A unified algebraic model description for interacting vibrational modes in ABA molecules

Abstract

A simple yet realistic model Hamiltonian which describes the essence of many aspects of the interaction of vibrational modes in polyatomics is discussed. The general form of the Hamiltonian is that of an intermediate case between the purely local mode and purely normal mode limits. Resonance interactions of the Fermi and Darling–Dennison types are shown to be special cases. The classical limit of the Hamiltonian is used to provide a geometrical content for the model and to illustrate the ‘‘phase-like’’ transition between local and collective (i.e., normal) mode behavior. Such transitions are evident as the coupling parameters in the Hamiltonian are changed and also for a given Hamiltonian as the energy is changed. Applications are provided to higher lying vibrational states of specific molecules (H2O, O3, SO2, C2H2, and C2D2).

A General Algebraic Model for Molecular Vibrational Spectroscopy

“…10,19) It should be noted that for most calculations, higher order terms are required in the Hamiltonian (2.14) in order to attain higher accuracy, as we shall see in the following sections. The physical interpretation of these interactions will also be explained.…”

“…This difficulty can be surmounted by treating the vibrational degrees of freedom separately from the rotations. In 1984 Van Roosmalen et al proposed a U(2)-based model to describe the stretching vibrational modes in ABA molecules, 10) later extended to describe the stretching vibrations of polyatomic molecules such as octahedral and benzene like molecules. 11) Recently the bending modes have also been incorporated to the framework, which was then applied to describe C 2v -triatomic molecules 12) and the lower excitations of tetrahedral molecules, 13) using a scheme which combines Lie-algebraic and point group methods.…”

Boson-realization model for the vibrational spectra of tetrahedral molecules

“…The first step toward the establishment of an algebraic approach was given by Iachello, Levine and their co-workers [2] with the vibron model, where the rotationvibration spectra of diatomic molecules are described in terms of a u(4) algebra. Although this model was extended [3] to polyatomic molecules by introducing a u(4) algebra for each bond, it is rather difficult to apply when the number of atoms in the molecule becomes larger than four [4].…”

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].…”