由於當前的Haber-Bosch製氨製程需要高溫（500°C）和高壓（300 bar），因此氨的生產具有很高的能源消耗成本。如果不考慮釕(Ru)的高成本和強烈氫中毒影響，則使用活性更高的釕基催化劑代替傳統的鐵基催化劑可以潛在地提高氨的生產效率。載體的使用使金屬原子分散到奈米顆粒或成為單原子催化劑，以增加活性表面積和成本效率。此外，氫原子可以溢流到載體上以減輕氫中毒影響並且開發出催化劑，透過將溢流能障最小化來改善氫從釕到載體的溢流。使用不穩定的極性表面（例如氧化鎂(111)）作為載體可改善氫的溢流，但機制細節尚不清楚。由於密度泛函理論（DFT）在原子尺度上的催化劑反應中已獲得成功研究，因此在這項工作中應用了DFT計算來研究氫在Ru/MgO(111)上的溢流細節。與其他切面相比，氣相中的氫氣分子解離並遷移到Ru/MgO(111)上氧離子頂部的吸附位點。這是因為Ru在MgO（111）上被氧化為Ru2 +離子，與附近的O2-離子形成了Frustrated Lewis對，從而促進了氫氣的解離。 氫溢流的活化能障從使用Ru1單離子（+ 1.22 eV）降低到使用團簇Ru4（+ 0.00 eV）和Ru10（+ 0.53 eV）之反應皆可發生，這意味著不管釕之顆數變化不會影響氫溢流到表面的特性。使用氧化鎂（111）時，也觀察到載體到金屬的氧溢出而形成RuO。這可能與Ru/MgO(111) 的強金屬-載體相互作用（SMSI）有關，將來可以對其進行詳細研究。總之，運用DFT理論計算成功地表徵了從金屬到載體的氫溢流和從載體到金屬的氧溢流。當使用氧化鎂(111)載體時，這些現象將有望改善釕催化劑上之氫活化的效益。

Ammonia production has a high energy cost because of the high temperature (500 ° C) and high pressure (300 bar) requirement in the current Haber-Bosch process. Replacing the traditional iron-based catalysts with more active Ruthenium (Ru)-based catalysts can potentially improve ammonia production efficiency if not for the high cost and strong H poisoning on Ru. The use of support enables dispersion of metal atoms to nanoparticles or single atom catalysts for increased active surface area and cost efficiency. Furthermore, H adatoms can spillover to the support to relieve H-poisoning and developing catalysts that improve H spillover from Ru to support by minimizing the spillover energy barrier is important. Using unstable polar surface, like MgO (111), as a support is known to improve H spillover but the details of the mechanism is unclear. Since density functional theory (DFT) has been successful in catalysts reaction in atomic scales DFT calculations is applied in this work to study the details of H spillover on Ru/MgO (111). The dissociation of H2 molecule in gas phase and the migration to the adsorption sites atop oxygen ion on Ru/MgO (111) compared to other facets. This is because of the oxidation of Ru to Ru2+ ions on MgO (111) forming a frustrated Lewis pair with nearby O2- ions that facilitate H2 dissociation. The occurence of all reactions, which activation energy barriers of H spillover decreases from Ru1 single ion (+1.22eV ) to Ru4 (+0.00eV) and Ru10 (+0.53eV) clusters, implying the invariant effect of the number of ruthenium atoms toward the properties of hydrogen spillover on surface. Support to metal oxygen spillover was also observed on when using MgO (111) forming RuO. This can be associated with strong metal-support interaction (SMSI) of Ru/MgO (111) that can be studied in detail in the future. In summary, DFT calculations successfully characterized support to metal oxygen spillover and metal to support H spillover. And these phenomena are expected to improve H activation over Ru catalyst when using MgO (111) support.

摘要 1
Abstract 2
Acknowledgement 3
目錄 4
圖目錄 10
表目錄 17
第一章 緒論 (Introduction) 20
1.1前言 (Preface) 20
1.2氨氣能源簡介 (Introduction for Ammonia Energy) 21
1.2.1哈勃法製氨及現今製造需求 (Haber-Bosch Process and Current Manufacturing Demands) 24
1.2.2 吸附氫和解離氫 (Hydrogen Adsorption and Dissociation) 25
1.3研究動機與要點 (Research Motivations and Focal Points) 27
1.3.1 氫中毒 (Hydrogen Poisoning) 29
1.3.2 單原子催化劑 (Single Atom Catalyst) 31
1. 4研究目標 (Research Objectives) 32
1.5 文章架構 (The Structure of Thesis) 34
第二章 文獻回顧 (Literature Review) 35
2.1 Stabilized Ru Metal Cluster Structure in Gas Phase 36
2.2 Ru and Ru/MgO as Catalysts in Reaction 38
2.3 Electronic Analysis of Au Clusters Decorated on MgO(111) Surfaces 43
2.4 Hydrogen Hopping on MgO(100) 45
2.5 Hydrogen Spillover Mechanism 47
2.5.1溢流現象 (Spillover Phenomenon) 47
2.6.2氫溢流機制的提出 (Proposal of Hydrogen Spillover Mechanisms) 47
2.5.3 Hydrogen Spillover Mechanisms of Pt4/Graphene and Pt4/Anatase (101) 49
2.5.4 Stable Structure on the Surface of Anatase Titanium Dioxide (101) 50
2.6 Metal-Support Interaction 52
2.6.1 金屬載體作用力機制 (Metal-Support Interaction Mechanism) 52
2.6.2 氧溢流機制 (Oxygen Spillover Mechanism) 53
第三章 研究相關計算理論(Relative Theory Calculations) 55
3.1 第一原理計算(First Principles Calculation) 55
3.1.1 薛丁格方程式（Schrödinger Equation） 55
3.1.2 基底函數組(Basis Set) 58
3.1.3平面波(Plane Wave) 59
3.1.4 Bloch Theorem 61
3.1.4.1 Reciprocal Lattice 62
3.1.4.1 First Brillouin Zone 63
3.1.5波恩–歐本海默近似法(Born-Oppenheimer Approximation) 64
3.1.6 Hartree-Fock Equation 66
3.2密度泛函理論(Density Functional Theory, DFT) 67
3.2.1 Hohenberg-Kohn Theorem 68
3.2.2科恩－沈方程(Kohn–Sham Equation) 69
3.2.3 Self-Consistent Field Method (SCF) 72
3.3交換相關能量(Exchange Correlation Energy) 74
3.3.1 局部密度近似(Local Density Approximation- LDA) 74
3.3.2 廣義梯度近似(Generalized Gradient Approximation- GGA) 75
3.3.2.1 PW91 76
3.3.2.2 PBE 77
3.4膺勢(Pseudopotentials) 77
3.5 優化(Optimization) 79
3.5.1位能面(Potential Energy Surface) 80
3.5.2最小化(Minimization) 81
第四章 計算及模擬方法 (Computational Details) 82
4.1 Simulation Software and Processes 82
4.1.1 Vienna Ab-initio Simulation Package (VASP) 83
4.1.1.1 Input Files 84
4.1.1.2 Output Files 84
4.2 Model Construction Planning with Calculation Procedure 86
4.2.1 氧化鎂模型建立及測試 (MgO Model Construction and Convergence Tests) 87
4.2.2凝聚力 (Cohesive Energy)、結合能 (Binding Energy)與吸附能 (Adsoption Energy) 90
4.2.3表面收斂及層數測試 (Surface Relaxation and Thickness Testing) 92
第五章 結果與討論 (Results and Discussion) 99
5. Overview of This Work 99
5.1 Run(n=4, 10) Clusters Configuration in Gas Phase 100
5.1.1 Structural and Energetic Analysis of Ru4 100
5.1.2 Structural and Energetic Analysis of Ru10 101
5.2 Surface Analysis of MgO(111), MgO(110), MgO(100) Facets 103
5.3 Run-MgO Interaction without O Spillover 104
5.3.1 Interaction of Ru Single Atom with MgO(111), (110), (100) Facets 104
5.3.1.1 Structural and Energetic Analysis 104
5.3.1.2 Bader Charge Analysis 113
5.3.1.3 DOS Analysis of Ru/MgO(111) and (110) 115
5.3.2 Interaction of Two Ru Single Atoms and Ru2 Dimer Decorated on MgO(111) 121
5.3.2.1 Structural and Energetic Analysis 121
5.3.2.2 Ru-Ru seperation effects 122
5.3.3 Interaction of Ru4 Cluster Decorated on 8H Saturated MgO(111) 123
5.3.3.1 Isomer Effects and Energetic Analysis 123
5.3.3.2 Structural and Energetic Analysis 125
5.3.4 Interaction of Ru10 cluster decorated on MgO(111) 127
5.3.4.1 Isomer Effects and Energetic Analysis 127
5.4 Hydrogen Dissociation, Adsorption and Spillover on Run/MgO without Oxygen Spillover 129
5.4.1 Hydrogen Adsorption on Ru Atom 130
5.4.2 Hydrogen Adsorption on MgO Surface 132
5.4.2.1 Adsorption Sites of Single Hydrogen Atom 132
5.4.2.2 Adsorption Sites of Hydrogen Molecule 134
5.4.2.3 Multiple of Hydrogen Atoms Adsorption on MgO(111) 136
5.4.3 Hydrogen Interaction with Ru1/MgO 137
5.4.3.1 Hydrogen Molecule Adsorption on Ru/MgO 137
5.4.3.2 Hydrogen Atom Adsorption on Ru/MgO 139
5.4.3.3 Multiple hydrogen atoms adsorption on Ru/MgO(111) 141
5.4.3.4 Multiple Hydrogen Atoms Adsorption on Ru/MgO(110) 142
5.4.3.5 Multiple Hydrogen Atoms Adsorption on Ru/MgO(100) 144
5.4.3.6 Mechanism of Hydrogen Spillover on Ru/MgO(111) 146
5.4.3.7 Mechanism of H spillover on Ru/MgO(110) and Ru/MgO(100) 152
5.4.3.8 Ru-H Separation Effect on Ru/MgO 155
5.4.3.9 Effects of Hydrogen Saturation of Support in Ru/MgO(111) 157
5.4.4 Hydrogen Interaction with Ru4/MgO(111) 162
5.4.4.1 Single Hydrogen Atom Adsorption 162
5.4.4.2 Multiple Hydrogen Atoms Adsorption 163
5.4.4.3 Mechanism of Hydrogen Spillover on Ru4/MgO(111) 166
5.4.4.4 Effects of Hydrogen Saturation of Support in Ru4/MgO(111) 168
5.4.5 Hydrogen Interaction with Ru10/MgO(111) 169
5.4.5.1 Single Hydrogen Atom Adsorption 169
5.4.5.2 Multiple Hydrogen Atoms Adsorption 172
5.4.5.3 Mechanism of Hydrogen Spillover on Ru10/MgO(111) 174
5.4.5.4 Ru-H Separation Effect on Ru10/MgO 176
5.4.5.5 Effects Htdrogen Saturation of Support in Ru10/MgO(111) 177
5.4.5.6 Adsorption of Hydrogen Atoms on 8H-Saturated Ru10/MgO(111) 181
5.4.5.8 Mechanism Hydrogen spillover on 8H-Saturated Ru10/MgO(111) 183
5.5 Oxygen spillover in Ru/MgO 185
5.5.1 Oxygen Spillover on Different Run Cluster Sizes on MgO(111) 186
5.5.2 Multiple Oxygen Spillover in Ru4/MgO(111) 189
5.5.3 Effect of Surface Polarity on Oxygen Spillover 191
5.5.5 Optimum number of Oxygen spillover for Ru4/MgO(111) 193
第六章 結論 (Conclusions) 195
第七章 研究挑戰及未來展望 (Research Challenge & Future Work) 199
參考資料 (Reference) 201
附錄 (Appendix) 208
Appendix-1 Kpoints Testing 208
Appendix-2 Cut-off Energy Testing 209
Appendix-3 Sigma Testing 209
Appendix-4 Lattice Constant Testing 210
Appendix-5 Surface Energy Testing 211
Appendix-6 N2 adsorption on MgO(111) & Ru1/MgO(111) catalyst 212
Appendix-7 Energetic Analysis of Run/MgO(111) 213
本研究相關之發表 216

1. Valera-Medina, A., Xiao, H., Owen-Jones, M., David, W. I. F. &Bowen, P. J. Ammonia for power. Progress in Energy and Combustion Science vol. 69 63–102 (2018).
2. Timmer, B., Olthuis, W. &Van DenBerg, A. Ammonia sensors and their applications - A review. Sensors Actuators, B Chem. 107, 666–677 (2005).
3. Klerke, A., Christensen, C. H., Nørskov, J. K. &Vegge, T. Ammonia for hydrogen storage: Challenges and opportunities. J. Mater. Chem. 18, 2304–2310 (2008).
4. Puspitasari, P. &Yahya, N. Development of ammonia synthesis. in 2011 National Postgraduate Conference - Energy and Sustainability: Exploring the Innovative Minds, NPC 2011 (2011). doi:10.1109/NatPC.2011.6136449.
5. Pfromm, P. H. Towards sustainable agriculture: Fossil-free ammonia. J. Renew. Sustain. Energy 9, (2017).
6. Prevention, I. P. Integrated Pollution Prevention and Control Large Volume Inorganic Chemicals - Ammonia , Acids and Fertilisers. I, (2007).
7. Czuppon, T. A., Knez, S. A., Schneider, R.V &Company, M. W. K. First Commercial Application of the Kellogg Advanced Ammonia Process. 236–251 (1992).
8. Rossetti, I., Pernicone, N. &Forni, L. Graphitised carbon as support for Ru/C ammonia synthesis catalyst. in Catalysis Today vols 102–103 219–224 (2005).
9. Czuppon, T. A., Knez, S. A., Strait, R. B. &Company, T. M. W. K. Commercial Experience with KAAP. (1994).
10. Haber Process for Ammonia Synthesis. GEN ERAL (2002).
11. Rosowski, F., Hinrichsen, O., Mulaler, M. &Ertl, G. The temperature-programmed desorption of N2 from a Ru / MgO catalyst used for ammonia synthesis. 36, 229–235 (1996).
12. Vojvodic, A. et al. Exploring the limits: A low-pressure, low-temperature Haber-Bosch process. Chem. Phys. Lett. 598, 108–112 (2014).
13. Muhler, M., Rosowski, E., Hinrichsen, O., Hornung, A. &Ertl, G. Ruthenium as Catalyst for Ammonia Synthesis. 101, 317–326 (1996).
14. Logadóttir, Á. &Nørskov, J. K. Ammonia synthesis over a Ru(0001) surface studied by density functional calculations. J. Catal. 220, 273–279 (2003).
15. Hellman, A. et al. Ammonia synthesis and decomposition on a Ru-based catalyst modeled by first-principles. Surf. Sci. 603, 1731–1739 (2009).
16. Taylor, P. Ruthenium Nanocatalysts for Ammonia Synthesis : A. 37–41 doi:10.1080/00986445.2014.923995.
17. K. AIKA, K. SHIMAZAKI, Y. HATTORI, A. OHYA, S. OHSHIMA, K. SHIROTA &OZAKI~, A. A. Support and Promoter Effect of Ruthenium Catalyst. 304, 296–304 (1985).
18. Murata, S. &Aika, K. Removal of chlorine ions from Ru / MgO catalysts for ammonia synthesis. 82, 1–12 (1992).
19. Apuzzo, J., Cimino, S. &Lisi, L. Ni or Ru supported on MgO/g-Al2O3 pellets for the catalytic conversion of ethanol into butanol. R. Soc. Chem. 25846–25855 (2018) doi:10.1039/c8ra04310h.
20. Lucentini, I., Casanovas, A. &Llorca, J. Catalytic ammonia decomposition for hydrogen production on Ni, Ru and Ni[sbnd]Ru supported on CeO2. Int. J. Hydrogen Energy 44, 12693–12707 (2019).
21. Wander, A., Bush, I. J. &Harrison, N. M. Stability of rocksalt polar surfaces : 1–4 (2003) doi:10.1103/PhysRevB.68.233405.
22. Zhang, W. &Tang, B. Stability of MgO ( 111 ) Polar Surface : Effect of the Environment. 3327–3333 (2008).
23. Hu, Z., Mahin, J., Datta, S., Bell, T. E. &Torrente-Murciano, L. Ru-Based Catalysts for H2 Production from Ammonia: Effect of 1D Support. Top. Catal. 62, 1169–1177 (2019).
24. Y, P. M., Predieri, G. &Maione, A. Ru / MgO sol-gel prepared catalysts for ammonia synthesis. _______Catalysis Lett. 79, (2002).
25. Larichev, Y.V. Valence State Study of Supported Ruthenium Ru / MgO Catalysts. J. Phys. Chem. C 14776–14780 (2010).
26. Papers, F. Influence of Reaction Conditions and Promoting Role of Ammonia Produced at Higher Temperature Conditions in Its Synthesis Process over Cs-Ru / MgO Catalyst. ChemistrySelect 2218–2224 (2019) doi:10.1002/slct.201803813.
27. Szmigiel, D. et al. The Kinetics of Ammonia Synthesis over Ruthenium-Based Catalysts : The Role of Barium and Cesium. 212, 205–212 (2002).
28. Larichev, Y.V. Effect of Cs+ promoter in Ru/MgO catalysts. J. Phys. Chem. C 115, 631–635 (2011).
29. Ju, X. et al. Highly Efficient Ru / MgO Catalyst with Surface-Enriched Basic Sites for Production of Hydrogen from Ammonia Decomposition. 4161–4170 (2019) doi:10.1002/cctc.201900306.
30. DaSilva Alvim, R., Borges, I. &Leitao, A. A. Proton Migration on Perfect, Vacant, and Doped MgO(001) Surfaces: Role of Dissociation Residual Groups. J. Phys. Chem. C 122, 21841–21853 (2018).
31. Paull, B. J. A Century of Synthetic Fertilizer : 1909-2009. (2014).
32. Ghuman, K. K., Tozaki, K. &Sadakiyo, M. Tailoring widely used ammonia synthesis catalysts for H and N poisoning resistance †. 5117–5122 (2019) doi:10.1039/c8cp05800h.
33. Manabe, R. et al. Electrocatalytic synthesis of ammonia by surface proton hopping. Chem. Sci. 8, 5434–5439 (2017).
34. Castelli, I. E., Soriga, S. G. &Man, I. C. Effects of the cooperative interaction on the diffusion of hydrogen on MgO(100). J. Chem. Phys. 149, (2018).
35. Wu, S. et al. Removal of Hydrogen Poisoning by Electrostatically Polar MgO Support for Low-Pressure NH 3 Synthesis at a High Rate over the Ru Catalyst. (2020) doi:10.1021/acscatal.0c00954.
36. Parkinson, G. S. Single-Atom Catalysis: How Structure Influences Catalytic Performance. Catal. Letters 0, 0 (2019).
37. Cheng, N., Zhang, L., Doyle, K. &Xueliang, D. Single ‑ Atom Catalysts : From Design to Application. Electrochemical Energy Reviews vol. 2 (Springer Singapore, 2019).
38. Baljeet Singh, S. K. and A. S. Cobalt Single Atom Heterogeneous Catalyst: Method of Preparation, Characterization, Catalysis, and Mechanism.
39. Kim, S., Lee, H. W., Pai, S. J. &Han, S. S. Activity , Selectivity , and Durability of Ruthenium Nanoparticle Catalysts for Ammonia Synthesis by Reactive Molecular Dynamics Simulation : The Size E ff ect. ACS Appl. Mater. Interfaces 10, 26188–26194 (2018).
40. Xiao, M. et al. A Single-Atom Iridium Heterogeneous Catalyst in Oxygen Reduction Reaction Forschungsartikel. 210008, 9742–9747 (2019).
41. Xu, Y. et al. The Synergetic Effect of Ni and Fe Bi-metal Single Atom Catalysts on Graphene for Highly Efficient Oxygen Evolution Reaction. 6, 1–8 (2020).
42. Li, S. et al. Structural and electronic properties of Ru n clusters „ n = 2 – 14 … studied by first-principles. 1–9 (2007) doi:10.1103/PhysRevB.76.045410.
43. Zhang, W., Zhao, H. &Wang, L. The Simple Cubic Structure of Ruthenium Clusters. 2140–2147 (2004) doi:10.1021/jp035995x.
44. You, A., Be, M. A. Y. &In, I. Coverage , lateral order , and vibrations of atomic nitrogen on Ru ( 0001 ). Chem. Phys. 8944, 1–8 (1998).
45. Cadigan, C. A. et al. Nanoscale (111) faceted rock-salt metal oxides in catalysis. 3, (2013).
46. Khoobiar, S. Particle to Particle Migration of Hydrogen Atoms on Platinum—Alumina Catalysts from Particle to Neighboring Particles. 68, 411–412 (1964).
47. Sihag, A. et al. DFT Insights into Comparative Hydrogen Adsorption and Hydrogen Spillover Mechanisms of Pt 4 / Graphene and Pt 4 / Anatase ( 101 ) Surfaces. (2019) doi:10.1021/acs.jpcc.9b04419.
48. Ti, H., Tosoni, S. &Pacchioni, G. Hydrogen Adsorption , Dissociation , and Spillover on Ru 10 Clusters Supported on Anatase TiO 2 and Tetragonal ZrO 2 ( 101 ) Surfaces. 2, (2015).
49. Tom W. van Deelen, C. H. M. and K. P. de J. Control of metal-support interactions in heterogeneous catalysts to enhance activity and selectivity. Nat. Catal. 2, 955–970 (2019).
50. Vayssilov, G. N. et al. Support nanostructure boosts oxygen transfer to catalytically active platinum nanoparticles. Nat. Mater. 10, (2011).
51. Thomas, L. H. The calculation of atomic fields. 542–548 (2020).
52. Phys, J. C., Rice, P. S. &Rice, P. S. Understanding supported noble metal catalysts using first-principles calculations Understanding supported noble metal catalysts using first-principles calculations. 180902, (2020).
53. Links, D. A. First-principles kinetic modeling in heterogeneous catalysis : an industrial perspective on best-practice , gaps and needs. Catal. Sci. Technol. 2010–2024 (2012) doi:10.1039/c2cy20261a.
54. Ventra, M.Di, Pantelides, S. T. &Lang, N. D. First-Principles Calculation of Transport Properties of a Molecular Device First-Principles Calculation of Transport Properties of a Molecular Device. (2014) doi:10.1103/PhysRevLett.84.979.
55. Grössing, G. Derivation of the Schrödinger Equation and the Klein-Gordon Equation from First Principles.
56. Kozlowski, M. . The Schrödinger equation A History. (2019).
57. Petersson, G. A. et al. A complete basis set model chemistry. I. The total energies of closed-shell atoms and hydrides of the first-row elements. 2193–2218 (1988).
58. Woon, D. E. &Dunning, T. H. Gaussian basis sets for use in correlated molecular calculations . III . The atoms aluminum through argon. 99352, (1993).
59. Guo, H., Chen, J. &Zhuang, S. Vector plane wave spectrum of an arbitrary polarized electromagnetic wave. 14, 2095–2100 (2006).
60. Mehrem, R. THE PLANEWAVE EXPANSION, INFINITE INTEGRALS AND IDENTITIES INVOLVING SPHERICAL BESSEL FUNCTIONS. 1–15.
61. Ortiz, G. &Viola, L. Generalization of Bloch’s theorem for arbitrary boundary conditions: Theory. (2017) doi:10.1103/PhysRevB.96.195133.
62. Fewster, P. Reciprocal Space Mapping. (2019). doi:10.1080/10408439708241259.
63. Group, M. O. On brillouin zones and related constructions. 57, 32–37 (2011).
64. Sherrill, C. D. The Born-Oppenheimer Approximation. (2005).
65. Echenique, P. &Alonso, J. L. A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry. (2010).
66. Chem, P. &Phys, C. Density functional theory and its applications. 14333 (2015) doi:10.1039/c4cp90074j.
67. Jones, R. O. Density functional theory : Its origins , rise to prominence , and future. 87, (2015).
68. Phys, J. C. &Becke, A. D. Perspective : Fifty years of density-functional theory in chemical physics Perspective : Fifty years of density-functional theory in chemical physics. 301, (2014).
69. Kohn, W., Becke, A. D. &Parr, R. G. Density Functional Theory of Electronic Structure. 0, 12974–12980 (1996).
70. Zhou, A. A Mathematical Aspect of Hohenberg-Kohn Theorem ∗. 1–6.
71. Ayers, P. W., Golden, S. &Levy, M. Generalizations of the Hohenberg- Kohn theorem : I . Legendre Transform Constructions of Variational Principles for Generalizations of the Hohenberg-Kohn theorem : I . Legendre Transform. Chem. Phys. 224108, (2006).
72. Wang, Y. &Parr, R. G. Construction of exact Kohn-Sham orbitals from a given electron density. Phys. Rev. A 47, 1591–1593 (1993).
73. Castro, A., Marques, M. A. L. &Rubio, A. Propagators for the time-dependent Kohn – Sham equations. 3425, (2016).
74. You, A., Be, M. A. Y. &In, I. The valence-bond self-consistent field method ( VB – SCF ): Theory and test calculations. 5699, (2013).
75. Assfeld, X. &Rivail, J. Quantum chemical computations on parts of large molecules: the ab initio local self consistent field method. Chem. Phys. Lett. 2614, (1996).
76. SHAM, W. K. A. L. J. Self-Consistent Equations Including Exchange and Correlation Effects. Phys. Rev. 385, (1965).
77. Perdew, P. Generalized correlation : gradient approximations for exchange and A look backward and forward. Phys. B Condens. Matter 172, (1991).
78. Levy, M. Density-functional exchange correlation through coordinate scaling in adiabatic connection and correlation hole. Phys. Rev. A 43, (1991).
79. Phys, J. C., Voorhis, T.Van &Scuseria, G. E. A novel form for the exchange-correlation energy functional. Chem. Phys. 400, (2006).
80. Hamprecht, F. A., Cohen, A. J., Tozer, D. J. &Handy, N. C. Development and assessment of new exchange-correlation functionals. Chem. Phys. 6264, (2010).
81. Stampfl, C. &Walle, C. G.Van De. Density-functional calculations for III-V nitrides using the local-density approximation and the generalized gradient approximation. Phys. Rev. B 59, (1999).
82. Yabana, K. Time-dependent local-density approximation in real time. Phys. Rev. B 54, 4484–4487 (1996).
83. Levinson, A. &Brueckner, A. Structure of Finite Nuclei in the Local-Density Approximation*. Phys. Rev. C 1, (1969).
84. Jackson, K. &Pederson, M. R. Accurate forces in a local-orbital approach to the local-density approximation. Phys. Rev. B 42, 3276–3281 (1990).
85. Perdew, J. P., Jackson, K. A., Pederson, M. R., Singh, D. J. &Fiolhais, C. Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46, (1992).
86. Mehl, D. C. L. and M. J. Beyond the local-density approximation in calculations of ground-state electronic properties. Phys. Rev. B (1983).
87. Perdew, J. P. &Yue, W. Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation. Phys. Rev. B 33, 12–14 (1986).
88. Functionals, P., Shapley, W. A. &Chong, D. P. PW86–PW91 Density Functional Calculation of Vertical Ionization Potentials: Some Implications for Present-Day Functionals. 81, 34–52 (2001).
89. Perdew, J. P. &Burke, K. Comparison Shopping for a Gradient-Corrected Density Functional. 57, 309–319 (1996).
90. Lu, H. P. Interaction energies of van der Waals and hydrogen bonded systems calculated using density functional theory : Assessing the PW91 model. Chem. Phys. 3949, (2010).
91. Projector augmented-wave method. Phys. Rev. B 50, (1994).
92. Kresse, G. &Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 3–4 (1999).
93. Ernzerhof, M. &Scuseria, G. E. Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional. Chem. Phys. 5029, (2006).
94. StarklofP, T. &Joannopoulos, J. D. Local psentiopotential theory for transition metals. Phys. Rev. B 16, (1977).
95. Yin, M. T. &Cohen, M. L. Theory of ab initio pseudopotential calculations. Phys. Rev. B 25, (1982).
96. Zhao, J., Lu, L., Chen, X. &Bai, Y. First-principles calculations for elastic properties of the rocksalt structure MgO. Phys. B Condens. Matter 387, 245–249 (2007).
97. Baltache, H. et al. Full potential calculation of structural , electronic and elastic properties of alkaline earth oxides MgO , CaO and SrO. Phys. B Condens. Matter 344, 334–342 (2004).
98. Phys, J. C. Systematics of elasticity : Ab initio study in -type alkaline earth oxides. Chem. Phys. 10086, (2002).
99. Ackland, G. J. &Crainj, J. Structure and elasticity of MgO at high pressure : s. 82, 51–60 (1997).
100. Ei, Y. I. F. Effects of temperature and composition on the bulk modulus of ( Mg , Fe ) O. 84, 272–276 (1999).
101. Duffy, S. &Hemley, J. Quasi-hydrostaticc ompressiono f magnesiumo xidet o 52 GPa: Implications for the pressure-volume-temperature equation of state. 106, 515–528 (2001).
102. Rajabpour, F. The synergistic effect of catalysts on hydrogen desorption properties of MgH 2 – TiO 2 – NiO nanocomposite. 1–9 (2016) doi:10.1007/s40243-016-0084-y.
103. Ning, H. et al. Synergistic effect of hydrogen absorption on ( Ti + Ni ), ( Ti + V ), ( Ni + V ) doped Mg 17 Al 12 ( 1 1 0 ) surfaces : A theoretical study. Appl. Surf. Sci. 514, 145884 (2020).
104. Saito, M., Itoh, M., Iwamoto, J., Li, C. &Machida, K. Synergistic effect of MgO and CeO 2 as a support for ruthenium catalysts in ammonia synthesis. 106, 3–6 (2006).