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Current issue   Ukr. J. Phys. 2017, Vol. 62, N 8, p. 661-665
https://doi.org/10.15407/ujpe62.08.0661    Paper

Choudhury M.D., Sen R., Sharma B.I.

Department of Physics, Assam University
(Silchar, Assam, India; e-mail: rupamsen@sscollegehkd.ac.in)

Vibrational IR Active Frequencies of C36: an Algebraic Approach

Section: Atoms and Molecules
Original Author's Text: Ukrainian

Abstract: The one-dimensional (2) Lie algebra is employed to calculate the structural and vibrational properties of C36. The lowest energy confguration of the C36 cage is confrmed to have
symmetry. The Lie algebraic method is based on the idea of dynamic symmetry, which can be
expressed in terms of (2) Lie algebra. By applying the algebraic techniques, a local Hamiltonian, which conveniently describes the rovibrational degrees of freedom of the physical system,
can be obtained. In this technique, the Hamiltonian is constructed, by considering the invariant
Casimir and Majorana operators replacing every bond of the molecule by a corresponding Lie
algebra. At the same time, the fundamental stretching vibrational energy levels of the molecule
C36 are calculated. Finally, the calculated results are compared with other theoretical fndings.

Key words: Lie algebra, Hamiltonian, C36, dynamic symmetry.

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