A nine-dimensional perturbative treatment of the vibrations of methane and its isotopomers

The vibrations of methane isotopomers with Td, C3v, and C2v symmetry are studied by means of high order Van Vleck perturbation theory. The vibrational states up to 9000 cm−1 are investigated by combining the ab initio force 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 numerical expression of the kinetic energy operator is considered. The quadratic and select cubic and quartic force constants are refined via a nonlinear least 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 different molecules. The convergence of the energy levels is discussed by carrying out the perturbation calculation up to eighth order.