Theoretical Basis for Interpretation of the Spectra

In this section, we outline a procedure for obtaining a Hamiltonian for the treatment of low-frequency vibrations in molecules. We do this, in particular, to point out the justification for some of the Hamiltonians used in the past and to make clear the nature of the approximations involved in arriving at a specific Hamiltonian. Since there is danger of overinterpreting the results obtained from approximate Hamiltonians, we indicate some of the pitfalls in doing so. 

The emphasis in this section is on the form of the kinetic energy operator. The choice of potential energy functions is considered in Section IV dealing with specific molecules. Emphasis is also placed on treatment of the vibrational data since a review emphasizing treatment of microwave data for ring puckering has appeared recently19). 

We start by writing the classical kinetic energy expression for a non-linear molecule.in a center-of-mass coordinate system. No distinction is made between small and large vibrational coordinates at this stage. We then rewrite the expres- 

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