Nirmal Kumar Sarkar

An algebraic approach to the study of the vibrational spectra of HCN

Using Lie algebra the vibrational energy levels of HCN were calculated using the local Hamiltonian for 35 vibrational bands. A comparative study was made with earlier results.

An algebraic approach to the comparative study of the vibrational spectra of monofluoroacetylene (HCCF) and deuterated acetylene (HCCD)

Using the Lie algebraic method the vibrational energy levels of HCCF and HCCD are calculated for 102 and 110 vibrational bands, respectively, using the local Hamiltonian. A comparative study is made between the two. Better results are obtained than those published earlier from local mode analysis.

Vibrational spectroscopy of Cm–H, C β –C β stretching vibrations of Nickel metalloporphyrins: An algebraic approach

An algebraic model of coupled anharmonic oscillators is introduced, capable of describing the stretching vibrations of medium and large polyatomic molecules. This model is applied to the calculation of Cm–H and C β –C β vibrational modes of nickel octaethyl porphyrins and nickel porphyrins molecules. The model appears to describe the data accurately.

Vibrational Spectroscopy of CH/CD Stretches in Propadiene: An Algebraic Approach

Using Hamiltonian based on Lie algebraic method, the stretching vibrational modes of C3H4 and C3D4 molecules are calculated up to higher overtones. The model appears to describe C–H and C–D stretching modes with less number of parameters. The locality parameter & confirms the highly local behaviour of the stretching modes of these molecules.

Vibrational Spectroscopy of Stretching and Bending Modes of Nickel Tetraphenyl Porphyrin: an Algebraic Approach

We calculate the vibrational frequencies of nickel tetraphenyl porphyrin for 36 vibrational bands by using the U(2) algebraic approach. The algebraic parameters in the calculations are accurate with the experimental data.

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.