Vibrational Hamiltonian of methylene chloride using U(2) Lie algebra

Abstract

This paper is the first to demonstrate the application of U(2) Lie algebraic Hamiltonian in reproducing and predicting the vibrational energy levels of an asymmetric penta-atomic molecule – methylene chloride (CH₂Cl₂) – having odorant properties similar to ether in the gas phase. The results indicated that the U(2) Lie algebraic Hamiltonian is successful in realising seven of the nine fundamental (stretching and bending) vibrational modes of CH₂Cl₂ observed experimentally. The lowest, highest, and RMS deviations of the derived vibrational fundamental frequencies stand, respectively, within 0.006%, 0.23%, and 0.7075 cm⁻¹ of the experimental values suggested that the proposed model is successful in predicting the experimental results at the realised fundamental mode vibrations. This study also suggests that further research is needed to make the U(2) Lie algebraic Hamiltonian more robust so as to accommodate for the unrealised out-of-the-plane complex bending vibrational modes of CH₂Cl₂ molecule. GRAPHICAL ABSTRACT