Rupam Sen

Vibrational Frequencies of Buckminsterfullerene: An Algebraic Study

ABSTRACT Using Hamiltonian based on Lie Algebraic method, the normal vibrational modes of Buckminsterfullerene were calculated. The model appeared to describe Carbon-Carbon stretching modes with lower number of algebraic parameters. The dynamical symmetry group of icosahedron molecule was taken into consideration to construct the model Hamiltonian in this framework. Casimir and Majorana invariant operators were also determined accordingly.

Spectroscopic Analysis of C20 Isomers by the U(2) Algebraic Model

The vibrational energy levels of C20 isomers are calculated considering the local Hamiltonian of Morse potential using the U(2) Lie algebra. Here each bond of the molecule is replaced by a corresponding Lie algebra. Finally the local Hamiltonian is constructed considering the interacting Casimir and Majorana invariant operators. By constructing the Hamiltonian, we calculate the local mode vibrational energy levels of C20 isomers and thus compare the accuracy of algebraic model with PM3 model.

Application of U(2) Algebraic Model in the Study of Stretching Vibrational Spectra of Large Fullerenes C180 and C240

In this study, the Hamiltonian describing the stretching vibrational spectra of fullerenes C180 and C240 are calculated within the framework of the vibron model by using the dynamical U(2) Lie algebra. Here, every C-C bond of the molecule is replaced by a corresponding Lie algebra and finally the Hamiltonian is constructed considering the interacting Casimir and Majorana operators. The fundamental stretching vibrational energy levels of the carbon cluster C180 and C240 are then calculated using this Hamiltonian to fit the semi-empirical MNDO calculation.

Infrared-active Vibrational Modes of Fullerene C7O

Using the Lie algebraic method, the stretching fundamental IR active modes of vibrational energies of fullerenes C70 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 framework, we calculate the fundamental stretching IR active modes of vibration of fullerene C70 and compare the results with theoretical and experimental values to show the precision of algebraic model.

Stretching Vibrational IR Active Spectra of Carbon Fullerenes

Molecular vibration spectra are of great significance in the study of molecular structures and characters. Here, an analytical method of Lie algebraic approach is imported into the domain of micro-scaled molecular spectra. The vibrational modes of fullerenes C50, C70 and C80 are calculated considering the C-C bond interactions. The algebraic Hamiltonian describing vibrational spectra of polyatomic molecules has been derived by using the dynamical U(2) Lie algebra. The calculations are performed within the framework of the vibron model with fewer numbers of algebraic parameters. The calculations show a reasonable agreement with previously published calculated and experimental results.

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

The article is aimed at calculating the stretching vibrational spectra of fluorobenzene (C6H5F) using one-dimensional algebraic model. The Model Hamiltonian so constructed which seems to describe the C-C, C-F C-H, H-F stretching modes accurately using a relatively small set of well-defined parameters.

Vibrational IR Active Spectra of Stable Isomers of Fullerene C80

Using Hamiltonian-based Lie Algebraic method, the stretching vibrational IR active modes of two stable isomers of fullerene C80 are calculated. The model appears to describe fundamental stretching modes with less number of algebraic parameters. In this study, the dynamical symmetry group of Cs symmetry is taken into consideration to construct the model Hamiltonian. Casimir and Majorana invariant operators are also determined accordingly. The calculated energies find an excellent exactitude with the simulated PM3 model.

Theoretical Vibrational Spectra of Carbon Fullerenes

This article investigates the stretching vibrational modes of carbon fullerenes (C24, C28, C32, and C50) by using one-dimensional U(2) algebra. Considering the molecular symmetry, the model Hamiltonian is constructed which is able to describe the fundamental “stretching modes” of the physical system with less number of algebraic parameters. The calculated energies find an excellent agreement with the theoretical data of harmonic force constant calculation.

The Vibrational Spectra of Monomer and Dimer of Benzene: An Algebraic Approach

In this article, we calculate the different fundamental modes of benzene monomer and dimers using the algebraic method by considering the symmetry and Wilson numbering. The model Hamiltonian constructed describes the C‒C and C‒H stretching modes accurately with only four numbers of algebraic parameters. The present calculation not only predicts the different fundamental modes but also shows good agreement with the few observed DFT data.

Lie Algebraic Study of Infra-Red Active Spectra of Single-Layer Graphene

In this article, using Lie algebraic technique and the expressions of the matrix elements of Majorana and Casimir operators, we obtain an effective Hamiltonian operator, which conveniently describes some stretching infra-red active mode of vibrations of monolayer graphene model of 30 atoms. The model finds the accuracy in results of density functional theory.