A study of the bending motion in tetratomic molecules by the algebraic operator expansion method

Abstract

We study the bending motion in the tetratomic molecules C2H2 (\documentclass[12pt]{minimal}\begin{document}$\tilde{X}$\end{document}X̃ \documentclass[12pt]{minimal}\begin{document}$^1 \Sigma _g^+$\end{document}Σg+1), C2H2 (\documentclass[12pt]{minimal}\begin{document}$\tilde{A}$\end{document}Ã 1Au) trans-S1, C2H2 (\documentclass[12pt]{minimal}\begin{document}$\tilde{A}$\end{document}Ã 1A2) cis-S1, and \documentclass[12pt]{minimal}\begin{document}$\tilde{X}$\end{document}X̃ 1A1 H2CO. We show that the algebraic operator expansion method with only linear terms comprised of the basic operators is able to describe the main features of the level energies in these molecules in terms of two (linear) or three (trans-bent, cis-bent, and branched) parameters. By including quadratic terms, the rms deviation in comparison with experiment goes down to typically ∼10 cm−1 over the entire range of energy 0–6000 cm−1. We determine the parameters by fitting the available data, and from these parameters we construct the algebraic potential functions. Our results are of particular interest in high-energy regions where spectra are very congested and conventional methods, force-field expansions or Dunham-expansions plus perturbations, are difficult to apply.