Vibrational IR Active Frequencies of C36: an Algebraic Approach
Keywords:Lie algebra, Hamiltonian, C36, dynamic symmetry
The one-dimensional U(2) Lie algebra is employed to calculate the structural and vibrational properties of C36. The lowest energy configuration of the C36 cage is confirmed to have D6ℎ symmetry. The Lie algebraic method is based on the idea of dynamic symmetry, which can be expressed in terms of U(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 findings.
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