A nine-dimensional perturbative treatment of the vibrations of methane andits isotopomers

The vibrations of methane isotopomers with T-d, C-3v, and C-2v symmetry are studied by means of high order Van Vleck perturbation theory. The vibratio nal states up to 9000 cm(-1) are investigated by combining the ab initio fo rce field of Lee, Martin and Taylor [J. Chem. Phys. 95, 254 (1995)] with a fourth order perturbative treatment based on curvilinear normal coordinates . Implementation of the perturbation theory using both analytical and numer ical expression of the kinetic energy operator is considered. The quadratic and select cubic and quartic force constants are refined via a nonlinear l east squares fit to experimental data The fit force constants reproduce 130 experimental band centers with a root mean squares deviation of 0.70 cm(-1 ). The choice of polyad quantum number is discussed with respect to differe nt molecules. The convergence of the energy levels is discussed by carrying out the perturbation calculation up to eighth order. (C) 1999 American Ins titute of Physics. [S0021-9606(99)00334-7].