Analysis of Higher Overtone Vibrational Frequencies in Cyclohexane Using a Lie Algebraic Approach

Abstract

This study contains a sophisticated computational approach to predict cyclohexane while maintaining the D3d point group symmetry higher overtone vibrational frequencies (C6H12), precisely, third, fourth, and fifth. We utilize a Lie algebraic approach within the context of the vibrational Hamiltonian. The method uses cyclohexane's carbon-hydrogen (C-H) and carbon-carbon (C-C) bonds as unitary Lie algebras, accurately modelling the molecular vibrational structure. Thus, the vibrational Hamiltonian takes Casimir and Majorana's invariant operators and parameters and successfully outlines the molecules' vibrational modes. This Lie algebraic approach clearly outlined cyclohexane's higher overtone vibrational dynamics and provided helpful information that can be applied in other fields of study and technology.

Keywords

• lie algebraic approach
• vibrational frequencies
• vibrational hamiltonian
• cyclohexane