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-meansquare deviation 11.61 cm −1 . The second scheme, where the bending oscillators are assumed to be harmonic and the interactions between the bending vibrations are neglected, provides a five-parameter fit with a root-mean-square deviation 12.42 cm −1 . * email address: MAZQ@BEPC3.IHEP.AC.CN

A Symmetry Adapted Algebraic Approach to Molecular Spectroscopy

“…Whereas the r.m.s. deviations of standard vibron model studies in [14] and [29] are 12.16 and 11.61 cm −1 for 19 energies, we find a value of 1.16 cm −1 for 44 energies.…”

Algebraic approach to vibrational spectra of tetrahedral molecules: a case study of silicon tetrafluoride

“…The assignments of the Cartesian coordinate system are the same as in Ref. [16]. Each U α (2) (1 ≤ α ≤ 10) is generated by the operators {N α ,Ĵ +,αĴ−,α ,Ĵ 0,α }, satisfying the following commutation relations:…”

“…For the stretch and bend states of tetrahedral molecules, the symmetrized bases were given in Ref. [16], where the spurious states in the bases were eliminated.…”

“…Its excited stretching vibrational states were explained in the local mode model [21]. In our previous papers, the vibrational spectrum of methane was analyzed in terms of bosonic operators [16] and q-deformed harmonic oscillators [23], however its infrared intensity was not taken into account. Recently new algebraic SU(2) model [24] has been proposed for tetrahedral molecules.…”

“…Extending U(2) algebraic model [3] to describe both the stretching and the bending vibrations in X 3 [13] and X 4 molecules [14], Frank and his co-workers have introduced a symmetry-adapted algebraic model, and established an explicit connection between algebraic and configuration space calculations. Developing the local mode model [15], we have recently proposed an algebraic model of boson realization [16][17][18] for the complete vibrations by taking full advantages of the discrete symmetries of molecular systems. It is worth mentioning that U(k-1) and U(n) algebraic approach have been introduced for the k=3m-3 rotational and vibrational degrees of freedom of m-atomic molecules [19], and for n-1 stretching vibrational degrees of freedom of polyatomic molecules [20], respectively.…”