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A more general algebraic expression for the calculation of the four-mode Franck-Condon factors was derived straightforwardly on the basis of the closed form expression of the Franck-Condon integrals between arbitrary multidimensional harmonic oscillators under the Duschinsky mixing effects. This new algebraic expression was applied to study the photoelectron spectra of $D_2CO^+(\widetilde{A} ^2B_1).$ Franck-Condon analyses and spectral simulations were carried out on the $D_2CO^+(\widetilde{A} ^2B_1)$-$D_2CO(\widetilde{X} ^1A_1)$ photoionization processes. The spectral simulations of vibrational structures based on the computed Franck-Condon factors are in excellent agreement with the observed spectra.
}, issn = {2079-7346}, doi = {https://doi.org/10.4208/jams.120110.011411a}, url = {http://global-sci.org/intro/article_detail/jams/8123.html} }A more general algebraic expression for the calculation of the four-mode Franck-Condon factors was derived straightforwardly on the basis of the closed form expression of the Franck-Condon integrals between arbitrary multidimensional harmonic oscillators under the Duschinsky mixing effects. This new algebraic expression was applied to study the photoelectron spectra of $D_2CO^+(\widetilde{A} ^2B_1).$ Franck-Condon analyses and spectral simulations were carried out on the $D_2CO^+(\widetilde{A} ^2B_1)$-$D_2CO(\widetilde{X} ^1A_1)$ photoionization processes. The spectral simulations of vibrational structures based on the computed Franck-Condon factors are in excellent agreement with the observed spectra.