The Geometry of Electronically -Excited States: Vibronic Intensity Distributions and Bond Length Changes.
Date of Award
Doctor of Philosophy (PhD)
Physics and Astronomy
Sean P. McGlynn
An exact power series expression has been obtained for the Franck-Condon integral (FCI) in the harmonic approximation. This expression is a function of a parameter Delta where Delta → 0 as the frequencies of vibration in the two combining electronic states approach equality. These two characteristics, that of a power series in Delta and the fact that Delta → 0 in certain situations, permit truncation of various functions involving FCI's. Such truncation was performed for the ratio S2v'0'' /S2v'-1 0'' , where the S2v'v'' are the FCI's, and the subscripts, in the usual notation, denote the vibrational quantum numbers in the two different electronic states. As a result, two approximations to the S2v'0'' /S2v'-1 0'' ratio were obtained: a linear approximation in Delta and a quadratic expression in Delta2. Maps of the Franck-Condon integrals, FCIM's, were found to be very useful. An FCIM is a plot of S2v'0'' DRe versus DeltaRe for various values of the parameter v'. These FCIM's facilitated a test of the linear and quadratic approximations and led to a precise specification of the ranges of a within which they are valid. They resulted in the concept of a "Franck-Condon window". A Franck-Condon window (FCW) is that specific region of the FCIM (i.e., the range of DeltaRe) in which the gross (i.e., non-numerical, vibronic intensity) pattern of some vibronic spectrum is represented. The vibrational intensity distributions in 60 different electronic transitions were subjected to Franck-Condon analysis using (i) the linear approximation, (ii) the quadratic approximation, (iii) the FCW approach, and (iv) the best fit to the FCIM. It was found that method (ii), (iii) & (iv) provided excellent agreement with experiment whereas method (i) produced mixed results. The analysis had some incidental benefits: it caused a reassignment of one vibronic spectrum and permitted a choice between two proposed alternative assignments for another vibronic spectrum.
Wood, Dorothy Marie, "The Geometry of Electronically -Excited States: Vibronic Intensity Distributions and Bond Length Changes." (2001). LSU Historical Dissertations and Theses. 328.