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

2017 ◽  
Vol 95 (2) ◽  
pp. 130-135 ◽  
Author(s):  
Mahua Acharjee ◽  
Rupam Sen ◽  
Bidhan Mohanta
Keyword(s):  
Energy Levels ◽  
Mean Field ◽  
Field Approximation ◽  
Fermi Resonance ◽  
Mean Field Approximation ◽  
Local Mode ◽  
Vibrational States ◽  
Fermi Operator ◽  
Vibrational Levels ◽  
Casimir Operators

The aim of this work is to study the highly excited vibrational states of hydrogen cyanide HCN in the exact vibron model and with mean field approximation in the vibron model. Considering the U(4) ⊗ U(4) spectrum-generating algebra for linear triatomic molecules, the standard Hamiltonian is constructed using the linear and quadratic combination of Casimir operators. For higher order corrections, 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 the 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 root mean square (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 the 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 30 000 cm−1, with very good accuracy. HCN is chosen for this study, because, its 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 and compared to those obtained using the vibron model. A good agreement is observed.

The vibrational spectra of carbon dioxide and nitrous oxide: A Lie algebraic study

2018 ◽  
Vol 96 (5) ◽  
pp. 560-565
Author(s):  
Mahua Acharjee ◽  
Joydeep Choudhury ◽  
Rupam Sen ◽  
Bidhan Mohanta
Keyword(s):  
Carbon Dioxide ◽  
Nitrous Oxide ◽  
Mean Field ◽  
Field Approximation ◽  
Interaction Parameters ◽  
Mean Field Approximation ◽  
Symmetry Type ◽  
Vibrational Levels ◽  
Accidental Degeneracy ◽  
The Mean

The infrared vibrational levels of nitrous oxide (N2O) and carbon dioxide (CO2) are studied in the framework of Lie algebra. The aim of this work is to compare the frequency obtained in two algebraic models: “the vibron model” and “the mean field approximation of the vibron model”. To compare the two models we choose two triatomic molecules: CO2 of symmetry type D∞h and N2O of symmetry type C∞v. To construct the energy levels in the vibron model, the vibron numbers N for the two molecules are estimated from the harmonic frequency and the anharmonicity constant. After the proper estimation of N, the algebraic interaction parameters for both the molecules are evaluated against a least square fit with the experimental values using MATLAB R2015. Using the algebraic interaction parameters, the vibrational frequencies for the two molecules are calculated. Because CO2 is a linear symmetric triatomic molecule, the higher vibrational levels are largely affected by the mode mixing due to accidental degeneracy. The accidental degeneracy is studied introducing the Majorana and Fermi interaction parameters and the rms deviations are observed. The effects of accidental degeneracy for each of the molecules are not equal. In the second part of this report, the harmonic frequencies of CO2 and N2O are calculated using the mean field approximation. It is found that the results show good agreement.

The Determination of the Magnetoelectric Coupling Coefficient in Ferroelectric–Ferromagnetic Composite Based on PZT–Ferrite

2013 ◽  
Vol 58 (4) ◽  
pp. 1401-1403 ◽  
Author(s):  
J.A. Bartkowska ◽  
R. Zachariasz ◽  
D. Bochenek ◽  
J. Ilczuk
Keyword(s):  
Dielectric Permittivity ◽  
Coupling Coefficient ◽  
Mean Field ◽  
Field Approximation ◽  
Theoretical Description ◽  
Magnetoelectric Coupling ◽  
Mean Field Approximation ◽  
Dielectric Measurements ◽  
Temperature Dependences ◽  
Multiferroic Composite

Abstract In the present work, the magnetoelectric coupling coefficient, from the temperature dependences of the dielectric permittivity for the multiferroic composite was determined. The research material was ferroelectric-ferromagnetic composite on the based PZT and ferrite. We investigated the temperature dependences of the dielectric permittivity (") for the different frequency of measurement’s field. From the dielectric measurements we determined the temperature of phase transition from ferroelectric to paraelectric phase. For the theoretical description of the temperature dependence of the dielectric constant, the Hamiltonian of Alcantara, Gehring and Janssen was used. To investigate the dielectric properties of the multiferroic composite this Hamiltonian was expressed under the mean-field approximation. Based on dielectric measurements and theoretical considerations, the values of the magnetoelectric coupling coefficient were specified.

scholarly journals Hexagonal-Shaped Spin Crossover Nanoparticles Studied by Ising-Like Model Solved by Local Mean Field Approximation

2021 ◽  
Vol 7 (5) ◽  
pp. 69
Author(s):  
Catherine Cazelles ◽  
Jorge Linares ◽  
Mamadou Ndiaye ◽  
Pierre-Richard Dahoo ◽  
Kamel Boukheddaden
Keyword(s):  
Spin Crossover ◽  
Hexagonal Lattice ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Ligand Field ◽  
Order And Disorder ◽  
The Matrix ◽  
Local Mean ◽  
Parameter Values

The properties of spin crossover (SCO) nanoparticles were studied for five 2D hexagonal lattice structures of increasing sizes embedded in a matrix, thus affecting the thermal properties of the SCO region. These effects were modeled using the Ising-like model in the framework of local mean field approximation (LMFA). The systematic combined effect of the different types of couplings, consisting of (i) bulk short- and long-range interactions and (ii) edge and corner interactions at the surface mediated by the matrix environment, were investigated by using parameter values typical of SCO complexes. Gradual two and three hysteretic transition curves from the LS to HS states were obtained. The results were interpreted in terms of the competition between the structure-dependent order and disorder temperatures (TO.D.) of internal coupling origin and the ligand field-dependent equilibrium temperatures (Teq) of external origin.

Geometrical and Transport Properties of Disordered Fibre Networks: Analytical Results

1997 ◽  
Vol 11 (20) ◽  
pp. 867-875 ◽  
Author(s):  
A. A. Rodríaguez ◽  
E. Medina
Keyword(s):  
Probability Distribution ◽  
Transport Properties ◽  
Geometrical Structure ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Fracture Networks ◽  
Simplified Models ◽  
Fibre Density ◽  
Line Network

We study novel geometrical and transport properties of a 2D model of disordered fibre networks. To assess the geometrical structure we determine, analytically, the probability distribution for the number of fibre intersections and resulting segment sizes in the network as a function of fibre density and length. We also determine, numerically, the probability distribution of pore perimeters and areas. We find a non-monotonous behavior of the perimeter distribution whose main features can be explained by solving for two simplified models of the line network. Finally we formulate a mean field approximation to conduction, above the percolation threshold, using the derived results. Relevance of the results to fracture networks will be discussed.

The gas-liquid surface of the penetrable sphere model. II

1978 ◽  
Vol 358 (1694) ◽  
pp. 267-280 ◽  
Keyword(s):  
Surface Tension ◽  
Correlation Function ◽  
Liquid Surface ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Intermolecular Potential ◽  
Direct Correlation Function ◽  
Sphere Model ◽  
One Dimensional

The direct correlation function between two points in the gas-liquid surface of the penetrable sphere model is obtained in a mean-field approximation. This function is used to show explicitly that three apparently different ways of calculating the surface tension all lead to the same result. They are (1) from the virial of the intermolecular potential, (2) from the direct correlation function, and (3) from the energy density. The equality of (1) and (2) is shown analytically at all temperatures 0 < T < T c where T c is the critical temperature; the equality of (2) and (3) is shown analytically for T ≈ T c , and by numerical integration at lower temperatures. The equality of (2) and (3) is shown analytically at all temperatures for a one-dimensional potential.

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