Higher Overtone Vibrational Frequencies of Cyclobutane-D8 Using Lie Algebraic Framework

This research study employs a Lie algebraic framework to investigate the second and third overtone vibrational frequencies and their combination bands in cyclobutane-d8 (C4D8). The application of this framework ensures the preservation of the point symmetry group D2d, characterized by the symmetry species A1, A2, B1, B2, and E. The analysis encompasses 23 normal vibrational modes within the molecular structure of cyclobutane-d8. Our study extensively explores the vibrational spectra, elucidating the intricate interactions among these vibrational modes. Preserving molecular symmetry allows for a deeper understanding of vibrational interactions, offering valuable insights into spectroscopy. The research enhances the comprehension of molecular structure and its applications in various fields, providing a detailed view of higher energy levels and complex vibrational transitions in cyclobutane-d8.