EFFECTS OF ANHARMONICITY OF THE VIBRATIONAL STRUCTURE OF AN ELECTRONIC TRANSITION

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1968

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Ohio State University

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Abstract

In zeroth approximation the vibrational wavefunction of a polyatomic molecule is a simple product of harmonic oscillator functions. In higher approximation the oscillator functions become mixed and the wavefunction, for the case of a triatomic structure, can be written $\Psi_{ijk}=\sum_{1mn} a^{1mn}_{ijk} \Psi^{\circ}{_{1mn}}$ in which the $\Psi^{\circ}$ are harmonic oscillator functions and the a's are coefficients which may be unity but in general are determined by the harmonic energy eigenvalues and the higher-than-quadratic force constants. In an electronic band system this mixing to some extent modifies the usual Franck-Condon considerations, and may cause transitions forbidden in the harmonic oscillator approximation---for example, the 2-0 transition in a non-totally symmetrical vibration---to appear with considerable intensity.

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This work was supported by the Army Research Office (Durham).
Author Institution: Department of Chemistry, Vanderbilt University

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