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Title: Franck–Condon spectra of unbound and imaginary-frequency vibrations via correlation functions: A branch-cut free, numerically stable derivation
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.  more » « less
Award ID(s):
2110489
PAR ID:
10528787
Author(s) / Creator(s):
; ;
Publisher / Repository:
AIP Publishing
Date Published:
Journal Name:
The Journal of Chemical Physics
Volume:
157
Issue:
12
ISSN:
0021-9606
Page Range / eLocation ID:
124102
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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