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

Abstract

Both the stretch and bend vibrational spectrum and the intensity of infrared transitions in a tetrahedral molecule are studied in a U(2) algebraic model, where the spurious states in the model Hamiltonian and the wavefunctions are exactly removed.As an example, we apply the model to silicon tetrafluoride SiF4.

Anharmonic force field and vibrational frequencies of tetrafluoromethane (CF4) and tetrafluorosilane (SiF4)

“…(3) In Table VIII our calculations are compared with those of the U (2) algebraic model. 36 Although the U (2) algebraic model yields a similar RMSD (0.79 cm −1 ), nine parameters were employed to fit the sixteen vibrational data. A fit of similar quality is also reported by the same authors 37 using a boson realization model.…”

“…McDowell and co-workers reported a partial set of anharmonicity constants as well. In recent theoretical work, the low lying vibrational spectrum of SiF 4 has been modeled 36,37 using an algebraic approach. 38 Patterson and Pine 39 determined B 0 ϭ0.136 76(3) cm Ϫ1 , whence r 0 ϭ1.559 82 (17) Å.…”

Fermi resonance-algebraic model for molecular vibrational spectra

“…In this approach the eigenvalues and the related wave functions are obtained through matrix diagonalization. Hence, the required computing time is short, and some other physical properties, such as transition intensities [5,11] , are allowed to calculate. It provides the possibility of using an algebraic model as a numerically efficient, phenomenological theory for studying molecular spectra, especially when no ab initio calculation is available.…”

Fermi Resonances and Vibrational Spectrum of a Polyatomic Molecule XY4: an Algebraic Approach

“…[3] Recently, an important development on algebraic approaches is to incorporate bending vibrations of polyatomic molecules. Sample molecules such as X 3 , [4] XY 2 , [5] and XY 4 [6] have been studied via algebraic methods. However, these approaches suffer from the neglect of Fermi resonances between the stretches and the bends.…”