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An analytical approach for computing Franck-Condon integrals of harmonic oscillators with arbitrary dimensions

Authors

  • Jia-Lin Chang,

    Corresponding author
    1. Department of Science Application and Dissemination, National Taichung University of Education, Taichung 403, Taiwan, Republic of China
    • Department of Science Application and Dissemination, National Taichung University of Education, Taichung 403, Taiwan, Republic of China
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  • Cyong-Huei Huang,

    1. Department of Science Application and Dissemination, National Taichung University of Education, Taichung 403, Taiwan, Republic of China
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  • Sue-Chang Chen,

    1. Department of Science Application and Dissemination, National Taichung University of Education, Taichung 403, Taiwan, Republic of China
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  • Tsung-Hao Yin,

    1. Department of Science Application and Dissemination, National Taichung University of Education, Taichung 403, Taiwan, Republic of China
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  • Yi-Tsung Chen

    1. Department of Science Application and Dissemination, National Taichung University of Education, Taichung 403, Taiwan, Republic of China
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Abstract

We have developed an analytical approach for computing Franck-Condon integrals (FCIs) of harmonic oscillators (HOs) with arbitrary dimensions in which the mode-mixing Duschinsky effect is taken into account. A general formula of FCIs of HOs was obtained and was applied to study the photoelectron spectroscopy of vinyl alcohol and ovalene (C32H14). The equilibrium geometries, harmonic vibrational frequencies and normal modes of vinyl alcohol, ovalene, and their cations were computed at the B3LYP/aug-cc-pVTZ or the B3LYP/6-31G(d) level, from which Franck-Condon factors were calculated and photoelectron spectra were simulated. The adiabatic ionization energies of vinyl alcohol were also computed by extrapolating the CCSD(T) energies to the complete basis set limit with aug-cc-pVXZ (X = D, T, Q, 5). The simulated photoelectron spectra of both vinyl alcohol and ovalene are in agreement with the experiments. The computed adiabatic ionization energies of syn- and anti-vinyl alcohol are in consistent with the experiment within 0.008 eV and 0.014 eV, respectively. We show, for the first time, that the analytical approach of computing FCIs is also efficient and promising for the studies of vibronic spectra of macrosystems. © 2012 Wiley Periodicals, Inc.

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