The effective vibration-rotation hamiltonian for triply-degenerate fundamentals of tetrahedral XY4 molecules

The effective vibration-rotation hamiltonian for the first excited state of a triply-degenerate vibration in a tetrahedral XY4 molecule is considered, and the principles involved in formulating totally symmetric operators for use in the hamiltonian are reviewed. Explicit expressions are given for all such operators up to fourth order in the Amat-Nielsen ordering scheme. A new systematic notation is proposed for the operators and their coefficients, and the hamiltonian is compared to those derived previously. Two commonly used sets of basis functions appropriate to this problem are discussed, and the infra-red and Raman selection rules in these basis functions are stated.

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