1
|
Bound-state solutions and thermal properties of the modified Tietz-Hua potential. Sci Rep 2021; 11:2129. [PMID: 33483571 PMCID: PMC7822887 DOI: 10.1038/s41598-021-81428-9] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/21/2020] [Accepted: 01/05/2021] [Indexed: 11/25/2022] Open
Abstract
An approximate solutions of the radial Schrödinger equation was obtained under a modified Tietz–Hua potential via supersymmetric approach. The effect of the modified parameter and optimization parameter respectively on energy eigenvalues were graphically and numerically examined. The comparison of the energy eigenvalues of modified Tietz–Hua potential and the actual Tietz–Hua potential were examined. The ro-vibrational energy of four molecules were also presented numerically. The thermal properties of the modified Tietz–Hua potential were calculated and the effect of temperature on each of the thermal property were examined under hydrogen fluoride, hydrogen molecule and carbon (ii) oxide. The study reveals that for a very small value of the modified parameter, the energy eigenvalues of the modified Tietz–Hua potential and that of the actual Tietz–Hua potential are equivalent. Finally, the vibrational energies for Cesium molecule was calculated and compared with the observed value. The calculated results were found to be in good agreement with the observed value.
Collapse
|
2
|
Elishav O, Mosevitzky Lis B, Miller EM, Arent DJ, Valera-Medina A, Grinberg Dana A, Shter GE, Grader GS. Progress and Prospective of Nitrogen-Based Alternative Fuels. Chem Rev 2020; 120:5352-5436. [PMID: 32501681 DOI: 10.1021/acs.chemrev.9b00538] [Citation(s) in RCA: 85] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
Alternative fuels are essential to enable the transition to a sustainable and environmentally friendly energy supply. Synthetic fuels derived from renewable energies can act as energy storage media, thus mitigating the effects of fossil fuels on environment and health. Their economic viability, environmental impact, and compatibility with current infrastructure and technologies are fuel and power source specific. Nitrogen-based fuels pose one possible synthetic fuel pathway. In this review, we discuss the progress and current research on utilization of nitrogen-based fuels in power applications, covering the complete fuel cycle. We cover the production, distribution, and storage of nitrogen-based fuels. We assess much of the existing literature on the reactions involved in the ammonia to nitrogen atom pathway in nitrogen-based fuel combustion. Furthermore, we discuss nitrogen-based fuel applications ranging from combustion engines to gas turbines, as well as their exploitation by suggested end-uses. Thereby, we evaluate the potential opportunities and challenges of expanding the role of nitrogen-based molecules in the energy sector, outlining their use as energy carriers in relevant fields.
Collapse
Affiliation(s)
- Oren Elishav
- The Nancy and Stephen Grand Technion Energy Program, Technion - Israel Institute of Technology, Haifa 3200003, Israel
| | - Bar Mosevitzky Lis
- The Wolfson Department of Chemical Engineering, Technion - Israel Institute of Technology, Haifa 3200003, Israel
| | - Elisa M Miller
- Materials and Chemical Science and Technology Directorate, National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, Colorado 80401, United States
| | - Douglas J Arent
- National Renewable Energy Laboratory, 15013 Denver West Parkway, Golden, Colorado 80401, United States
| | - Agustin Valera-Medina
- College of Physical Sciences and Engineering, Cardiff University, Wales, United Kingdom
| | - Alon Grinberg Dana
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Gennady E Shter
- The Wolfson Department of Chemical Engineering, Technion - Israel Institute of Technology, Haifa 3200003, Israel
| | - Gideon S Grader
- The Nancy and Stephen Grand Technion Energy Program, Technion - Israel Institute of Technology, Haifa 3200003, Israel.,The Wolfson Department of Chemical Engineering, Technion - Israel Institute of Technology, Haifa 3200003, Israel
| |
Collapse
|
3
|
Buchowiecki M, Prątnicki F. High temperature partition function – a key role of ro-vibrational coupling and inflection points. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1334132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Marcin Buchowiecki
- Institute of Physics, Department of Mathematics and Physics, University of Szczecin, Szczecin, Poland
| | - Filip Prątnicki
- Institute of Physics, Department of Mathematics and Physics, University of Szczecin, Szczecin, Poland
| |
Collapse
|
4
|
|
5
|
Wang W, Zhao Y. The dissociation and recombination rates of CH 4 through the Ni(111) surface: The effect of lattice motion. J Chem Phys 2017; 147:044703. [PMID: 28764359 DOI: 10.1063/1.4995299] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Methane dissociation is a prototypical system for the study of surface reaction dynamics. The dissociation and recombination rates of CH4 through the Ni(111) surface are calculated by using the quantum instanton method with an analytical potential energy surface. The Ni(111) lattice is treated rigidly, classically, and quantum mechanically so as to reveal the effect of lattice motion. The results demonstrate that it is the lateral displacements rather than the upward and downward movements of the surface nickel atoms that affect the rates a lot. Compared with the rigid lattice, the classical relaxation of the lattice can increase the rates by lowering the free energy barriers. For instance, at 300 K, the dissociation and recombination rates with the classical lattice exceed the ones with the rigid lattice by 6 and 10 orders of magnitude, respectively. Compared with the classical lattice, the quantum delocalization rather than the zero-point energy of the Ni atoms further enhances the rates by widening the reaction path. For instance, the dissociation rate with the quantum lattice is about 10 times larger than that with the classical lattice at 300 K. On the rigid lattice, due to the zero-point energy difference between CH4 and CD4, the kinetic isotope effects are larger than 1 for the dissociation process, while they are smaller than 1 for the recombination process. The increasing kinetic isotope effect with decreasing temperature demonstrates that the quantum tunneling effect is remarkable for the dissociation process.
Collapse
Affiliation(s)
- Wenji Wang
- College of Chemistry & Pharmacy, Northwest A&F University, Yangling, 712100 Shaanxi Province, People's Republic of China
| | - Yi Zhao
- State Key Laboratory for Physical Chemistry of Solid Surfaces and Fujian Provincial Key Lab of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People's Republic of China
| |
Collapse
|
6
|
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]
|
7
|
|
8
|
Zhao H, Wang W, Zhao Y. Thermal Rate Constants for the O( 3P) + CH 4 → OH + CH 3 Reaction: The Effects of Quantum Tunneling and Potential Energy Barrier Shape. J Phys Chem A 2016; 120:7589-7597. [PMID: 27640428 DOI: 10.1021/acs.jpca.6b07029] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The rate constants and kinetic isotope effects for the O(3P) + CH4 reaction have been investigated with the quantum instanton method in full dimensionality. The calculated rate constants are in good agreement with the experimental values above 400 K, below which the measured values are scattered. Compared to other theoretical approaches, the quantum instanton method predicts the largest quantum tunneling effect, so it gives the largest rate constants at low temperatures. The calculated kinetic isotope effects are always much larger than 1 and increase with decreasing temperature, due to the zero-point energy and quantum tunneling. Our calculations on different potential energy surfaces demonstrate that the potential energy barrier shape dominates the magnitude of quantum tunneling and has a great effect on the kinetic isotope effect.
Collapse
Affiliation(s)
- Huali Zhao
- College of Science, Northwest A&F University , Yangling, 712100 Shaanxi Province, P. R. China
| | - Wenji Wang
- College of Science, Northwest A&F University , Yangling, 712100 Shaanxi Province, P. R. China
| | - Yi Zhao
- State Key Laboratory for Physical Chemistry of Solid Surfaces and Fujian Provincial Key Lab of Theoretical and Computational Chemistry, College of Chemistry and Chemical Engineering, Xiamen University , Xiamen 361005, P. R. China
| |
Collapse
|
9
|
The ratios of partition functions at different temperatures – Sensitivity to potential energy shape II. Chem Phys Lett 2016. [DOI: 10.1016/j.cplett.2016.04.017] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
|
10
|
Wang W, Zhao Y. The direct and precursor mediated dissociation rates of H2 on a Ni(111) surface. Phys Chem Chem Phys 2015; 17:5901-12. [PMID: 25630487 DOI: 10.1039/c4cp05624h] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The dissociation and recombination rates of physisorbed H2, and the direct and steady state dissociation (i.e., the precursor mediated dissociation) rates of gas phase H2 on Ni(111), as well as the corresponding kinetic isotope effects, are calculated using the quantum instanton method, together with path integral Monte Carlo and adaptive umbrella sampling techniques. All these rates except the recombination one first decrease and then increase with the increasing temperature, and their minimum values appear at about 250, 300 and 250 K, respectively. These non-monotonic behaviors reveal that the quantum effect of H2 should be very remarkable at low temperatures. The steady state rates are smaller than the direct rates at low temperatures, however, they become larger than the direct ones at high temperatures, these two kinds of rates become equal at about 400 and 300 K on the rigid and quantum lattices, respectively. The quantum motion of the lattice can enhance the direct and steady state rates, and it increases the steady state rate much more than the direct one, for instance, the direct and steady state rates on the quantum lattice are 1.30 and 2.08 times larger than that on the rigid one at 300 K. The calculated kinetic isotope effects are much larger than 1, which reveals that H2 always has a larger rate than that of D2, and the direct process predicts much larger kinetic isotope effects than the steady state process at low temperatures. In addition, the kinetic isotope effects are not affected by the lattice motion.
Collapse
Affiliation(s)
- Wenji Wang
- College of Science, Northwest A&F University, Yangling, 712100, Shaanxi Province, P. R. China.
| | | |
Collapse
|
11
|
Path integral Monte Carlo with the Takahashi–Imada approximation for the temperature dependence of the equilibrium constant. Chem Phys 2014. [DOI: 10.1016/j.chemphys.2014.01.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
12
|
Wang W, Zhao Y. Dissociation rates of H2on a Ni(100) surface: the role of the physisorbed state. Phys Chem Chem Phys 2014; 16:13318-28. [DOI: 10.1039/c4cp01705f] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
|
13
|
Buchowiecki M, Vaníček J. Monte Carlo evaluation of the equilibrium isotope effects using the Takahashi–Imada factorization of the Feynman path integral. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2013.09.070] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
|
14
|
BUCHOWIECKI MARCIN. TI/PIMC METHOD WITH THE TAKAHASHI–IMADA APPROXIMATION FOR THE EQUILIBRIUM CONSTANT OF THE O + HCl ⇌ OH + Cl REACTION. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2013. [DOI: 10.1142/s0219633613500260] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The thermodynamic integration/path integral Monte Carlo (TI/PIMC) method of calculating the temperature dependence of the equilibrium constant quantum mechanically is applied to O + HCl ⇌ OH + Cl reaction. The method is based upon PIMC simulations for energies of the reactants and the products and subsequently on thermodynamic integration for the ratios of partition functions. PIMC calculations are performed with the primitive approximation (PA) and the Takahashi–Imada approximation (TIA).
Collapse
Affiliation(s)
- MARCIN BUCHOWIECKI
- Institute of Physics, University of Szczecin, Wielkopolska 15, Szczecin, 70-451, Poland
| |
Collapse
|
15
|
Wang W, Zhao Y. Quantum instanton calculation of rate constant for CH4 + OH → CH3 + H2O reaction: torsional anharmonicity and kinetic isotope effect. J Chem Phys 2013; 137:214306. [PMID: 23231230 DOI: 10.1063/1.4768874] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Thermal rate constants for the title reaction are calculated by using the quantum instanton approximation within the full dimensional Cartesian coordinates. The results reveal that the quantum effect is remarkable for the reaction at both low and high temperatures, and the obtained rates are in good agreement with experimental measurements at high temperatures. Compared to the harmonic approximation, the torsional anharmonic effect of the internal rotation has a little influence on the rates at low temperatures, however, it enhances the rate by about 20% at 1000 K. In addition, the free energy barriers for the isotopic reactions and the temperature dependence of kinetic isotope effects are also investigated. Generally speaking, for the title reaction, the replacement of OH with OD will reduce the free energy barrier, while substituting D for H (connected to C) will increase the free energy barrier.
Collapse
Affiliation(s)
- Wenji Wang
- College of Science, Northwest A&F University, Shaanxi Province, Yangling, 712100, People's Republic of China.
| | | |
Collapse
|