High dimensional anharmonic potential energy surfaces: The case of methane

The overtone vibrational spectra of all Td symmetry isotopomers of methane have been analyzed simultaneously. A Hamiltonian expressed in internal curvilinear coordinates expanded to the fourth order has been employed, with a nine-dimensional basis of harmonic oscillator wave functions in symmetry coordinates. Near-resonant anharmonic interactions are treated to first order, while weaker interactions are handled as second order perturbations. A set of optimized Born–Oppenheimer force constants is obtained, which reproduces the observations up to 9500 cm−1 and shows an excellent agreement with the results of ab initio calculations.