Lie Algebraic Modeling of Higher Overtone Vibrational Frequencies in PCl₅ and SbCl₅
Resumen
The third and fourth overtone vibrational frequencies of Phosphorus Pentachloride (PCl₅) and Antimony Pentachloride (SbCl₅), belonging to the D3h point group, have been studied using the symmetry-adapted Lie algebra technique. The vibrational Hamiltonian, incorporating Casimir and Majorana operators, provides both harmonic and anharmonic contributions, enabling the systematic calculation of higher-order vibrational excitations. The study demonstrates the effectiveness of the Lie algebraic method for modelling overtone structures of high-symmetry molecules. It elucidates the importance of vibrational analysis for PCl₅ and SbCl₅ in molecular spectroscopy and atmospheric chemistry.
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12. Jaliparthi, V. J. (2024). Analyzing cyclobutane: A vibrational hamiltonian approach using dynamical U(2) Lie Algebras. Bulletin of the Chemical Society of Ethiopia, 38(6), 1887–1896. https://doi.org/10.4314/bcse.v38i6.29
13. Teppala, S.; Jaliparthi, V. Exploring cyclohexane vibrational dynamics through a Lie algebraic Hamiltonian framework. Ukr. J. Phys. Opt. 2024, 25, 03093–03100
14. Vijayasekhar, J.; Suneetha, P.; Lavanya, K. Vibrational spectra of cyclobutane-d8 using symmetry-adapted one-dimensional Lie algebraic framework. Ukr. J. Phys. Opt. 2023, 24,193–199
15. S. Nallagonda, and V. Jaliparthi, “Higher Overtone Vibrational Frequencies in Naphthalene Using the Lie Algebraic Technique,” Ukr. J. Phys. Opt. 25(2), 02080–02085 (2024). https://doi.org/10.3116/16091833/Ukr.J.Phys.Opt.2024.02080
16. Vijayasekhar, J., Lavanya, K., & Phani Kumari, M. (2024). Vibrational Frequencies of Phosphorus Trichloride with the Vibrational Hamiltonian. East European Journal of Physics, (2), 407-410. https://doi.org/10.26565/2312-4334-2024-2-52
17. Lavanya, K., Rao, A. G., & Vijayasekhar, J. (2024). Vibrational Hamiltonian of Carbonyl Sulphide and Hydrogen Cyanide. East European Journal of Physics, (1), 432-435. https://doi.org/10.26565/2312-4334-2024-1-46
18. Jaliparthi, V., & Alali, A. (2025). Spectroscopic modelling of PCl₅ and SbCl₅ vibrations via Lie algebraic Hamiltonian with Casimir and Majorana operators. Ukrainian Journal of Physical Optics, 26, 03078–03087. https://doi.org/10.3116/16091833/Ukr.J.Phys.Opt.2025.03078
2. Malicka, M. I., Field, R. W., Ryzner, S., Stasik, A., Ubachs, W., Heays, A. N., de Oliveira, N., Szajna, W., & Hakalla, R. (2024). FT-spectroscopy of the ¹²C¹⁸O rare isotopologue and deperturbation analysis of the A¹Π(v = 3) level. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 312, 124011. https://doi.org/10.1016/j.saa.2024.124011
3. J. L. Dunham, The energy levels of a rotating vibrator, Physical Review 41 (1932), no. 6, 721–731. https://doi.org/10.1103/PhysRev.41.721.
4. Molski, M., & Konarski, J. (1992). Expansion of the rotational energy of diatomic molecules into a continued fraction. Acta Physica Polonica A, 81, 495–501. https://doi.org/10.12693/APhysPolA.81.495
5. Zheng, R., Zhang, Z., Wang, S., Li, X., Luo, W., Liu, Z., & Zhao, A. (2025). Potential energy surfaces and bound state calculations for the Kr–AgF complex: A detailed comparison between Ar–AgF and Kr–AgF complexes. Molecular Physics. https://doi.org/10.1080/00268976.2025.2550569
6. Wang, J. C., & Yu, Y. J. (2024). The theoretical study of the analytical potential energy functions, spectroscopic parameters and vibrational spectra of GeO molecules. Ferroelectrics, 618(9–10), 1742–1750. https://doi.org/10.1080/00150193.2024.2320560
7. Myatt, P. T., Dham, A. K., Chandrasekhar, P., McCourt, F. R. W., & Le Roy, R. J. (2018). A new empirical potential energy function for Ar2. Molecular Physics, 116(12), 1598–1623. https://doi.org/10.1080/00268976.2018.1437932
8. Guerroudj, A. R., Mughal, E. U., Naeem, N., Sadiq, A., Al-Fahemi, J. H., Asghar, B. H., Boukabcha, N., Chouaih, A., & Ahmed, S. A. (2024). Exploring pyrimidine-based azo dyes: Vibrational spectroscopic assignments, TD-DFT investigation, chemical reactivity, HOMO-LUMO, ELF, LOL and NCI-RDG analysis. Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, 313, 124093. https://doi.org/10.1016/j.saa.2024.124093
9. Menaria, G. L., Rani, U., Kamlesh, P. K., Rani, M., Singh, N., Sharma, D. C., & Verma, A. S. (2024). Comprehensive theoretical investigation of NaAlX (X = C, Si, and Ge) half-Heusler compounds: Unveiling the multifaceted properties for advanced applications. International Journal of Modern Physics B, 39(7), 2550052. https://doi.org/10.1142/S02179792255005
10. F. Iachello, and R.D. Levine, Algebraic theory of molecules, (Oxford University Press, Oxford, 1995).
11. S. Oss, “Algebraic models in molecular spectroscopy,” in: Advances in Chemical Physics: New Methods in Computational Quantum Mechanics, edited by I. Prigogine, and S.A. Rice, vol. 93, (John Wiley & Sons, Inc., 1996). pp. 455 649. https://doi.org/10.1002/9780470141526.ch8
12. Jaliparthi, V. J. (2024). Analyzing cyclobutane: A vibrational hamiltonian approach using dynamical U(2) Lie Algebras. Bulletin of the Chemical Society of Ethiopia, 38(6), 1887–1896. https://doi.org/10.4314/bcse.v38i6.29
13. Teppala, S.; Jaliparthi, V. Exploring cyclohexane vibrational dynamics through a Lie algebraic Hamiltonian framework. Ukr. J. Phys. Opt. 2024, 25, 03093–03100
14. Vijayasekhar, J.; Suneetha, P.; Lavanya, K. Vibrational spectra of cyclobutane-d8 using symmetry-adapted one-dimensional Lie algebraic framework. Ukr. J. Phys. Opt. 2023, 24,193–199
15. S. Nallagonda, and V. Jaliparthi, “Higher Overtone Vibrational Frequencies in Naphthalene Using the Lie Algebraic Technique,” Ukr. J. Phys. Opt. 25(2), 02080–02085 (2024). https://doi.org/10.3116/16091833/Ukr.J.Phys.Opt.2024.02080
16. Vijayasekhar, J., Lavanya, K., & Phani Kumari, M. (2024). Vibrational Frequencies of Phosphorus Trichloride with the Vibrational Hamiltonian. East European Journal of Physics, (2), 407-410. https://doi.org/10.26565/2312-4334-2024-2-52
17. Lavanya, K., Rao, A. G., & Vijayasekhar, J. (2024). Vibrational Hamiltonian of Carbonyl Sulphide and Hydrogen Cyanide. East European Journal of Physics, (1), 432-435. https://doi.org/10.26565/2312-4334-2024-1-46
18. Jaliparthi, V., & Alali, A. (2025). Spectroscopic modelling of PCl₅ and SbCl₅ vibrations via Lie algebraic Hamiltonian with Casimir and Majorana operators. Ukrainian Journal of Physical Optics, 26, 03078–03087. https://doi.org/10.3116/16091833/Ukr.J.Phys.Opt.2025.03078
Publicado
2025-12-21
Sección
Mathematics and Computing - Innovations and Applications (ICMSC-2025)
Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática
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