Head and tail deformations, torsional coriolis coupling, and E-1d-E-2d vibrational mixing in ethane-like molecules

The mechanism of torsional Coriolis interaction of E-1d and E-2d vibrationa l modes in ethane-like molecules is investigated, and it is shown that this coupling can drastically affect the torsional splitting in the degenerate vibrational states. A basic point of our treatment is that the sets of coor dinates of head and tail which combine with the + sign to generate E-1d nor mal coordinates are in general different from those which combine with the - sign to generate E-2d normal coordinates. It is shown that the zeta(gamma ) torsional Coriolis coefficients calculated by the usual methods of normal mode analysis are related to the vibrational angular moments within head a nd tail referred to the internal rotor axis systems. With knowledge of the L and L-1 matrices it is possible to transform these coefficients for refer ence to the molecule-fixed frame. It is peculiar that torsional Coriolis ma trix elements occur between E-1d and E-2d vibrational components with the s ame x or y orientation in the molecule-fixed frame. The matrix elements of the torsional Coriolis operator and other operators responsible for the end -to-end coupling are determined, and a method for calculating vibration-tor sion energies, and then torsional splittings, in degenerate vibrational sta tes is outlined. Detailed calculations require a global model, involving al l the degenerate vibrational basis states in a complex mechanism of interac tions, but it is shown that useful information can be obtained by means of simplified models. Our semiempirical rule that degenerate vibrational state s with a large negative value of the diagonal vibration-rotation Coriolis c oefficient are likely to deviate much from the behavior of E-1d or E-2d vib rational states, with a sensible decrease of the torsional splittings, is c onfirmed, (C) 1999 Academic Press.