TWO METHODS FOR THE CALCULATION OF POLYATOMIC FRANCK-CONDON INTEGRALS: APPLICATION TO THE $^{1}A_{1g} - ^{1}B_{2u}$ ABSORPTION BAND OF BENZENE
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Date
1978
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Ohio State University
Abstract
Two theoretical/computational approaches to the calculation of polyatomic Franck-Condon integrals are presented. The first method uses an intermediate transformation of the normal coordinates in both the ground and excited electronic states. This transformation effectively removes any Duschinsky mixing and allows the multi-dimensional Franck-Condon Integral to be reduced to a sum of products of simple one-dimensional integrals. The second method uses standard contact transformation-perturbation theory to develop the vibrational wavefunctions of the excited electronic state in terms of the ground electronic state vibrational wave-functions. The polyatomic Franck-Condon integral can then be evaluated using harmonic oscillator integrals involving only the ground electronic state normal coordinates and moment. Both methods are applied in the calculation of the relative intensities of the A series of the forbidden $^{1}A_{1g} \rightarrow\ ^{1}B_{2u}$ absorption band of benzene. The advantages and disadvantages of both methods are discussed and compared.
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Author Institution: Department of Chemistry, University of Virginia