SOME PROPERTIES AND USES OF TORSIONAL OVERLAP INTEGRALS

The first diagonalization step in a rho-axis-method treatment of methy l-top internal rotation problems involves finding eigenvalues and eige nvectors of a torsional Hamiltonian, which depends on the rotational p rojection quantum number K as a parameter. Traditionally the torsional quantum number v(t) = 0, 1, 2... is assigned to eigenfunctions of giv en K in order of increasing energy. In this paper we propose an altern ative 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 assigne d 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 rela ted to the free-rotor quantum number for levels above the barrier. Bec ause of the latter fact, we believe v(T) will in general be a physical ly more meaningful torsional quantum number for levels above the barri er. The usefulness of (v(T), K\v(T)', K') overlap integrals for qualit ative prediction of torsion-rotation band intensities and for rational izing the magnitudes of perturbations involving some excitation of the small-amplitude vibrations in an internal rotor problem is also discu ssed. (C) 1998 Academic Press.