15min:

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 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 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.