A Study of Vibrational Spectra of Fullerene C₇₀and C₈₀: An Algebraic Approach

Abstract

Using the Lie algebraic method, the stretching vibrational energies of fullerenes C 70 and C 80 are calculated in the one-dimensional U(2) framework. By constructing the model Hamiltonian with the help of Casimir and Majorana invariant operators in this frame work, we calculated the local mode vibrational energy levels of the fullerenes C 70 and C 80 .

Successful Applications of Lie Algebraic Model to Analyze the Vibrational Spectra of Fluorobenzene

“…As the dynamical algebra can be incorporated by the language of Lie algebra and thus after the introduction of U(2) Lie algebra to describe n stretching bonds, two possible chains of molecular dynamical groups of fluorobenzene are as (11)(12)(13):…”

“…According to the general algebraic description for one-dimensional degrees of freedom, a dynamically symmetric Hamiltonian operator for n interacting (not necessarily equivalent) oscillators of a polyatomic molecule in terms of Morse anharmonic oscillators by introducing the U(2) algebra for each bonds can be written as (8)(9)(10)(11)(12): where C i ,C ij , and M ij are the invariant algebraic operators. In the local basis the operators C i are the diagonal matrix with eigenvalues…”

Vibrational IR Active Frequencies of C36: an Algebraic Approach

“…In the onedimensional (2) model, the replacement of the interaction bond co-ordinates by a unitary algebra provides a specific formulation of the algebraic expressions of eigenvalues and eigenvectors of complex Hamiltonian operators, which also includes the intermode coupling term and the expectation values as well. Since the (4) algebra is very much complicated, when the number of molecules is more than four, we need to construct a simple version of the vibron model with (2) algebra that can be used for the vibrational analysis of polyatomic molecules [17].…”

A comparative study of the vibrational spectra of HCN in exact vibron model and in mean field approximation

“…Complex molecules are also being studied by the algebraic approach [8]. Different works are going on the Lie algebraic approach to study the different levels of molecular spectra [9][10][11][12][13][14][15][16]. But, in practice the vibron model also has a drawback.…”