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