Vibrational Frequencies of Dichlorodifluoromethane Using a Lie Algebraic Framework
Abstract
This study introduces a symmetry-adapted Lie algebraic framework, a highly efficient tool for calculating vibrational frequencies in dichlorodifluoromethane (CCl₂F₂). With its C2v point group symmetry, the molecule under consideration is particularly suited for this approach. By formulating carbon-hydrogen(C-H) and carbon-chlorine (C-Cl) bond structures in unitary Lie algebras, the determination of the vibrational quantum states of the molecule becomes remarkably straightforward. The Hamiltonian, including Casimir and Majorana invariant operators and fitted parameters, accurately reproduces the desired vibrational modes using fundamental and higher overtone frequencies. This approach, which compares modern and classical models, underscores the Lie algebraic techniques as efficient tools for modelling anharmonic interactions and transition dynamics on a molecular scale. Beyond its theoretical relevance, the model constructed provides a deep understanding of the vibrational aspects of molecules, a knowledge crucial for practical applications such as spectroscopic data interpretation, the design of materials with desired vibrational characteristics, or the study of molecules in complex environments. These practical applications enhance the versatility of the methodology and have enabled its successful application to molecular spectroscopy, chemical kinetics, and the design of energy-efficient materials and sensors, among other areas. This study provides experimentalists with confidence in the Lie algebraic approach and paves the way for further polyatomic molecule experiments. By significantly contributing to reducing the error margin in computational molecular physics, this methodology opens exciting possibilities for future research and development
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