Can we precisely predict the vibrations of essential molecules? This study investigates the vibrational frequencies of carbonyl sulphide (12C16O32S) and hydrogen cyanide (HCN) up to the fifth harmonic level. Using the Hamiltonian operator formalism and a one-dimensional Lie algebraic method, the research offers comprehensive insights into vibrational modes. It focuses on invariant operators and algebraic parameters to understand the molecular dynamics of these compounds. Ultimately, the findings are significant for atmospheric chemistry, spectroscopy, and quantum chemistry, contributing to a deeper understanding of molecular dynamics. This research sets the groundwork for future studies in comparable compounds and applications.
Published in the East European Journal of Physics, this research aligns with the journal's coverage of theoretical and experimental physics. By providing detailed calculations and analysis of vibrational frequencies, the study contributes to fundamental knowledge in molecular physics and spectroscopy.