Lie-algebraic approach to vibrational spectra of a linear symmetrical tetratomic molecule:C2H2

Abstract

Using Lie-algebraic techniques and the simpler expressions of the matrix elements of Majorana operators given by us, we obtain an effective Hamiltonian operator which conveniently describes vibrational spectra of linear tetratomic molecules, including both stretching and bending modes. For a linear symmetrical four-atom molecule ${\mathrm{C}}_{2}{\mathrm{H}}_{2},$ the highly excited vibrational levels are obtained by applying the $\mathrm{u}(4)$ algebraic approach. We have found that the spectra are made up of a clustering structure. The number of levels in one cluster depends on the total quantum number of stretching and bending vibrations. In addition, some other properties, such as the level assignment and the labeling of calculated theoretical results, are also discussed.