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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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Onate CA, Okon IB, Onyeaju MC, Ebomwonyi O. Vibrational energies of some diatomic molecules for a modified and deformed potential. Sci Rep 2021; 11:22498. [PMID: 34795376 PMCID: PMC8602305 DOI: 10.1038/s41598-021-01998-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/10/2021] [Accepted: 10/29/2021] [Indexed: 11/21/2022] Open
Abstract
A molecular potential model is proposed and the solutions of the radial Schrӧdinger equation in the presence of the proposed potential is obtained. The energy equation and its corresponding radial wave function are calculated using the powerful parametric Nikiforov–Uvarov method. The energies of cesium dimer for different quantum states were numerically obtained for both negative and positive values of the deformed and adjustable parameters. The results for sodium dimer and lithium dimer were calculated numerically using their respective spectroscopic parameters. The calculated values for the three molecules are in excellent agreement with the observed values. Finally, we calculated different expectation values and examined the effects of the deformed and adjustable parameters on the expectation values.
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Affiliation(s)
- C A Onate
- Physics Programme, Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria. .,Landmark University SDG 4 (Quality Education), Omu-Aran, Nigeria.
| | - I B Okon
- Theoretical Physics Group, Department of Physics, University of Uyo, Uyo, Nigeria
| | - M C Onyeaju
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, P.M.B. 5323 Choba, Port Harcourt, Nigeria
| | - O Ebomwonyi
- Department of Physics, University of Benin, Benin City, Nigeria
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Horchani R, Al-Kindi N, Jelassi H. Ro-vibrational energies of caesium molecules with the Tietz-Hua oscillator. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1812746] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Ridha Horchani
- Department of Physics, College of Science, Sultan Qaboos University, Muscat, Sultanate of Oman
| | - Noor Al-Kindi
- Department of Physics, College of Science, Sultan Qaboos University, Muscat, Sultanate of Oman
| | - Haikel Jelassi
- Department of Physics, College of Science, Sultan Qaboos University, Muscat, Sultanate of Oman
- Laboratory on Energy and Matter for Nuclear Sciences Development (LR16CNSTN02), National Center for Nuclear Sciences and Technologies, Ariana, Tunisia
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Approximate energy spectra of improved generalized Mobius square potential (IGMSP) for some diatomic hydride molecules. J Mol Model 2020; 26:195. [DOI: 10.1007/s00894-020-04449-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/09/2019] [Accepted: 06/16/2020] [Indexed: 10/23/2022]
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Kisoglu HF, Yanar H, Aydogdu O, Salti M. Relativistic spectral bounds for the general molecular potential: application to a diatomic molecule. J Mol Model 2019; 25:143. [PMID: 31049705 DOI: 10.1007/s00894-019-4021-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2018] [Accepted: 03/29/2019] [Indexed: 10/26/2022]
Abstract
We tackle with the Dirac equation in the presence of the general molecular potential (GMP). The spin symmetric solution of the relativistic wave equation is obtained by considering the Pekeris-type approximation scheme to deal with the centrifugal term, and in order to solve second-order differential equation, the asymptotic iteration method (AIM) is used. The closed form of the energy eigenvalue equation is found out for any values of the angular momentum quantum number. We calculate the relativistic vibrational bound state energies of 51Δg state of Na2 molecule and compare them with the Rydberg-Klein-Rees (RKR) data. We show that relativistic vibrational energies of this molecule, which are found in the spin symmetric case, are more convenient with experimental RKR data than non-relativistic vibrational energies. We also obtain normalization constant by considering inductive approach and investigate the radial eigenfunctions and probability density functions corresponding to different eigenvalues graphically for the Na2(51Δg) molecule.
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Affiliation(s)
- Hasan Fatih Kisoglu
- Department of Basic Sciences, Faculty of Maritime, Mersin University, 33200, Mersin, Turkey
| | - Hilmi Yanar
- Department of Physics, Faculty of Science and Letters, Mersin University, 33343, Mersin, Turkey.
| | - Oktay Aydogdu
- Department of Physics, Faculty of Science and Letters, Mersin University, 33343, Mersin, Turkey
| | - Mustafa Salti
- Department of Physics, Faculty of Science and Letters, Mersin University, 33343, Mersin, Turkey
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Affiliation(s)
- Hilmi Yanar
- Department of Physics, Faculty of Arts and Science, Mersin University, Mersin, 33143, Turkey
| | - Oktay Aydoğdu
- Department of Physics, Faculty of Arts and Science, Mersin University, Mersin, 33143, Turkey
| | - Mustafa Saltı
- Department of Physics, Faculty of Arts and Science, Mersin University, Mersin, 33143, Turkey
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Abstract
We explore thermodynamic properties of a vapor in the range of state parameters where the contribution to thermodynamic functions from bound states of atoms (clusters) dominates over the interaction between the components of the vapor in free states. The clusters are assumed to be light and sufficiently "hot" for the number of bonds to be minimized. We use the technique of calculation of the cluster partition function for the cluster with a minimum number of interatomic bonds to calculate the caloric properties (heat capacity and velocity of sound) for an ideal mixture of the lightest clusters. The problem proves to be exactly solvable and resulting formulas are functions solely of the equilibrium constant of the dimer formation. These formulas ensure a satisfactory correlation with the reference data for the vapors of cesium, mercury, and argon up to moderate densities in both the sub- and supercritical regions. For cesium, we extend the model to the densities close to the critical one by inclusion of the clusters of arbitrary size. Knowledge of the cluster composition of the cesium vapor makes it possible to treat nonequilibrium phenomena such as nucleation of the supersaturated vapor, for which the effect of the cluster structural transition is likely to be significant.
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Affiliation(s)
- D I Zhukhovitskii
- Joint Institute of High Temperatures, Russian Academy of Sciences, Izhorskaya 13, Bd. 2, 125412 Moscow, Russia
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Abstract
We solve the Schrödinger equation with the improved Rosen−Morse potential energy model in D spatial dimensions. The D-dimensional rotation-vibrational energy spectra have been obtained by using the supersymmetric shape invariance approach. The energies for the 33[Formula: see text]g+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule increase as D increases in the presence of fixed vibrational quantum number and various rotational quantum numbers. We observe that the change in behavior of the vibrational energies in higher dimensions remains similar to that of the three-dimensional system.
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Affiliation(s)
- Xue-Tao Hu
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
- School of Petroleum Engineering, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
| | - Lie-Hui Zhang
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
| | - Chun-Sheng Jia
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
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Abstract
We solve the Schrödinger equation with the improved Rosen−Morse empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The interaction potential energy curves for the 33Σg+ state of the Cs2 molecule and the 51Δg state of the Na2 molecule are modeled by employing the improved Rosen−Morse potential and the Morse potential. Favourable agreement for the improved Rosen−Morse potential is found in comparing with the Rydberg−Klein−Rees potential. The vibrational energy levels predicted by using the improved Rosen−Morse potential for the 33Σg+ state of Cs2 and the 51Δg state of Na2 are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential.
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Affiliation(s)
- Jian-Yi Liu
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
| | - Xue-Tao Hu
- School of Petroleum Engineering, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
| | - Chun-Sheng Jia
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
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Li D, Xie F, Li L, Ahmed EH, Lyyra AM. Collisional Line Assignments and Hyperfine Structure Interpretation in Cs2 23Δ1g State. CHINESE J CHEM PHYS 2013. [DOI: 10.1063/1674-0068/26/01/13-19] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Two-photon excitations of the Cs2 33Σg+ state: Assignment and analysis with the deformed ab initio potential. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2012.12.030] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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