On the numerical determination of Dunham’s coefficients: An application to X1Σ+HCl isotopomers

Vibrational Hamiltonian of tetrachloro-, tetrafluoro-, and mono- silanes using U(2) Lie algebras

In this paper, we have applied the symmetry adapted one-dimensional framework of the U(2) Lie algebras to estimate the vibrational frequencies of tetrachloro-, tetrafluoro-, and mono- silanes in the gas phase having the spectroscopic interest of terrestrial volcanic plumes and other planetary atmospheres. A vibrational Hamiltonian that preserves the T_d point group symmetry of each of these silane molecules is devised using ten interacting Morse oscillator bound state spectra. The calculated vibron numbers and locality parameters indicate that the vibrational motion is highly anharmonic in SiH₄ (nearest to local mode), moderately anharmonic in SiF₄ (mixed mode) and the least anharmonic in SiCl₄ (near to local mode). RMS deviations of the derived vibrational frequencies [0.41 cm^-1 (SiH₄), 0.83 cm^-1 (SiCl₄), and 0.63 cm^-1 (SiF₄)], with reference to their experimental counterparts, assert that the U(2) Lie algebraic Hamiltonian is successful in deriving all the fundamental vibrations, their higher overtones and combination bands up to the fifth excitation, of each of the three silane molecules at the sub-cm^-1 level of accuracy, possibly at a much lower computational cost as compared to other theoretical methods.