1
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Jiang J. Diabatic Valence-Hole Concept. J Phys Chem A 2024; 128:3253-3265. [PMID: 38647413 DOI: 10.1021/acs.jpca.4c00289] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2024]
Abstract
A global diabatization scheme, based on the "valence-hole" concept, has been previously applied to model webs of avoided crossings that exist in four electronic-state symmetry manifolds of C2 (1Πg, 3Πg, 1Σu+, and 3Σu+). Here, this model is extended to the electronically excited states of four more molecules: CN (2Σ+), N2 (3Πu), SiC (3Π), and Si2 (3Πg). Many strangenesses in the spectroscopic observations (e.g., energy level structure, predissociation linewidths, and radiative lifetimes) for all four electronic state systems discussed here are accounted for by this unified model. The key concept of the model is valence-hole electron configurations: 3σ24σ11π45σ2 in CN (2Σ+), 2σg22σu11πu43σg21πg1 in N2 (3Πu), 5σ26σ17σ22π3 in SiC (3Π), and 4σg24σu15σg22πu3 in Si2 (3Πg), all of which have a triply occupied "valence-core" (i.e., 2σg22σu1 or the equivalent). These valence-hole configurations have a nominal bond order of three or higher and correlate with high-energy separated-atom limits with an np ← ns (n = 2, 3) promotion in one of the atomic constituents. On its way to dissociation, the strongly bound diabatic valence-hole state crosses multiple weakly bound or repulsive states, which belong to electron configurations with a completely filled valence-core. These curve crossings between diabatic potentials result in a network of many avoided crossings among multiple electronic states, analogous to the well-studied electronic structure landscape of ionic-covalent crossings in strongly ionic molecules. Considering the unique role of valence-hole states in shaping the global electronic structure, the valence-hole concept should be added to our intuitive framework of chemical bonding.
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Affiliation(s)
- Jun Jiang
- Center for Accelerator Mass Spectrometry, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
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2
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Omugbe E, Eyube ES, Onate CA, Njoku IJ, Jahanshir A, Inyang EP, Emeje KO. Non-relativistic energy equations for diatomic molecules constrained in a deformed hyperbolic potential function. J Mol Model 2024; 30:74. [PMID: 38374405 DOI: 10.1007/s00894-024-05855-x] [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: 12/30/2023] [Accepted: 01/26/2024] [Indexed: 02/21/2024]
Abstract
CONTEXT In this paper, the approximate analytical energy equations for the deformed hyperbolic potential have been obtained for arbitrary parameters of the potential. The potential function was transformed to a molecular potential by subjecting it to the Varshni conditions which allows for the determination of the energy levels of diatomic molecules. The molecular vibrational energy spectra for [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] diatomic molecules were obtained and found to match with the results obtained with another analytical approach, potential functions, and experimental data. The noticeable slight differences in the approximate energy spectra obtained in this work and existing literature may be ascribed to the analytical method, computational approach, and the accuracy of the molecular potential functions. The obtained energy equations were used to determine the energy of a particle for arbitrary parameters of the potential function. The obtained energy is bounded and increases with the increase in the quantum numbers. The results conformed to the ones obtained via the path integral approach and numerical solutions obtained via the MATHEMATICA program. METHOD The energy spectra equations were obtained via the Nikiforov-Uvarov approach and semi-classical WKB approximation. The Pekeris approximation has been applied to resolve the difficulty in solving the complete energy spectrum of the non-relativistic wave equation for the potential function. The numerical data of the energy spectra was obtained using the MATHEMATICA program.
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Affiliation(s)
- E Omugbe
- Department of Physics, University of Agriculture and Environmental Sciences, P.M.B. 1038, Umuagwo, Imo State, Nigeria.
| | - E S Eyube
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria
| | - C A Onate
- Department of Physics, Kogi State University, Anyigba, Kogi State, Nigeria
- Physics Programme, Department of Physical Sciences, Bowen University, Iwo, Osun State, Nigeria
| | - I J Njoku
- Department of Physics, Federal University of Technology Owerri, Ihiagwa, P.M.B.1526, Owerri, Imo State, Nigeria
| | - A Jahanshir
- Department of Physics and Engineering Sciences, Buein Zahra Technical University, Buein Zahra, Iran
| | - E P Inyang
- Department of Physics, National Open University of Nigeria, Jabi-Abuja, Nigeria
| | - K O Emeje
- Department of Physics, Kogi State University, Anyigba, Kogi State, Nigeria
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3
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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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4
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Eyube E, Notani P, Onate C, Wadata U, Omugbe E, Bitrus B, Najoji S. Energy eigenvalues and finite-temperature magnetization for the improved Scarf II potential in the presence of external magnetic and Aharonov-Bohm flux fields. Heliyon 2023; 9:e20848. [PMID: 37867897 PMCID: PMC10585287 DOI: 10.1016/j.heliyon.2023.e20848] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2023] [Revised: 10/06/2023] [Accepted: 10/09/2023] [Indexed: 10/24/2023] Open
Abstract
In this paper, the bound state solutions of the radial Schrödinger equation are obtained in closed form under an improved Scarf II potential energy function (ISPEF) constrained by external magnetic and Aharonov-Bohm (AB) flux fields. By constructing a suitable Pekeris-like approximation scheme for the centrifugal barrier, approximate analytical expressions for the bound-states and thermal partition function were obtained. With the aid of the partition function, an explicit equation for magnetization at finite temperatures is developed. The obtained equations were then applied to calculate the energy levels and magnetic properties of 7Li2 (2 3Πg), K2 (X 1Σg+), Mg2 (X 1Σg+) and NaBr (X 1Σ+) diatomic molecules. The obtained numerical results of the vibrational energies for these molecules were found to be in good agreement with theoretic and experimental values reported in the existing literature. The results indicated that by turning off the magnetic and AB fields, the energy levels of the diatomic molecules degenerate. The results further revealed that an increase in the temperature of the molecules and the AB field strengths leads to a linear decrease in magnetization.
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Affiliation(s)
- E.S. Eyube
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, P.M.B. 2076, Yola, Adamawa State, Nigeria
| | - P.P. Notani
- Department of Pure and Applied Sciences, Taraba State Polytechnic, Suntai, P.M.B. 1030, Jalingo, Taraba State, Nigeria
| | - C.A. Onate
- Department of Physics, Kogi State University, Anyigba, Nigeria
| | - U. Wadata
- Department of Physics, School of Sciences, Aminu Saleh College of Education, P.M.B. 044, Azare, Bauchi State, Nigeria
| | - E. Omugbe
- Department of Physics, University of Agriculture and Environmental Sciences, Umuagwo, P.M.B. 1038, Imo State, Nigeria
| | - B.M. Bitrus
- Department of Physics, Faculty of Science, Taraba State University, P.M.B. 1176, Jalingo, Taraba State, Nigeria
| | - S.D. Najoji
- Department of Science Laboratory Technology, School of Science and Technology, The Federal Polytechnic, P.M.B. 1006, Damaturu, Yobe State, Nigeria
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5
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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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6
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Kasapoglu E, Yücel MB, Duque CA. Parabolic-Gaussian Double Quantum Wells under a Nonresonant Intense Laser Field. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:1360. [PMID: 37110945 PMCID: PMC10144647 DOI: 10.3390/nano13081360] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/08/2023] [Revised: 03/29/2023] [Accepted: 04/08/2023] [Indexed: 06/19/2023]
Abstract
In this paper, we investigate the electronic and optical properties of an electron in both symmetric and asymmetric double quantum wells that consist of a harmonic potential with an internal Gaussian barrier under a nonresonant intense laser field. The electronic structure was obtained by using the two-dimensional diagonalization method. To calculate the linear and nonlinear absorption, and refractive index coefficients, a combination of the standard density matrix formalism and the perturbation expansion method was used. The obtained results show that the electronic and thereby optical properties of the considered parabolic-Gaussian double quantum wells could be adjusted to obtain a suitable response to specific aims with parameter alterations such as well and barrier width, well depth, barrier height, and interwell coupling, in addition to the applied nonresonant intense laser field.
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Affiliation(s)
- Esin Kasapoglu
- Department of Physics, Faculty of Science, Sivas Cumhuriyet University, 58140 Sivas, Türkiye;
| | - Melike Behiye Yücel
- Department of Physics, Faculty of Science, Akdeniz University, 07058 Antalya, Türkiye;
| | - Carlos A. Duque
- Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín 050003, Colombia
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7
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Kasapoglu E, Yücel MB, Duque CA. Harmonic-Gaussian Symmetric and Asymmetric Double Quantum Wells: Magnetic Field Effects. NANOMATERIALS (BASEL, SWITZERLAND) 2023; 13:nano13050892. [PMID: 36903770 PMCID: PMC10005184 DOI: 10.3390/nano13050892] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Revised: 02/16/2023] [Accepted: 02/24/2023] [Indexed: 05/14/2023]
Abstract
In this study, we considered the linear and non-linear optical properties of an electron in both symmetrical and asymmetrical double quantum wells, which consist of the sum of an internal Gaussian barrier and a harmonic potential under an applied magnetic field. Calculations are in the effective mass and parabolic band approximations. We have used the diagonalization method to find eigenvalues and eigenfunctions of the electron confined within the symmetric and asymmetric double well formed by the sum of a parabolic and Gaussian potential. A two-level approach is used in the density matrix expansion to calculate the linear and third-order non-linear optical absorption and refractive index coefficients. The potential model proposed in this study is useful for simulating and manipulating the optical and electronic properties of symmetric and asymmetric double quantum heterostructures, such as double quantum wells and double quantum dots, with controllable coupling and subjected to externally applied magnetic fields.
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Affiliation(s)
- Esin Kasapoglu
- Physics Department, Science Faculty, Sivas Cumhuriyet University, Sivas 58140, Turkey
| | - Melike Behiye Yücel
- Physics Department, Science Faculty, Akdeniz University, Antalya 07058, Turkey
| | - Carlos A. Duque
- Grupo de Materia Condensada-UdeA, Instituto de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia UdeA, Calle 70 No. 52-21, Medellín AA 1226, Colombia
- Correspondence:
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8
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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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9
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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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10
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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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11
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Edet CO, Al EB, Ungan F, Ali N, Rusli N, Aljunid SA, Endut R, Asjad M. Effects of Applied Magnetic Field on the Optical Properties and Binding Energies Spherical GaAs Quantum Dot with Donor Impurity. NANOMATERIALS (BASEL, SWITZERLAND) 2022; 12:2741. [PMID: 36014609 PMCID: PMC9412272 DOI: 10.3390/nano12162741] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/01/2022] [Revised: 08/03/2022] [Accepted: 08/09/2022] [Indexed: 06/15/2023]
Abstract
The screened modified Kratzer potential (SMKP) model is utilized to scrutinize the impacts of an applied magnetic field (MF) on the binding energies and linear and nonlinear optical properties spherical GaAs quantum dot with donor impurity (DI). To accomplish this goal, we have used the diagonalization method to numerically solve the Schrödinger equation under the effective mass approximation for obtaining the electron energy levels and related electronic wave functions. The expressions used for evaluating linear, third-order nonlinear, and total optical absorption coefficients and relative refractive index changes were previously derived within the compact density matrix method. It has been shown here that the MF and DI impacts the characteristics of the absorption coefficients and the refractive index changes. This study's results will find application in optoelectronics and related areas.
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Affiliation(s)
- Collins Okon Edet
- Faculty of Applied and Human Sciences, Universiti Malaysia Perlis, Arau 02600, Malaysia
- Faculty of Electronic Engineering Technology, Universiti Malaysia Perlis, Arau 02600, Malaysia
- Department of Physics, Cross River University of Technology, Calabar 540252, Nigeria
| | - Emre Bahadir Al
- Physics Department, Faculty of Science, Cumhuriyet University, Sivas 58140, Turkey
| | - Fatih Ungan
- Physics Department, Faculty of Science, Cumhuriyet University, Sivas 58140, Turkey
| | - Norshamsuri Ali
- Faculty of Electronic Engineering Technology, Universiti Malaysia Perlis, Arau 02600, Malaysia
| | - Nursalasawati Rusli
- Institute of Engineering Mathematics, Universiti Malaysia Perlis, Arau 02600, Malaysia
| | - Syed Alwee Aljunid
- Faculty of Electronic Engineering Technology, Universiti Malaysia Perlis, Arau 02600, Malaysia
| | - Rosdisham Endut
- Faculty of Electronic Engineering Technology, Universiti Malaysia Perlis, Arau 02600, Malaysia
| | - Muhammad Asjad
- Department of Mathematics, Khalifa University, Abu Dhabi 127788, United Arab Emirates
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12
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Onate CA, Okon IB, Oyewumi KJ, Falaye BJ, Eyube ES, Omugbe E, Onyeaju MC, Araujo JP. Energies of some halogen molecules for the improved Tietz potential model. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2098195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
Affiliation(s)
- C. A. Onate
- Physics Programme, Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria
| | - I. B. Okon
- Theoretical Physics Group, Department of Physics, University of Uyo, Uyo, Nigeria
| | - K. J. Oyewumi
- Theoretical Physics Section, Department of Physics, University of Ilorin, Ilorin, Nigeria
| | - B. J. Falaye
- Department of Physics, Federal University Lafia, Lafia, Nigeria
| | - E. S. Eyube
- Department of Physics, Faculty of Physical Sciences, Modibbo Adama University, Yola, Nigeria
| | - E. Omugbe
- Physics Department Federal, University of Petroleum Resources Effurun, Effurun, Nigeria
- Department of science Laboratory TechnologyS, Delta State Polytechnic, Otefe, Oghara
| | - M. C. Onyeaju
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Harcourt, Nigeria
| | - J. P. Araujo
- Department of Mathematics, Instituto Federal do Sudeste de Minas Gerais, Juiz de Fora, Brazil
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13
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Jiang J, Ye HZ, Nauta K, Van Voorhis T, Schmidt TW, Field RW. Diabatic Valence-Hole States in the C 2 Molecule: "Putting Humpty Dumpty Together Again". J Phys Chem A 2022; 126:3090-3100. [PMID: 35544770 DOI: 10.1021/acs.jpca.2c00495] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Despite the long history of spectroscopic studies of the C2 molecule, fundamental questions about its chemical bonding are still being hotly debated. The complex electronic structure of C2 is a consequence of its dense manifold of near-degenerate, low-lying electronic states. A global multi-state diabatic model is proposed here to disentangle the numerous configuration interactions that occur within four symmetry manifolds of excited states of C2 (1Πg, 3Πg, 1Σu+ , and 3Σu+ ). The key concept of our model is the existence of two "valence-hole" configurations, 2σg22σu11πu33σg2 for 1,3Πg states and 2σg22σu11πu43σg1 for 1,3Σu+ states, that are derived from 3σg ← 2σu electron promotion. The lowest-energy state from each of the four C2 symmetry species is dominated by this type of valence-hole configuration at its equilibrium internuclear separation. As a result of their large binding energy (nominal bond order of 3) and correlation with the 2s22p2 + 2s2p3 separated-atom configurations, the presence of these valence-hole configurations has a profound impact on the global electronic structure and unimolecular dynamics of C2.
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Affiliation(s)
- Jun Jiang
- Center for Accelerator Mass Spectrometry, Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - Hong-Zhou Ye
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Klaas Nauta
- School of Chemistry, UNSW, Sydney, NSW 2052, Australia
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | | | - Robert W Field
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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14
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Edet CO, Amadi PO, Ettah EB, Ali N, Asjad M, Ikot AN. The magnetocaloric effect, thermo-magnetic and transport properties of LiH diatomic molecule. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2059025] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- C. O. Edet
- Department of Physics, Cross River University of Technology, Calabar, Nigeria
| | - P. O. Amadi
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Nigeria
| | - E. B. Ettah
- Department of Physics, Cross River University of Technology, Calabar, Nigeria
| | - Norshamsuri Ali
- Faculty of Electronic Engineering Technology, Universiti Malaysia Perlis, Arau, Malaysia
| | - Muhammad Asjad
- Department of Applied Mathematics and Sciences, Khalifa University, Abu Dhabi, United Arab Emirates
| | - A. N. Ikot
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Nigeria
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15
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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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16
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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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17
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Nwabuzor P, Edet C, Ndem Ikot A, Okorie U, Ramantswana M, Horchani R, Abdel-Aty AH, Rampho G. Analyzing the Effects of Topological Defect (TD) on the Energy Spectra and Thermal Properties of LiH, TiC and I 2 Diatomic Molecules. ENTROPY 2021; 23:e23081060. [PMID: 34441200 PMCID: PMC8393240 DOI: 10.3390/e23081060] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/21/2021] [Revised: 06/24/2021] [Accepted: 06/28/2021] [Indexed: 11/25/2022]
Abstract
In this study, the impacts of TD on the energy spectra and thermal properties of LiH, TiC and I2 diatomic molecules is considered. The Schrodinger equation in cosmic string spacetime is solved with the generalized Morse potential using the well-known (NU) method. The energy spectra and eigenfunction are obtained respectively. The energy spectra is used to obtain the partition function which is then used to evaluate the thermal properties of the system is evaluated accordingly. We find that the energy spectra in the presence of the TD differ from their flat Minkowski spacetime analogue. The effects of the deformation parameter and TD on the thermal properties of the system is also analysed in detail. We observe that the specific heat capacity of the system tends to exhibit quasi-saturation as the deformation parameter and topological defect approaches unity. The results of our study can be applied in the astrophysical situation where these modifications exist in the understanding of spectroscopical data and it may be used as a probe of the presence of a cosmic string or a global monopole in the Universe.
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Affiliation(s)
- Peter Nwabuzor
- Physics Production Technology, School of Science Laboratory Technology, University of Port Harcourt, Choba PMB 5323, Rivers State, Nigeria;
| | - Collins Edet
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba PMB 5323, Rivers State, Nigeria; (A.N.I.); (U.O.)
- Correspondence:
| | - Akpan Ndem Ikot
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba PMB 5323, Rivers State, Nigeria; (A.N.I.); (U.O.)
| | - Uduakobong Okorie
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba PMB 5323, Rivers State, Nigeria; (A.N.I.); (U.O.)
- Department of Physics, Akwa Ibom State University, Ikot Akpaden, Uyo PMB 1167, Akwa Ibom, Nigeria
| | - Morris Ramantswana
- Department of Physics, University of South Africa, Johannesburg 1710, Florida, South Africa; (M.R.); (G.R.)
| | - Ridha Horchani
- Department of Physics, College of Science, Sultan Qaboos University, Al-Khod 123, Muscat P.O. Box 36, Oman;
| | - Abdel-Haleem Abdel-Aty
- Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia;
- Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt
| | - Gaotsiwe Rampho
- Department of Physics, University of South Africa, Johannesburg 1710, Florida, South Africa; (M.R.); (G.R.)
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18
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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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19
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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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20
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Onate CA, Onyeaju MC, Bankole DT, Ikot AN. Eigensolution techniques, expectation values and Fisher information of Wei potential function. J Mol Model 2020; 26:311. [PMID: 33089429 DOI: 10.1007/s00894-020-04573-4] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/19/2020] [Accepted: 10/15/2020] [Indexed: 11/30/2022]
Abstract
An approximate solution of the one-dimensional relativistic Klein-Gordon equation was obtained under the interaction of an improved expression for Wei potential energy function. The solution of the non-relativistic Schrödinger equation was obtained from the solution of the relativistic Klein-Gordon equation by certain mappings. We have calculated Fisher information for position space and momentum space via the computation of expectation values. The effects of some parameters of the Wei potential energy function on the Fisher information were fully examined graphically. We have also examined the effects of the quantum number n and the angular momentum quantum number ℓ on the expectation values and Fisher information respectively for some selected molecules. Our results revealed that the variation of most of the parameters of the Wei potential energy function against the Fisher information does not obey the Heisenberg uncertainty relation for Fisher information while that of the quantum number and angular momentum quantum number on Fisher information obeyed the relation.
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Affiliation(s)
- C A Onate
- Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria.
| | - M C Onyeaju
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Port Harcourt, Nigeria
| | - D T Bankole
- Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria
| | - A N Ikot
- Theoretical Physics Group, Department of Physics, University of Port Harcourt, Choba, Port Harcourt, Nigeria
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21
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Jia CS, Li J, Liu YS, Peng XL, Jia X, Zhang LH, Jiang R, Li XP, Liu JY, Zhao YL. Predictions of thermodynamic properties for hydrogen sulfide. J Mol Liq 2020. [DOI: 10.1016/j.molliq.2020.113751] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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22
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A four-parameters model for molar entropy calculation of diatomic molecules via shifted Tietz-Wei potential. Chem Phys Lett 2020. [DOI: 10.1016/j.cplett.2020.137583] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
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23
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Accurate and general model to predict molar entropy for diatomic molecules. SOUTH AFRICAN JOURNAL OF CHEMICAL ENGINEERING 2020. [DOI: 10.1016/j.sajce.2020.07.001] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/23/2022] Open
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24
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Okorie US, Ikot AN, Chukwuocha EO. The Improved Deformed Exponential‐type Potential Energy Model for
N
2
,
NI
,
ScI
, and
RbH
Diatomic Molecules. B KOREAN CHEM SOC 2020. [DOI: 10.1002/bkcs.12039] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Uduakobong S. Okorie
- Department of Physics, Theoretical Physics GroupUniversity of Port Harcourt Choba Nigeria
| | - Akpan N. Ikot
- Department of Physics, Theoretical Physics GroupUniversity of Port Harcourt Choba Nigeria
| | - Ephraim O. Chukwuocha
- Department of Physics, Theoretical Physics GroupUniversity of Port Harcourt Choba Nigeria
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25
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Jia CS, Wang YT, Wei LS, Wang CW, Peng XL, Zhang LH. Predictions of Entropy and Gibbs Energy for Carbonyl Sulfide. ACS OMEGA 2019; 4:20000-20004. [PMID: 31788634 PMCID: PMC6882136 DOI: 10.1021/acsomega.9b02950] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/10/2019] [Accepted: 10/29/2019] [Indexed: 06/10/2023]
Abstract
Many chemical and physical equilibrium conditions can be determined from minimizing the Gibbs free energies of the system. Efficient analytical representations of the entropy and Gibbs free energy of carbonyl sulfide remain elusive in the communality of science and engineering. Here, we report two analytical representations of the entropy and Gibbs free energy for carbonyl sulfide, and the prediction procedures only involve six molecular constants of the carbonyl sulfide molecule. In the temperature range from 300 to 6000 K, the average relative deviations of the predicted molar entropy and reduced Gibbs free energy values of carbonyl sulfide from the National Institute of Standards and Technology database are arrived at 0.150 and 0.189%, respectively.
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Affiliation(s)
- Chun-Sheng Jia
- State
Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, Sichuan, People’s Republic
of China
| | - Yi-Ting Wang
- State
Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, Sichuan, People’s Republic
of China
| | - Lin-Sheng Wei
- Engineering
Technology Research Institute, PetroChina
Southwest Oil and Gasfield Company, Chengdu 610017, People’s
Republic of China
| | - Chao-Wen Wang
- State
Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, Sichuan, People’s Republic
of China
| | - Xiao-Long Peng
- State
Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, Sichuan, People’s Republic
of China
| | - Lie-Hui Zhang
- State
Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, Sichuan, People’s Republic
of China
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26
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Wang J, Jia CS, Li CJ, Peng XL, Zhang LH, Liu JY. Thermodynamic Properties for Carbon Dioxide. ACS OMEGA 2019; 4:19193-19198. [PMID: 31763543 PMCID: PMC6868907 DOI: 10.1021/acsomega.9b02488] [Citation(s) in RCA: 30] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/05/2019] [Accepted: 10/21/2019] [Indexed: 05/13/2023]
Abstract
We first report three reliable analytical expressions of the entropy, enthalpy and Gibbs free energy of carbon dioxide (CO2) and perform predictions of these three thermodynamic quantities on the basis of the proposed analytical expressions and in terms of experimental values of five molecular constants for CO2. The average relative deviations of the calculated values from the National Institute of Standards and Technology database over the temperature range from 300 to 6000 K are merely 0.053, 0.95, and 0.070%, respectively, for the entropy, enthalpy, and Gibbs free energy. The present predictive expressions are away from the utilization of plenty of experimental spectroscopy data and are applicable to treat CO2 capture and storage processes.
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27
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Chen XY, Li J, Jia CS. Thermodynamic Properties of Gaseous Carbon Disulfide. ACS OMEGA 2019; 4:16121-16124. [PMID: 31592480 PMCID: PMC6777084 DOI: 10.1021/acsomega.9b02303] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/23/2019] [Accepted: 08/30/2019] [Indexed: 06/10/2023]
Abstract
Efficient analytical representations of the thermodynamic properties for carbon disulfide remain open challenges in the communality of science and engineering. We present two analytical representations of the entropy and Gibbs free energy for gaseous carbon disulfide which we find to be of satisfactory accuracy and convenient for future use. The proposed two analytical representations merely rely on five molecular constants of the carbon disulfide molecule and avoid applications of a large number of experimental spectroscopy data. In the temperature range from 300 to 6000 K, the average relative deviations of the predicted molar entropy and reduced Gibbs free energy values from the National Institute of Standards and Technology database are 0.250 and 0.108%, respectively.
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Affiliation(s)
- Xiao-Yu Chen
- Petroleum
Engineering School and State Key Laboratory of Oil and Gas Reservoir
Geology and Exploitation, Southwest Petroleum
University, Chengdu 610500, People’s Republic
of China
| | - Ji Li
- Petroleum
Engineering School and State Key Laboratory of Oil and Gas Reservoir
Geology and Exploitation, Southwest Petroleum
University, Chengdu 610500, People’s Republic
of China
| | - Chun-Sheng Jia
- Petroleum
Engineering School and 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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28
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29
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Jiang R, Jia CS, Wang YQ, Peng XL, Zhang LH. Prediction of Gibbs free energy for the gases Cl2, Br2, and HCl. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2019.04.040] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023]
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30
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Analytical calculations of thermodynamic functions of lithium dimer using modified Tietz and Badawi-Bessis-Bessis potentials. COMPUT THEOR CHEM 2019. [DOI: 10.1016/j.comptc.2019.03.019] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/23/2022]
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31
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32
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Jiang R, Jia CS, Wang YQ, Peng XL, Zhang LH. Prediction of enthalpy for the gases CO, HCl, and BF. Chem Phys Lett 2019. [DOI: 10.1016/j.cplett.2018.11.044] [Citation(s) in RCA: 53] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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33
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34
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35
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36
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37
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Jia CS, Wang CW, Zhang LH, Peng XL, Tang HM, Liu JY, Xiong Y, Zeng R. Predictions of entropy for diatomic molecules and gaseous substances. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2017.12.013] [Citation(s) in RCA: 73] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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38
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Lim TC, Dawson JA. A convenient and accurate wide-range parameter relationship between Buckingham and Morse potential energy functions. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1407003] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Teik-Cheng Lim
- School of Science and Technology, Singapore University of Social Sciences, Singapore
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39
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40
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Jia CS, Wang CW, Zhang LH, Peng XL, Zeng R, You XT. Partition function of improved Tietz oscillators. Chem Phys Lett 2017. [DOI: 10.1016/j.cplett.2017.03.068] [Citation(s) in RCA: 96] [Impact Index Per Article: 13.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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41
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42
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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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43
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Ovando G, Peña JJ, Morales J. On the equivalence of radial potential models for diatomic molecules. Theor Chem Acc 2016. [DOI: 10.1007/s00214-016-1809-9] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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44
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45
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Jia CS, Peng XL, He S. Molecular Spinless Energies of the Modified Rosen-Morse Potential Energy Model. B KOREAN CHEM SOC 2014. [DOI: 10.5012/bkcs.2014.35.9.2699] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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46
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47
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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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48
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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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49
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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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50
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Yahya W, Issa K, Falaye B, Oyewumi K. Nonrelativistic and relativistic bound state solutions of the molecular Tietz potential via the improved asymptotic iteration method. CAN J CHEM 2014. [DOI: 10.1139/cjc-2013-0479] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
Abstract
We have obtained the approximate analytical solutions of the relativistic and nonrelativistic molecular Tietz potential using the improved asymptotic iteration method. By approximating the centrifugal term through the Greene–Aldrich approximation scheme, we have obtained the energy eigenvalues and wave functions for all orbital quantum numbers [Formula: see text]. Where necessary, we made comparison with the result obtained previously in the literature. The relative closeness of the two results reveal the accuracy of the method presented in this study. We proceed further to obtain the rotational-vibrational energy spectrum for some diatomic molecules. These molecules are CO, HCl, H2, and LiH. We have also obtained the relativistic bound state solution of the Klein−Gordon equation with this potential. In the nonrelativistic limits, our result converges to that of the Schrödinger system.
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Affiliation(s)
- W.A. Yahya
- Theoretical Physics Section, Department of Physics, University of Ilorin, Nigeria
- Department of Physics and Material Science, Kwara State University, Malete, P.M.B 1530, Ilorin, Kwara State, Nigeria
| | - K. Issa
- Department of Statistics and Mathematical Sciences, Kwara State University, Malete, Nigeria
| | - B.J. Falaye
- Theoretical Physics Section, Department of Physics, University of Ilorin, Nigeria
| | - K.J. Oyewumi
- Theoretical Physics Section, Department of Physics, University of Ilorin, Nigeria
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