Algebraic approach to molecular rotation-vibration spectra. II. Triatomic molecules

Abstract

The algebraic approach to molecular rotation-vibration spectra introduced in a previous article is extended from di-to tri-and polyatomic molecules. The spectrum generating algebra appropriate to triatomic molecules U(4) ® U(4) is explicitly constructed. Its dynamical symmetries and their relation to rigid, nonrigid, linear, and nonlinear structures are discussed. Applications to the spectra of HCN, CO 2 , and Hj are considered. In particular, it is shown that the algebraic description can account for the Fermi resonances occurring in CO 2 , Some remarks are made on the spectrum generating algebras appropriate to polyatomic molecules.

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

“…U(4) and U(2) algebraic model have mostly been used so far in the analysis of experimental data. U(4) model [5,6] takes the rotation and the vibration into account simultaneously but becomes quite complex when the number of atoms in the molecules becomes larger than 4, while U(2) model is particularly well suited for dealing with the stretching vibrations of polyatomic molecules such as the octahedral and benzene-like systems [7,8]. Those two models are still extensively used for small molecules [9,10].…”

A Study on Vibrational Spectra of PH3 and NF3: An Algebraic Approach

“…On the other hand, the U(2) model introduced by Wulfman and Levine [3] is found to be successful in explaining the stretching vibrations of polyatomic molecules such as tetrahedral, octahedral, Icosahedral, and benzene-like molecules. The brief review and the research work done with the algebraic models up to the year 2000 and its outlook and perception in the first decade of the 21st century was presented by Iachello and Oss [4][5][6][7]. Recently, it is found that Lie algebraic method [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] is extremely successful and accurate in calculating the vibrational frequencies of polyatomic molecules compare to the other methods such as Dunham expansion and potential approach method reported earlier.…”

Vibrational Spectroscopy of H2O by Lie Algebraic Methods

“…This new model seems to oer a concrete and complementary technique to the traditional approaches used in molecular spectroscopy. The algebraic model (vibron model) originally developed for diatomic and tri-atomic molecules [3,4]. U(4) and U(2) algebraic models have been used so far in the analysis of experimental data.…”