ANALYSIS OF FERMI RESONANCES AND LOCAL MODES IN $CH_{2}Cl_{2}$ AND $CD_{2}Cl_{2}$ USING AN INTERNAL COORDINATE HAMILTONIAN

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1988

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Ohio State University

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Abstract

A curvilinear internal coordinate Hamiltonian is used to analyze Fermi resonances between CH (CD) stretching and $CH_{2} (CD_{2})$ scissoring vibrations in $CH_{2}Cl_{2}$ and $CD_{2}Cl_{2}$. The Hamiltonian is constracted by expanding the g matrix elements and the potential energy function in terms of the Morse variable $y = 1 - \exp (-ar)$ for the stretches and the curvilinear internal bending coordinate for the scissoring vibration. The important local mode and Fermi resonance terms are retained in the final Hamiltonian. The eigen-values are obtained variationally using a symmetrized Morse oscillator basis set for the stretching vibrations and a harmonic oscillator basis set for the scissoring vibration. The least squares method is used to optimize the potential energy parameters. The observed vibrational levels of $CH_{2}Cl_{2}$ and $CD_{2}Cl_{2}$ are reproduced well with a single potential energy surface.

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Author Institution: Department of Physical Chemistry, University of Helsinki

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