The Vibrational Spectrum of Methane in an Extended Boson-Realization Model

The vibrational spectrum of methane, including both stretching and bending vibrations, is calculated in terms of an extended boson-realization model, by taking into account the interactions between vibrations up to the fourth order. The problem of removal of spurious states is discussed in detail. The term number in the Hamiltonian increases very fast as the interaction order increases. When the spurious states are removed from the configuration space, the effective Hamiltonian is not unique. We find a method to greatly simplify the T_d invariant Hamiltonian without any error. Fitting 45 experimental data with the Hamiltonian gives a root-mean-square energy deviation 3.96 cm^-1.