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Updated: Aug 27, 2025

ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
Published on: August 19, 2021
Franck-Condon spectra of unbound and imaginary-frequency vibrations via correlation functions: A branch-cut free,
P Bryan Changala1, Nadav Genossar2, Joshua H Baraban2
1Center for Astrophysics | Harvard and Smithsonian, Cambridge, Massachusetts 02138, USA.
Abstract:
Molecular electronic spectra can be represented in the time domain as auto-correlation functions of the initial vibrational wavepacket. We present a derivation of the harmonic vibrational auto-correlation function that is valid for both real and imaginary harmonic frequencies. The derivation rests on Lie algebra techniques that map otherwise complicated exponential operator arithmetic to simpler matrix formulas. The expressions for the zero- and finite-temperature harmonic auto-correlation functions have been carefully structured both to be free of branch-cut discontinuities and to remain numerically stable with finite-precision arithmetic. Simple extensions correct the harmonic Franck-Condon approximation for the lowest-order anharmonic and Herzberg-Teller effects. Quantitative simulations are shown for several examples, including the electronic absorption spectra of F2, HOCl, CH2NH, and NO2.
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