SOME PROPERTIES AND USES OF TORSIONAL OVERLAP INTEGRALS

\underline{MIRZA A. MEKHTIEV} and JON T. HOUGEN, Optical Technology Division, National Institute of Standards and Technology, Gaithersburg, MD 20899.

The first diagonalization step in a rho-axis-method treatment of methyl-top internal rotation problems involves finding eigenvalues and eigenvectors of a torsional Hamiltonian which depends on the rotational projection quantum number K as a parameter. Traditionally the torsional quantum number v_{t} = 0,1,2 ... is assigned to eigenfunctions of given K in order of increasing energy. In this talk we propose an alternative labeling scheme, using the torsional quantum number v_{T}, which is based on properties of the K-dependent torsional overlap integrals < v_{t}, K|v′_{t}, K′ >. In particular, the quantum number v_{T} is assigned in such a way that torsional wavefunctions |v_{T}, K > vary as slowly as possible when K changes by unity. Roughly speaking, v_{T} = v_{t} for torsional levels below the barrier, whereas v_{T} is more closely related to the free-rotor quantum number for levels above the barrier. Because of the latter fact, we believe v_{T} will in general be a physically more meaningful torsional quantum number for levels above the barrier. The usefulness of < v_{t}, K|v′_{t}, K′ > overlap integrals for qualitative prediction of torsion- rotation band intensities and for rationalizing the magnitudes of perturbations involving some excitation of the small-amplitude vibrations in an internal rotor problem is also discussed.