Analyzing cyclobutane: A vibrational hamiltonian approach using dynamical U(2) Lie Algebras

Abstract

This study uses a one-dimensional Lie algebraic framework, precisely adapted to the symmetry of molecules, to investigate the vibrational frequencies of cyclobutane. A vibrational Hamiltonian is also constructed using one-dimensional Morse oscillators, preserving the D_2d point group symmetry for each molecule. The analysis compares the calculated fundamental vibrational frequencies with the observed experimental frequencies, resulting in a root mean square deviation of 0.886 cm^-1. The result highlights the exceptional precision of the U(2) Lie algebraic Hamiltonian in accurately predicting the vibrational frequencies and their combination bands at the sub-cm^-1 level of precision. Specifically, this computational approach has the potential to achieve these results with lower computational costs compared to traditional theoretical approaches. The broader implications of our study suggest that the U(2) Lie algebraic framework can be effectively applied to a wide range of molecular systems, offering significant advantages in fields such as material science, drug design, and environmental monitoring by providing precise and efficient vibrational spectral analyses.

KEY WORDS: Vibrational Hamiltonian, Vibrational frequencies, Morse oscillator, Cyclobutane, Lie algebraic method

Bull. Chem. Soc. Ethiop. 2024, 38(6), 1887-1896.                                                    

DOI: https://dx.doi.org/10.4314/bcse.v38i6.29