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Abu-Shady M, Khokha EM. A precise estimation for vibrational energies of diatomic molecules using the improved Rosen-Morse potential. Sci Rep 2023; 13:11578. [PMID: 37463934 DOI: 10.1038/s41598-023-37888-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Accepted: 06/29/2023] [Indexed: 07/20/2023] Open
Abstract
In the context of the generalized fractional derivative, novel solutions to the D-dimensional Schrödinger equation are investigated via the improved Rosen-Morse potential (IRMP). By applying the Pekeris-type approximation to the centrifugal term, the generalized fractional Nikiforov-Uvarov method has been used to derive the analytical formulations of the energy eigenvalues and wave functions in terms of the fractional parameters in D-dimensions. The resulting solutions are employed for a variety of diatomic molecules (DMs), which have numerous uses in many fields of physics. With the use of molecular parameters, the IRMP is utilized to reproduce potential energy curves for numerous DMs. The pure vibrational energy spectra for several DMs are determined using both the fractional and the ordinary forms to demonstrate the effectiveness of the method utilized in this work. As compared to earlier investigations, it has been found that our estimated vibrational energies correspond with the observed Rydberg-Klein-Rees (RKR) data much more closely. Moreover, it is observed that the vibrational energy spectra of different DMs computed in the existence of fractional parameters are superior to those computed in the ordinary case for fitting the observed RKR data. Thus, it may be inferred that fractional order significantly affects the vibrational energy levels of DMs. Both the mean absolute percentage deviation (MAPD) and average absolute deviation (AAD) are evaluated as the goodness of fit indicators. According to the estimated AAD and MAPD outcomes, the IRMP is an appropriate model for simulating the RKR data for all of the DMs under investigation.
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Affiliation(s)
- M Abu-Shady
- Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shibin El Kom, 32511, Menoufia, Egypt
| | - E M Khokha
- Faculty of Computer Science and Engineering, King Salman International University (KSIU), El Tor 46511, South Sinai, Egypt.
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2
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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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3
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Onate C, Okon I, Vincent U, Eyube E, Omugbe E. Pure-vibrational spectrum of diatomic molecules using an improved Pöschl-Teller potential. Chem Phys 2022. [DOI: 10.1016/j.chemphys.2022.111770] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Onate CA, Okon IB, Vincent UE, Eyube ES, Onyeaju MC, Omugbe E, Egharevba GO. Non-relativistic molecular modified shifted Morse potential system. Sci Rep 2022; 12:15188. [PMID: 36071068 PMCID: PMC9452569 DOI: 10.1038/s41598-022-19179-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/07/2022] [Accepted: 08/25/2022] [Indexed: 11/09/2022] Open
Abstract
A shifted Morse potential model is modified to fit the study of the vibrational energies of some molecules. Using a traditional technique/methodology, the vibrational energy and the un-normalized radial wave functions were calculated for the modified shifted Morse potential model. The condition that fits the modified potential for molecular description were deduced together with the expression for the screening parameter. The vibrational energies of SiC, NbO, CP, PH, SiF, NH and Cs2 molecules were computed by inserting their respective spectroscopic constants into the calculated energy equation. It was shown that the calculated results for all the molecules agreement perfectly with the experimental RKR values. The present potential performs better than Improved Morse and Morse potentials for cesium dimer. Finally, the real Morse potential model was obtained as a special case of the modified shifted potential.
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Affiliation(s)
- C A Onate
- Department of Physical Sciences, Redeemer's University, Ede, Nigeria.
| | - I B Okon
- Theoretical Physics Group, 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, LA14YB, UK
| | - E S Eyube
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, Yola, Nigeria
| | - M C Onyeaju
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Port Harcourt, Nigeria
| | - E Omugbe
- Department of Physics, Federal University of Petroleum Resources, Effurun, Delta State, Nigeria.,Department of Science Laboratory Technology, Delta State Polytechnic, Otefe Oghara, Nigeria
| | - G O Egharevba
- Department of Physical Sciences, Redeemer's University, Ede, Nigeria
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5
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Al-Raeei M. The bond length of the improved Rosen Morse potential, applying for: Cesium, hydrogen, hydrogen fluoride, hydrogen chloride, lithium, and nitrogen molecules. RESULTS IN CHEMISTRY 2022. [DOI: 10.1016/j.rechem.2022.100560] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022] Open
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6
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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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7
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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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8
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Onate CA, Akanbi TA, Okon IB. Ro-vibrational energies of cesium dimer and lithium dimer with molecular attractive potential. Sci Rep 2021; 11:6198. [PMID: 33737625 PMCID: PMC7973739 DOI: 10.1038/s41598-021-85761-x] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2021] [Accepted: 03/05/2021] [Indexed: 11/23/2022] Open
Abstract
An approximate solution of the Schrӧdinger equation for a molecular attractive potential was obtained using the parametric Nikiforov–Uvarov method. The energy equation and the corresponding radial wave functions were calculated. The effects of the potential parameters on the energy eigenvalues were examined. The thermal properties under the molecular attractive potential were calculated and the behaviour of the thermal properties with the maximum quantum state (λ) and the temperature parameter (β) respectively, were studied. Using the molecular spectroscopic parameters, the Rydberg–Klein–Rees (RKR) of cesium dimer and lithium dimer were both obtained and compared with the experimental values. The RKR values of both cesium dimer and lithium dimer calculated aligned with the observed values. The deviation and average deviation of the RKR for each molecule were also calculated.
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Affiliation(s)
- C A Onate
- Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria.
| | - T A Akanbi
- Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria
| | - I B Okon
- Theoretical Physics Group, Department of Physics, University of Uyo, Uyo, Nigeria
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10
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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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Okorie US, Ikot AN, Onyeaju MC, Chukwuocha EO. Bound state solutions of Schrödinger equation with modified Mobius square potential (MMSP) and its thermodynamic properties. J Mol Model 2018; 24:289. [PMID: 30242483 DOI: 10.1007/s00894-018-3811-8] [Citation(s) in RCA: 41] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2018] [Accepted: 08/27/2018] [Indexed: 11/25/2022]
Abstract
We solved the Schrödinger equation with the modified Mobius square potential model using the modified factorization method. Within the framework of the Greene-Aldrich approximation for the centrifugal term and using a suitable transformation scheme, we obtained the energy eigenvalues equation and the corresponding eigenfunction in terms of the hypergeometric function. Using the resulting eigenvalues equation, we calculated the vibrational partition function and other relevant thermodynamic properties. We also showed that the modified Mobius square potential can be reduced to the Hua potential model using appropriate potential constant values.
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Affiliation(s)
- Uduakobong S Okorie
- Department of Physics, Akwa Ibom State University, Ikot Akpaden, P.M.B. 1167, Uyo, Nigeria.
| | - Akpan N Ikot
- Department of Physics, Theoretical Physics Group, University of Port Harcourt, Choba, Port Harcourt, Nigeria
| | - Michael C Onyeaju
- Department of Physics, Theoretical Physics Group, University of Port Harcourt, Choba, Port Harcourt, Nigeria
| | - Ephraim O Chukwuocha
- Department of Physics, Theoretical Physics Group, University of Port Harcourt, Choba, Port Harcourt, Nigeria
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13
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14
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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 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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16
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Tang HM, Liang GC, Zhang LH, Zhao F, Jia CS. Diatomic molecule energies of the modified Rosen−Morse potential energy model. CAN J CHEM 2014. [DOI: 10.1139/cjc-2013-0563] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
We solve the Schrödinger equation with the modified Rosen−Morse empirical potential model to obtain rotation-vibrational energy spectra and unnormalized radial wave functions. The vibrational energy levels calculated with the modified Rosen−Morse potential model for the 61Πu state of the 7Li2 molecule and the X3Π state of the SiC radical are in better agreement with the Rydberg−Klein−Rees data than the predictions of the Morse potential model.
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Affiliation(s)
- Hong-Ming Tang
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
- School of Resources and Environment Engineering, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
| | - Guang-Chuan Liang
- 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
| | - Feng Zhao
- School of Resources and Environment 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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Tang HM, Liang GC, Zhang LH, Zhao F, Jia CS. Molecular energies of the improved Tietz potential energy model. CAN J CHEM 2014. [DOI: 10.1139/cjc-2013-0466] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
We solve the Schrödinger equation with the improved Tietz empirical potential energy model. The rotation-vibrational energy spectra and the unnormalized radial wave functions have been obtained. The vibrational energy levels predicted by using the improved Tietz potential model for the 51Δg state and C1Πu state of the Na2 molecule are in good agreement with the experimental Rydberg−Klein−Rees data.
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Affiliation(s)
- Hong-Ming Tang
- State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
- School of Resources and Environment Engineering, Southwest Petroleum University, Chengdu 610500, People’s Republic of China
| | - Guang-Chuan Liang
- 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
| | - Feng Zhao
- School of Resources and Environment 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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