and excited states of zinc phthalocyanine, zinc tetrabenzoporphyrin, and azaporphyrin analogs using DFT and TDDFT with Franck-Condon analysis

“…[17][18][19][20] Even though the additional assignments in the first four bands have been debated in literature, Gouterman and Edwards made a key observation in 1970. They noted that the Q band, in particular, would be subject to Franck-Condon (FC) [21][22][23] vibrational displacement, and point to an earlier publication by Gouterman and Fulton, in which the higher energy bands were believed to take on much more peculiar shapes, especially at the investigated temperature of 0 K. 24 Some believe the four orbital model is simplistic, but the framework is generally still reliable for the major transitions, and is used in this present work. Most functionals used for time-dependent density functional theory (TDDFT) have not been extremely accurate, leading to low energy excitations that are usually blue shifted.…”

Multilinear analysis of Time-Resolved Laser-Induced Fluorescence Spectra of U(VI) containing natural water samples

“…could be used to determine Rm through fitting to linear harmonic oscillator Franck-Condon factor [52][53][54][55] ratio as suggested in [1] (page 5).…”