Boson-realization model for the vibrational spectra of tetrahedral molecules

Abstract

An algebraic model of Boson-realization is proposed to study the vibrational spectra of a tetrahedral molecule, where ten sets of boson creation and annihilation operators are used to construct the Hamiltonian with $T_d$ symmetry. There are two schemes in our model. The first scheme provides an eight-parameter fit to the published experimental vibrational eigenvalues of methane with a root-mean-square deviation 11.61 $c{m}^{-1}$. The second scheme, where the bending oscillators are assumed to be harmonic and the interactions between the bending vibrations are neglected, provided a five-parameter fit with a root-mean-square deviation 12.42 $c{m}^{-1}$

12 pages, 1 figure, Latex, Phys. Rev. A. to appear

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