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.
Downloads
References
I.S. Butler, R.P. Kengne-Momo, G. Jaouen, C. Policar, and A. Vessières, “Recent Analytical Applications of Molecular Spectroscopy in Bioorganometallic Chemistry—Part I: Metal Carbonyls,” Appl. Spectrosc. Rev. 47(7), 531–549 (2012). https://doi.org/10.1080/05704928.2012.673189
I.S. Butler, R.P. Kengne-Momo, A. Vessières, G. Jaouen, and C. Policar, “Recent Applications of Molecular Spectroscopy in Bioorganometallic Chemistry–Part 2: Ferrocenes and Other Organometallic Complexes,” Appl. Spectrosc. Rev. 47(8), 620–632 (2012). https://doi.org/10.1080/05704928.2012.697088
S. Brodersen, and J.-E. Lolck, “Calculation of rotation-vibrational energies directly from an anharmonic potential function,” J. Mol. Spectrosc. 126(2), 405-426 (1987). https://doi.org/10.1016/0022-2852(87)90246-3
P.T. Panek, A.A. Hoeske, and C.R. Jacob, “On the choice of coordinates in anharmonic theoretical vibrational spectroscopy: Harmonic vs. anharmonic coupling in vibrational configuration interaction,” J. Chem. Phys. 150(5), 054107 (2019). https://doi.org/10.1063/1.5083186
K.B. Beć, J. Grabska, and C.W. Huck, “Current and future research directions in computer-aided near-infrared spectroscopy: A perspective,” Spectrochim. Acta A. 254, 119625 (2021). https://doi.org/10.1016/j.saa.2021.119625
G. Pitsevich, and A. Malevich, “Symmetry properties, tunneling splittings of some vibrational energy levels and torsional IR spectra of the trans- and cis-conformers of hydroquinone molecule,” J. Mol. Spectrosc. 404, 111937 (2024). https://doi.org/10.1016/j.jms.2024.111937
G. Pandimeena, T. Mathavan, E.J.J. Samuel, and A.M.F. Benial, “Quantum chemical, spectroscopic and molecular docking studies on methyl 2-chloro-6-methyl pyridine-4-carboxylate: A potential inhibitor for irritable bowel syndrome,” Spectrochim. Acta Part A: Mol. Biomol. Spectrosc. 294, 122544 (2023). https://doi.org/10.1016/j.saa.2023.122544
A.V. Nikitin, A. Campargue, A.E. Protasevich, M. Rey, K. Sung, and Vl.G. Tyuterev, “Analysis of experimental spectra of phosphine in the Tetradecad range near 2.3 μm using ab initio calculations,” Spectrochim. Acta Part A: Mol. Biomol. Spectrosc. 302, 122896 (2023). https://doi.org/10.1016/j.saa.2023.122896
I.M. Chandramalar, and V.P. Subhasini, “Vibrational spectroscopic analysis of 2,3:4,5-Bis-O-(1-methylethylidene)beta-D-fructopyranose Sulfamate (Topiramate) by density functional method,” Spectrochim. Acta Part A: Mol. Biomol. Spectrosc. 302, 122997 (2023). https://doi.org/10.1016/j.saa.2023.122997
V. Jaliparthi, “Vibrational Energies of Silylene, Difluorosilylene and Dichlorosilylene, Using U(2) Lie Algebraic Model,” Ukr. J. Phys. Opt. 23(3), 126-132 (2022). https://doi.org/10.3116/16091833/23/3/126/2022
A.G. Rao, K. Lavanya, and J. Vijayasekhar, “Higher Overtone Vibrational Frequencies of Cyclobutane-D8 Using Lie Algebraic Framework,” East Eur. J. Phys. (2), 411-415 (2024). https://doi.org/10.26565/2312-4334-2024-2-53
J. Vijayasekhar, P. Suneetha, and K. Lavanya, “Vibrational spectra of cyclobutane-d8 using symmetry-adapted one-dimensional Lie algebraic framework,” Ukr. J. Phys. Opt. 24, 193-199 (2023). https://doi.org/10.3116/16091833/24/3/193/2023
F. Iachello, and R.D. Levine, Algebraic theory of molecules, (Oxford University Press, Oxford, 1995).
S. Oss, “Algebraic models in molecular spectroscopy,” Adv. Chem. Phys. 93, 455-649 (1996).
T. Sreenivas, and J. Vijayasekhar, “Exploring Cyclohexane Vibrational Dynamics Through a Lie Algebraic Hamiltonian Framework,” Ukr. J. Phys. Opt. 25(3), 03093-03100 (2024). https://doi.org/10.3116/16091833/Ukr.J.Phys.Opt.2024.03093
Copyright (c) 2025 M.V. Subba Rao, T. Sreenivas, J. Vijayasekhar
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
