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Ahmed AD, Eyube ES, Omugbe E, Onate CA, Timtere P. Bound-state energy spectrum and thermochemical functions of the deformed Schiöberg oscillator. Sci Rep 2023; 13:20386. [PMID: 37989877 PMCID: PMC10663450 DOI: 10.1038/s41598-023-47235-0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2023] [Accepted: 11/10/2023] [Indexed: 11/23/2023] Open
Abstract
In this study, a diatomic molecule interacting potential such as the deformed Schiöberg oscillator (DSO) have been applied to diatomic systems. By solving the Schrödinger equation with the DSO, analytical equations for energy eigenvalues, molar entropy, molar enthalpy, molar Gibbs free energy and constant pressure molar heat capacity are obtained. The obtained equations were used to analyze the physical properties of diatomic molecules. With the aid of the DSO, the percentage average absolute deviation (PAAD) of computed data from the experimental data of the 7Li2 (2 3Πg), NaBr (X 1Σ+), KBr (X 1Σ+) and KRb (B 1Π) molecules are 1.3319%, 0.2108%, 0.2359% and 0.8841%, respectively. The PAAD values obtained by employing the equations of molar entropy, scaled molar enthalpy, scaled molar Gibbs free energy and isobaric molar heat capacity are 1.2919%, 1.5639%, 1.5957% and 2.4041%, respectively, from the experimental data of the KBr (X 1Σ+) molecule. The results for the potential energies, bound-state energy spectra, and thermodynamic functions are in good agreement with the literature on diatomic molecules.
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Affiliation(s)
- A D Ahmed
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria
| | - E S Eyube
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria.
| | - E Omugbe
- Department of Physics, University of Agriculture and Environmental Sciences, P.M.B. 1038, Umuagwo, Imo State, Nigeria
| | - C A Onate
- Department of Physics, Kogi State University, Anyigba, Nigeria
| | - P Timtere
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria
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William ES, Okon IB, Inyang EP, Akpan IO, Ita B, Nwachukwu AN, Onate CA, Omugbe E, Okorie US, Araujo JP, Ikot AN. Quantum description of magnetocaloric effect, thermo-magnetic properties and energy spectra of LiH, TiH, and ScH diatomic molecules under the influence of magnetic and Aharonov-Bohm (AB) flux fields with Deng-Fan-Screened Coulomb potential model. Mol Phys 2023. [DOI: 10.1080/00268976.2023.2195952] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/31/2023]
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Ding QC, Jia CS, Wang CW, Peng XL, Liu JY, Zhang LH, Jiang R, Zhu SY, Yuan H, Tang HX. Unified non-fitting formulation representation of thermodynamic properties for diatomic substances. J Mol Liq 2023. [DOI: 10.1016/j.molliq.2022.121088] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
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Onate CA, Okon IB, Vincent UE, Omugbe E, Eyube ES, Onyeaju MC, Jude GO. Theoretic measure and thermal properties of a standard Morse potential model. J Mol Model 2023; 29:34. [PMID: 36625977 DOI: 10.1007/s00894-022-05441-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Accepted: 12/27/2022] [Indexed: 01/11/2023]
Abstract
Since the proposition of the standard form of Morse potential [Formula: see text] model over the years, there has not been much attention on the potential. Its application to different studies such as the thermodynamic properties and information theory are yet to be reported to the best of our understanding. In this study, the solutions of the radial Schrödinger equation for the standard Morse potential is obtained using supersymmetric approach. The effect of the quantum number on the energy eigenvalue for the standard Morse potential is examined numerically for the hydrogen molecule (H2), lithium molecule (Li2), and potassium molecule (K2). Using the energy equation and the wave function obtained, the theoretic measures and thermodynamic properties of hydrogen, lithium, and potassium molecules are calculated via maple program. It has been shown that the energy of the standard Morse potential is fully bounded for the three molecules studied. A higher concentration of electron density corresponds to a strongly localized distribution in the position configuration. The Beckner, Bialynicki-Birula, and Mycieslki (BBM) inequality is satisfied for both the ground state and the first excited state. Finally, the product of uncertainty obtained obeyed the Heisenberg uncertainty relation.
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Affiliation(s)
- C A Onate
- Department of Physics, Kogi State University, Anyigba, Nigeria.
| | - I B Okon
- Department of Physics, University of Uyo, Uyo, Nigeria
| | - U E Vincent
- Department of Physical Sciences, Redeemer's University, P.M.B. 230, Ede, Nigeria.,Department of Physics, Lancaster University, Lancaster, LA1 4YB, UK
| | - E Omugbe
- Department of Physics, University of Agriculture and Environmental Sciences, Umuagwo, Imo State, Nigeria
| | - E S Eyube
- Department of Physics, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria
| | - M C Onyeaju
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Nigeria
| | - G O Jude
- Department of Physics, University of Uyo, Uyo, Nigeria
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Abu-Shady M, Khokha EM. On prediction of the fractional vibrational energies for diatomic molecules with the improved Tietz potential. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2140720] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Affiliation(s)
- M. Abu-Shady
- Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shibin El Kom, Egypt
| | - E. M. Khokha
- Department of Basic Science, Modern Academy for Engineering and Technology, Maadi, Egypt
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Liu JZ, Jia CS. Prediction of vibrational energy levels for the CO molecule and 7Li2 dimer. Chem Phys Lett 2022. [DOI: 10.1016/j.cplett.2022.139791] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Ding QC, Jia CS, Liu JZ, Li J, Du RF, Liu JY, Peng XL, Wang CW, Tang HX. Prediction of thermodynamic properties for sulfur dimer. Chem Phys Lett 2022. [DOI: 10.1016/j.cplett.2022.139844] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Al-Raeei M. Morse oscillator equation of state: An integral equation theory based with virial expansion and compressibility terms. Heliyon 2022; 8:e09328. [PMID: 35520603 PMCID: PMC9062208 DOI: 10.1016/j.heliyon.2022.e09328] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2021] [Revised: 01/03/2022] [Accepted: 04/21/2022] [Indexed: 11/30/2022] Open
Abstract
A number of interaction energy types are employed in the vibrations studies, especially in the spectroscopic analysis, such as the harmonic oscillator and Morse oscillator. In this research, a derivation of an analytical formula of equation of state of Morse oscillator is considered by employing the approximations used in the simple fluids theory. The compressibility formula of the pressure and the virial expansion formula of the pressure using the solutions of the main equation of the simple fluids theory with one of the approximations of the theory are employed for the purpose of the derivation. The virial coefficients of the total Morse oscillator pressure (the first order one, and the second order one) are found for Morse oscillator with respect to the fractional volume of the components, where we conclude that the first order term is proportional to the absolute temperature directly and depends on the diameter of the particles, while we concluded that the second order coefficient term is more complicated than the first order one with temperature, and also, depends on the three Morse oscillator parameters and the diameter of the particles. Besides, we conclude that the total pressure of Morse oscillator, generally, depends on the minimum energy of the well of Morse oscillator, the width parameter of Morse oscillator, and the equilibrium bond distance of the oscillator, in addition to their dependence on the absolute temperature of the components, and the diameter of the particles. The formula of the Morse oscillator equation of state which is found in this research can be applied to multiple materials described using Morse oscillator such as lots of dimers in the vibrations spectroscopy.
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Eyube E. Reparametrised Pöschl–Teller oscillator and analytical molar entropy equation for diatomic molecules. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2037774] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- E.S. Eyube
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, Yola, Nigeria
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Eyube E, Notani P, Izam M. Potential parameters and eigen spectra of improved Scarf II potential energy function for diatomic molecules. Mol Phys 2021. [DOI: 10.1080/00268976.2021.1979265] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
Affiliation(s)
- E.S. Eyube
- Department of Physics, School of Physical Sciences, Modibbo Adama University of Technology, Yola, Nigeria
| | - P.P. Notani
- Department of Pure and Applied Sciences, Taraba State Polytechnic, Suntai, Jalingo, Nigeria
| | - M.M. Izam
- Department of Physics, Faculty of Natural Sciences, University of Jos, Jos, Nigeria
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Hesam A, Nikoofard H, Sargolzaei M. Prediction of thermodynamic properties of formation of HCl at temperatures 200–1000 K. Chem Phys Lett 2021. [DOI: 10.1016/j.cplett.2020.138276] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Wang CW, Wang J, Liu YS, Li J, Peng XL, Jia CS, Zhang LH, Yi LZ, Liu JY, Li CJ, Jia X. Prediction of the ideal-gas thermodynamic properties for water. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2020.114912] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/27/2022]
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