A comparative study of the vibrational spectra of OCS and HCP using the Lie algebraic method

Sarkar, Nirmal Kumar; Choudhury, Joydeep; Karumuri, Srinivasa Rao; Bhattacharjee, Ramendu

doi:10.1140/epjd/e2009-00094-8

Cited by 28 publications

(10 citation statements)

References 24 publications

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“…8 For diatomic molecules, accurate information on force fields is available now. [9][10][11][12] But in case of polyatomic molecules, the knowledge of force fields is poor due to large number of force constants. The potential may be modeled by representing the anharmonicity of bonds by a sum of anharmonic Hamiltonian; among these Morse potential is most commonly used.…”

Section: Theoretical Lie Algebraic Methodsmentioning

confidence: 99%

Vibrational Spectra of Copper Oxides—Synthesis, Characterization and Theoretical Reconsideration by Lie Algebra

Thakurata¹,

Kalyan²,

Sen³

et al. 2014

Jnl of Comp & Theo Nano

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In this paper, we have reported the vibrational spectra (FTIR) of Copper (I) Oxide and Copper (II) oxide. Both the compounds are synthesized in the laboratory by maintaining standard chemical procedure. We have also analysed these spectra theoretically by using the U(2) algebraic model based on the dynamic symmetry of the molecules. In this framework, the Hamiltonian is constructed considering the interacting Casimir and Majorana operators, replacing every inter atomic bonds of the molecules by a corresponding Lie algebra. Finally the fundamental stretching vibrational energy levels of the transition metal (Copper) oxides are calculated using this model Hamiltonian in one dimensional algebraic framework. Here, we have tried to authenticate the experimental findings by theoretical model.

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Section: Theoretical Lie Algebraic Methodsmentioning

confidence: 99%

Vibrational Spectra of Copper Oxides—Synthesis, Characterization and Theoretical Reconsideration by Lie Algebra

Thakurata¹,

Kalyan²,

Sen³

et al. 2014

Jnl of Comp & Theo Nano

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“…where  e and  e x e are the spectroscopic constants of diatomic molecules [30][31][32][33]. The value of N must be as initially guessed from the Equation (7); however one can expect changes in an estimated N, not be larger than ± 20% of the original value.…”

Section: Resultsmentioning

confidence: 99%

A Study on Vibrational Spectra of PH3 and NF3: An Algebraic Approach

Karumuri¹,

Gadipelli²,

Jaliparthi³

et al. 2013

OJM

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“…This is equivalent to change the single bond anharmonicity according to the specific molecular environment [25]. …”

Section: Estimation Of the Algebraic Parametersmentioning

confidence: 99%

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

Acharjee¹,

Sen²,

Mohanta

2017

Can. J. Phys.

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The aim of this work is to study the highly excited vibrational states of Hydrogen Cyanide HCN in exact vibron model and with mean field approximation in vibron model. Considering the     44 UU  spectrum generating algebra for linear triatomic molecules the standard Hamiltonian is constructed by the linear and quadratic combination of Casimir operators. For higher order correction, the quadratic contributions of Casimir operators are used to construct the Hamiltonian. Using this Hamiltonian the higher excited vibrational levels of HCN are calculated in local mode approximation. The energy levels are observed as a function of vibron number N. The best fit is obtained for N=184 (N1= 139, N2=45) with r.m.s. deviation 5.598 cm-1. The intermodal coupling within the same polyad is studied and addressed properly by introducing Majorana operator. The r.m.s. deviation is then reduced to 4.755 cm -1 . The modification is negligible which indicates the local nature of HCN. In this work, 35 experimental levels are taken for fit. Out of which only two sets of levels are accidentally degenerate. The Fermi resonances of the accidentally degenerate levels are studied using the Fermi operator and r.m.s. deviation becomes 4.835. The coefficient of Majorana and Fermi coupling for different levels are obtained by diagonalzing the Majorana and Fermi matrices for each polyad. The Majorana and Fermi matrices for each polyad are diagonalized with MATRIX CALCULATOR program. The algebraic parameters are evaluated by a least square fit against the experimental data using MATLAB R2015a. Using this model, a set of energy levels is predicted up to 30000cm-1, with a very good accuracy.HCN is chosen for this study, because, it's vibrational states can be fairly described without any modification due to Fermi resonance. The fundamental vibrational levels of HCN are again calculated, using mean field approximation (MFA) and compared them to that are obtained using vibron model. A good agreement is observed.

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A comparative study of the vibrational spectra of OCS and HCP using the Lie algebraic method

Cited by 28 publications

References 24 publications

Vibrational Spectra of Copper Oxides—Synthesis, Characterization and Theoretical Reconsideration by Lie Algebra

Vibrational Spectra of Copper Oxides—Synthesis, Characterization and Theoretical Reconsideration by Lie Algebra

A Study on Vibrational Spectra of PH3 and NF3: An Algebraic Approach

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

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