Ukrainian Journal of Physical Optics


2023 Volume 24, Issue 3


ISSN 1816-2002 (Online), ISSN 1609-1833 (Print)

Vibrational spectra of cyclobutane-d8 using symmetry-adapted one-dimensional Lie algebraic framework

1Vijayasekhar J., 1,2Suneetha P. and 1,3Lavanya K.

1Department of Mathematics, School of Science, GITAM (Deemed to be University), Hyderabad, India. e-mail: vijayjaliparthi@gmail.com
2Department of Mathematics, V. R. Siddhartha Engineering College, Vijayawada, India
3Department of Mathematics, St. Francis College for Women, Begumpet, Hyderabad, India

ABSTRACT

We use a one-dimensional U(2) Lie algebraic model to study fundamental and first-overtone vibrational frequencies, as well as their combination bands for cyclobutane-d8, C4D8. The model preserves the point symmetry group D2d, with the symmetry species A1, A2, B1, B2 and E, and involves 23 normal vibrational modes. A comparison of the calculated vibrational frequencies and the available reference data results in the root-mean-square deviation as small as 1.557 cm-1.

Keywords: vibrational Hamiltonian, Morse oscillator, U(2) Lie algebras, cyclobutane-d8

UDC: 535.333

    1. Oss S, 1996. Algebraic models in molecular spectroscopy. Adv. Chem. Phys. 93: 455-649. doi:10.1002/9780470141526.ch8
    2. Iachello F and Levine R D. Algebraic Theory of Molecules. Oxford: Oxford University Press, 1995. doi:10.1093/oso/9780195080919.001.0001
    3. Frank A, Lemus R, Bijker R, Péilez Bernal F and Arias J M, 1996. A general algebraic model for molecular vibrational spectroscopy. Ann. Phys. 252: 211-238. doi:10.1006/aphy.1996.0129
    4. Choudhury J, Karumuri S R, Rupali Sinha, Sarkar N K and Bhattacharjee R, 2010. Vibrational spectra of H2O and CF4 molecules using Lie algebraic approach. Indian J. Phys. 84: 659-664. doi:10.1007/s12648-010-0067-2
    5. Srinivasa Rao K and Girija Sravani K, 2016. Calculation of vibrational spectra of some tetraphenyl porphyrins. Mol. Phys. 114: 643-649. doi:10.1080/00268976.2015.1110628
    6. Balla M R and Vijayasekhar J, 2021. Vibrational Hamiltonian of methylene chloride using U(2) Lie algebra. Mol. Phys. 115: e1828634. doi:10.1080/00268976.2020.1828634
    7. Balla M R, Venigalla S and Vijayasekhar J, 2021. Calculation of vibrational frequencies of sulfur dioxide by Lie algebraic framework. Acta Phys. Polon. A. 140: 138-140. doi:10.12693/APhysPolA.140.138
    8. Vijayasekhar J, 2022. Vibrational energies of silylene, difluorosilylene and dichlorosilylene, using U(2) Lie algebraic mode. Ukr. J. Phys. Opt. 23: 126-132. doi:10.3116/16091833/23/3/126/2022
    9. Lord R C and Nakagawa I, 1963. Normal vibrations, potential constants, and vibration-rotation interaction constants in cyclobutane and cyclobutane‐d8. J. Chem. Phys. 39: 2951-2965. doi:10.1063/1.1734128
    10. Miller F A and Capwell R J, 1971. The ring-puckering vibration of cyclobutane and cyclobutane-d8 in their gas phase Raman and infrared spectra. Spectrochim. Acta A. 27: 947-956. doi:10.1016/0584-8539(71)80177-0
    11. Miller F A, Capwell R J, Lord R C and Rea D G, 1972. Infrared and Raman spectra of cyclobutane and cyclobutane-d8. Spectrochim. Acta A. 28: 603-618. doi:10.1016/0584-8539(72)80029-1
    12. Bijker R, Frank A, Lemus R, Arias J M and Pérez-Bernal F, 1998. A comparison between algebraic models of molecular spectroscopy. In: Symmetries in Science X, Ed. by Gruber B and Ramek M (Boston: Springer). pp. 37-46. doi:10.1007/978-1-4899-1537-5_2
    13. Balla M R and Vijayasekhar J, 2022. Vibrational Hamiltonian of naphthalene (C10H8) using dynamical U(2) Lie algebras. Polycycl. Aromat. Compd. 42: 4684-4699. doi:10.1080/10406638.2021.1901126
    14. Vijayasekhar J and Balla M R, 2022. Vibrational Hamiltonian of tetrachloro-, tetrafluoro-, and mono-silanes using U(2) Lie algebras. Spectrochim. Acta A. 264: 120289. doi:10.1016/j.saa.2021.120289
    15. Irikura K K, 2007. Experimental vibrational zero-point energies: diatomic molecules. J. Phys. Chem. Ref. Data. 36: 389-397. doi:10.1063/1.2436891
    16. Shimanouchi T, 1972. Tables of Molecular Vibrational Frequencies Consolidated, National Bureau of Standards. Vol. I: pp. 1-60. doi:10.6028/NBS.NSRDS.39

    У цій статті ми використовуємо одновимірну U(2) алгебраїчну модель Лі для дослідження основних коливальних частот першого обертону та їх комбінованих смуг циклобутану-d8 (C4D8), який має точкову групу симетрії D2d із незвідними представленнями A1, A2, B1, B2 і E і складається з 23 нормальних коливальних мод. Проведено порівняння між розрахованими частотами коливань і доступними довідковими даними, і виявлено, що середньоквадратичне відхилення становить 1,5566 см-1.

    Ключові слова: коливальний гамільтоніан, осцилятор Морзе, U(2) алгебра Лі, циклобутан-d8

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