Ukrainian Journal of Physical Optics


2025 Volume 26, Issue 4


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

SYMMETRY-ADAPTED LIE ALGEBRAIC FRAMEWORK FOR MODELING THE VIBRATIONAL MODES OF SULFUR HEXAFLUORIDE

Vijayasekhar Jaliparthi, Venkateswara Rao Mannepalli and Amal S. Alali

Author Information
1Vijayasekhar Jaliparthi ORCID logo , 2Venkateswara Rao Mannepalli ORCID logo , 3*Amal S. Alali ORCID logo
1Department of Mathematics and Statistics, School of Science, GITAM (Deemed to be University), Hyderabad-502329, India
2Department of Physics, School of Sciences, Woxsen University, Hyderabad, India
3Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
*Corresponding author: E-mail: asalali@pnu.edu.sa

ABSTRACT

The vibrational modes of sulfur hexafluoride (SF6) are analyzed using a symmetry-adapted U(2) Lie algebraic approach. In the context of Oh point group symmetry, the Hamiltonian constructed with Casimir and Majorana operators includes anharmonicity and intermode coupling. The fundamental modes, measured with high precision, show a very close match, with RMS deviations of less than 1 cm-1, aligning well with experimental data. The model also predicts the positions of combination bands and overtones to demonstrate its capabilities further. This method greatly enhances spectroscopic studies of atmospheric science compared to traditional approaches for modeling high-symmetry polyatomic molecules.

Keywords: Sulfur hexafluoride, vibrational modes, Hamiltonian, Casimir and Majorana operators

UDC: 539.17, 539.2, 530.12, 539.120.2

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    В роботі досліджені коливальні моди гексафториду сірки (SF6) за допомогою симетрично адаптованого алгебраїчного підходу Лі U(2). У контексті симетрії точкової групи Oh , гамільтоніан, сформований за допомогою операторів Казиміра та Майорани, включає ангармонізм та міжмодовий зв'язок. Фундаментальні моди демонструють високий рівень точності, зі середньоквадратичними відхиленнями менше одного см-1, що відмінно узгоджується з експериментальними значеннями. Модель також прогнозує розташування комбінаційних смуг та обертонів, щоб додатково продемонструвати її можливості. Цей метод робить значний внесок у спектроскопічні дослідження атмосферної науки, на відміну від традиційних підходів до моделювання поліатомних молекул з високою симетрією.

    Ключові слова: гексафторид сірки, коливальні моди, гамільтоніан, оператори Казиміра та Майорани

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