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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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Fan QC, Jian J, Fan ZX, Fu J, Li HD, Ma J, Xie F. A method for predicting the molar heat capacities of HBr and HCl gases based on the full set of molecular rovibrational energies. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2022; 267:120564. [PMID: 34749112 DOI: 10.1016/j.saa.2021.120564] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/27/2021] [Revised: 10/20/2021] [Accepted: 10/26/2021] [Indexed: 06/13/2023]
Abstract
A new method is presented for one to obtain the molar heat capacities of diatomic macroscopic gas with a full set of microscopic molecular rovibrational energies. Based on an accurate experimental vibrational energies subset of a diatomic electronic ground state, the full vibrational energies can be obtained by using the variational algebraic method (VAM), the potential energy curves (PECs) will be constructed by the Rydberg-Klein-Rees (RKR) method, the full set of rovibrational energies will be calculated by the LEVEL program, and then the partition functions and the molar heat capacities of macroscopic gas can be calculated with the help of the quantum statistical ensemble theory. Applying the method to the ground state HBr and HCl gases, it is found that the relative errors of the partition functions calculated in the temperature range of 300 ∼ 6000 K are in excellent agreement with those obtained from TIPS database, and the calculated molar heat capacities are closer to the experimental values than those calculated by other methods without considering the energy levels of highly excited quantum states. The present method provides an effective new way for one to obtain the full set of molecular rovibrational energies and the molar heat capacities of macroscopic gas through the microscopic spectral information of a diatomic system.
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Affiliation(s)
- Qun-Chao Fan
- School of Science, Key Laboratory of High Performance Scientific Computation, Xihua University, Chengdu 610039, China
| | - Jun Jian
- School of Science, Key Laboratory of High Performance Scientific Computation, Xihua University, Chengdu 610039, China
| | - Zhi-Xiang Fan
- School of Science, Key Laboratory of High Performance Scientific Computation, Xihua University, Chengdu 610039, China.
| | - Jia Fu
- School of Science, Key Laboratory of High Performance Scientific Computation, Xihua University, Chengdu 610039, China.
| | - Hui-Dong Li
- School of Science, Key Laboratory of High Performance Scientific Computation, Xihua University, Chengdu 610039, China
| | - Jie Ma
- State Key Laboratory of Quantum Optics and Quantum Optics Devices, Laser Spectroscopy Laboratory, College of Physics and Electronics Engineering, Shanxi University, Taiyuan 030006, China
| | - Feng Xie
- Institute of Nuclear and New Energy Technology, Collaborative Innovation Center of Advanced Nuclear Energy Technology, Key Laboratory of Advanced Reactor Engineering and Safety of Ministry of Education, Tsinghua University, Beijing 100084, China
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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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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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Ghanbari A, Khordad R. Theoretical prediction of thermodynamic properties of N2 and CO using pseudo harmonic and Mie-type potentials. Chem Phys 2020. [DOI: 10.1016/j.chemphys.2020.110732] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Tang B, Wang YT, Peng XL, Zhang LH, Jia CS. Efficient predictions of Gibbs free energy for the gases CO, BF, and gaseous BBr. J Mol Struct 2020. [DOI: 10.1016/j.molstruc.2019.126958] [Citation(s) in RCA: 36] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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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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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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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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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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Khordad R, Avazpour A, Ghanbari A. Exact analytical calculations of thermodynamic functions of gaseous substances. Chem Phys 2019. [DOI: 10.1016/j.chemphys.2018.09.038] [Citation(s) in RCA: 47] [Impact Index Per Article: 9.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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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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Buchowiecki M. Ro-vibrational coupling in high temperature thermochemistry of the BBr molecule. Chem Phys Lett 2018. [DOI: 10.1016/j.cplett.2017.12.051] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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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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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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