scholarly journals Superstatistics of Diatomic Molecules with the Shifted Deng-Fan Potential Model

2021 ◽  
Vol 12 (3) ◽  
pp. 4126-4139
Keyword(s):  
Partition Function ◽  
Short Range ◽  
Deformation Parameter ◽  
Potential Model ◽  
Diatomic Molecules ◽  
Thermal Fluctuations ◽  
Boltzmann Factor ◽  
Molecular Systems ◽  
Dirac Delta ◽  
Delta Distribution

In this article, we discuss the thermodynamic properties of the shifted Deng-Fan potential for HCl, CrH, CuLi, and ScF diatomic molecules using the q-deformed superstatistics approach. The partition function is obtained with the help of the generalized Boltzmann factor from the modified Dirac delta distribution. In addition, thermodynamic functions such as entropy, specific heat capacity, free energy, and mean energy are obtained using the partition function. Our results are presented graphically, and the ordinary statistical quantities are recovered when the deformation parameter tends to zero. Our results may be useful in the study of thermal fluctuations in atomic and molecular systems involving short-range interactions.

Superstatistics of the Klein–Gordon equation in deformed formalism for modified Dirac delta distribution

2018 ◽  
Vol 33 (10n11) ◽  
pp. 1850060 ◽  
Author(s):  
S. Sargolzaeipor ◽  
H. Hassanabadi ◽  
W. S. Chung
Keyword(s):  
Deformation Parameter ◽  
Gordon Equation ◽  
Wave Functions ◽  
Boltzmann Factor ◽  
Dirac Delta ◽  
Cornell Potential ◽  
Delta Distribution ◽  
Klein Gordon ◽  
Aharonov Bohm ◽  
Klein Gordon Equation

The Klein–Gordon equation is extended in the presence of an Aharonov–Bohm magnetic field for the Cornell potential and the corresponding wave functions as well as the spectra are obtained. After introducing the superstatistics in the statistical mechanics, we first derived the effective Boltzmann factor in the deformed formalism with modified Dirac delta distribution. We then use the concepts of the superstatistics to calculate the thermodynamics properties of the system. The well-known results are recovered by the vanishing of deformation parameter and some graphs are plotted for the clarity of our results.

Equivalence of the Wei potential model and Tietz potential model for diatomic molecules

2012 ◽  
Vol 137 (1) ◽  
pp. 014101 ◽  
Author(s):  
Chun-Sheng Jia ◽  
Yong-Feng Diao ◽  
Xiang-Jun Liu ◽  
Ping-Quan Wang ◽  
Jian-Yi Liu ◽  
...  
Keyword(s):  
Potential Model ◽  
Diatomic Molecules ◽  
Tietz Potential

scholarly journals Generalization of the Winfree model to the high-dimensional sphere and its emergent dynamics

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hansol Park
Keyword(s):  
Influence Function ◽  
Equilibrium Solution ◽  
Phase Locking ◽  
Small Diameter ◽  
High Dimensional ◽  
Dimensional Sphere ◽  
Sphere Model ◽  
Dirac Delta ◽  
Delta Distribution ◽  
Winfree Model

<p style='text-indent:20px;'>We present a high-dimensional Winfree model in this paper. The Winfree model is a mathematical model for synchronization on the unit circle. We generalize this model compare to the high-dimensional sphere and we call it the Winfree sphere model. We restricted the support of the influence function in the neighborhood of the attraction point to a small diameter to mimic the influence function as the Dirac delta distribution. We can obtain several new conditions of the complete phase-locking states for the identical Winfree sphere model from restricting the support of the influence function. We also prove the complete oscillator death(COD) state from the exponential <inline-formula><tex-math id="M1">\begin{document}$ \ell^1 $\end{document}</tex-math></inline-formula>-stability and the existence of the equilibrium solution.</p>

Diatomic molecules energy spectra for the generalized Mobius square potential model

2020 ◽  
Vol 34 (21) ◽  
pp. 2050209
Author(s):  
U. S. Okorie ◽  
A. N. Ikot ◽  
M. U. Ibezim-Ezeani ◽  
Hewa Y. Abdullah
Keyword(s):  
Dissociation Energy ◽  
Approximation Scheme ◽  
Potential Model ◽  
Vibrational Energy ◽  
Diatomic Molecules ◽  
Energy Spectra ◽  
Equilibrium Bond Length ◽  
Quantum Numbers ◽  
Vibrational Energies ◽  
Potential Parameters

The modified version of the generalized Mobius square (GMS) potential has been obtained by employing the dissociation energy and equilibrium bond length as explicit parameters. The potential parameters have been defined in terms of the molecular parameters. The modified GMS potential has also been used to model internuclear interaction potential curves for different states of diatomic molecules. Also, we have obtained the rotational–vibrational energy spectra of the new GMS potential model, both analytically and numerically for the different diatomic molecules. This was done by employing a Pekeris-type approximation scheme and an appropriate coordinate transformation to solve the Schrodinger equation. Our results have been compared with the experimental Rydberg–Klein–Rees (RKR) data and its corresponding average absolute deviations in terms of the dissociation energy computed. The effects of the vibrational and rotational quantum numbers on the rotational–vibrational energies for the different states of the various diatomic molecules have also been discussed. This paper has shown to be highly relevant to the studies of thermodynamic and thermochemical functions of diatomic molecules.

scholarly journals Thermodynamical Quantities of Chalcogenide Dimers (O2, S2, Se2, and Te2) from Spectroscopic Data

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Shipra Tiwari ◽  
Pavitra Tandon ◽  
K. N. Uttam
Keyword(s):  
Partition Function ◽  
Spectroscopic Data ◽  
Function Theory ◽  
Diatomic Molecules ◽  
Molecular Motions ◽  
Temperature Range

Attempts have been made to calculate the thermodynamical quantities of diatomic molecules such as O2, S2, Se2, and Te2from spectroscopic data with the help of partition function theory. The results have been calculated in the temperature range 100–3000°C. In order to increase accuracy of the calculated quantities, we have incorporated nonrigidity, anharmonicity, and stretching effects of molecules. The variation of these quantities with temperature have been studied and explained in terms of various modes of molecular motions.

Sign in / Sign up

Export Citation Format

Share Document