Lie Algebraic Modeling of Vibrational Frequencies in Hexachlorobenzene: A Symmetry-Adapted Approach for the D₆ₕ Point Group
Abstract
This work uses a symmetry-adapted Lie algebraic framework to study the vibrational frequencies of hexachlorobenzene (C₆Cl₆). A U(2)-based vibrational Hamiltonian captures the fundamental modes and the first and second overtones by exploiting the molecule's D6h point group symmetry. The algebraic approach considers anharmonicity and symmetry constraints to provide a compact and manageable analytical portrayal of the vibrational spectrum. The computed fundamental frequencies agree strongly with the observed values, validating the approach. Moreover, the extension to overtones underlines the algebraic model's capability to evaluate higher-order vibrational excitations in polyatomic molecules systematically. These results confirm the effectiveness of Lie algebraic methods in modelling vibrational features of highly symmetric molecules and serve as a solid basis for further work in molecular spectroscopy.
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