#### Date of Award

2001

#### Document Type

Dissertation

#### Degree Name

Doctor of Philosophy (PhD)

#### Department

Physics and Astronomy

#### First Advisor

Sean P. McGlynn

#### Abstract

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.

#### Recommended Citation

Wood, Dorothy Marie, "The Geometry of Electronically -Excited States: Vibronic Intensity Distributions and Bond Length Changes." (2001). *LSU Historical Dissertations and Theses*. 328.

https://digitalcommons.lsu.edu/gradschool_disstheses/328

#### ISBN

9780493273020

#### Pages

157

#### DOI

10.31390/gradschool_disstheses.328