SOME PROPERTIES AND USES OF TORSIONAL OVERLAP INTEGRALS
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Date
1997
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Ohio State University
Abstract
The first diagonalization step in a rho-axis-method treatment of methyl-top internal rotation problems involves finding eigenvalues and eigenvectors of 3 torsional Hamiltonian which depends on the rotational projection quantum number K as a parameter. Traditionally die the torsional quantum number $\nu_{t} = 0.1.2\ldots$ is assigned to eigenfunctions of given K in order of increasing energy. In this talk we propose an alternative labeling scheme using the torisional quantum number $\nu_{T}$ which is based on properties of the K-dependent torsional overlap integrals $< \nu_{t}, K|\nu_{t}^{\prime} t,K^{\prime}>$. In particular, the quantum number $\nu_{T}$ is assigned in such a way that torsional wavefunctions $|\nu_{T},K>$ vary as slowly as possible when K changes by unity. Roughly speaking, $\nu_{T} = \nu_{t}$, for torsional levels below the barrier, whereas $\nu_{T}$ is more closely related lo the free-rotor quantum number for levels above the barrier. Because of the latter fact, we believe $\nu_{T}$ will in general be a physically more meaningful torsional quantum number for levels above the barrier. The usefulness of $<\nu_{t}, K|\nu^{\prime}_{t},K^{\prime}>$ overlap integrals for qualitative prediction of torsion- rotation hand intensities and for rationalizing the magnitudes of perturbations involving some excitation of the small-amplitude vibrations in an internal rotor problem is also discussed.
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Author Institution: Optical Technology Division, National institute of Standards and Technology