儲氫量的的提升是實現氫經濟關鍵的阻礙之一，美國能源局(DOE)的目標是在2020年達到環境壓力和溫度下氫存儲材料重量分別為4.5wt%和H2的體積密度為30kg H2 / m3。我們團隊使用密度泛函理論將根據氫的吸附來設計合適的金屬修飾於石墨烯/銳鈦礦二氧化鈦(101)材料，但我們關注的是透過使用模型催化劑Pt4/銳鈦礦二氧化鈦(101)和Pt4/石墨烯吸附氫氣進而增強氫溢流機制，在不同的氫覆蓋條件下。我們的結果意指，Pt4 /石墨烯體系中氫溢流發生可能在高氫氣覆蓋的情形下且氫與鉑的比例為六比一，這與一般的氫溢流機制這與一般的氫溢流機制相一致。不同的是，在有Pt4存在下吸附氫原子在銳鈦礦二氧化鈦(101)表面其吸附能比氫原子吸附銳鈦礦二氧化鈦(101)表面強0.48 eV，關於Pt4/銳鈦礦二氧化鈦(101)的氫溢流機制，我們注意到在些許氫氣的覆蓋且氫與鉑的比例為二點五比一的情形下，氫可以從金屬顆粒溢流於銳鈦礦二氧化鈦(101)表面上。

關鍵字:氫溢流機制，密度泛函理論，鉑，石墨烯，銳鈦礦二氧化鈦(101)，氫吸附

Storing hydrogen is one of the pivotal hurdles to achieve hydrogen economy from the use of fossil fuels. The U.S. Department of Energy (DOE) aims at reaching the gravimetric H2 density of 4.5wt% and volumetric H2 density of 30kg H2/m3 in 2020 for hydrogen storage materials at the ambient pressure and temperature. Our role (theoretical team by using Density Function Theory, DFT) is to design appropriate metal-decorated graphene-based materials in term of generation, adsorption and desorption of hydrogen, but focusing to enhance the hydrogen spillover mechanism, hydrogen adsorption by using the model catalysts, Pt4/anatase TiO2 (101) and Pt4/Graphene in the conditions of different hydrogen coverage. The outcomes implies that hydrogen spillover in Pt4/Graphene system might be able to occurs at high hydrogen converage with the H:Pt ration = 6:1 that is in agreement with general hydrogen spillover mechanism. Different is that the magnitude of single hydrogen atom adsorption energy on anatase TiO2 (101) is enhanced 0.48 eV in the presence of Pt4. Concerning hydrogen spillover mechanism in Pt4/TiO2 system, we note hydrogen could spill over from the metal particle to TiO2 support at mediate hydrogen coverage with H:Pt ration = 2.5: 1.


Keywords: Hydrogen spillover mechanism, DFT , Pt ,Graphene,TiO2 , Hydrogen adsorption .

摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 viii
表目錄 xii
第一章 緒論 1
1.1前言 1
1.2氫能源簡介 1
1.3研究動機與要點 3
1.4文章架構 3
第二章 文獻回顧 5
2.1關於氣相穩定之Pt金屬團簇結構 5
2.2金屬團簇修飾於石墨烯/anatase二氧化鈦(101)表面上的穩定結構 6
2.2.1金屬團簇於石墨烯表面上之穩定結構 6
2.2.2鉑(一、二、三顆)於anatase二氧化鈦(101)表面上的穩定結構 7
2.3 氫吸附於石墨烯/anatase二氧化鈦(101)表面上的穩定結構 8
2.3.1單顆氫原子和氫分子吸附於石墨烯表面上的穩定結構 8
2.3.2單顆氫原子和氫分子吸附於anatase二氧化鈦(101)表面上的穩定結構 9
2.4 氫吸附金屬團簇修飾石墨烯/anatase二氧化鈦(101)表面上的穩定結構 10
2.4.1氫吸附金屬團簇修飾石墨烯表面上的穩定結構 10
2.4.2氫吸附金屬團簇修飾anatase二氧化鈦(101)表面上之穩定結構 11
2.5氫溢流的機制 12
2.5.1溢流現象 12
2.5.2氫溢流理論的提出 12
第三章 計算方法 14
3.1 薛丁格方程式（Schrödinger equation）[14] [15] 14
3.1.1波恩–歐本海默近似法(Born-Oppenheimer approximation) [15] [19] [20] 15
3.2密度泛函理論(Density functional theory, DFT) [15] [21] 16
3.2.1科恩－沈方程(Kohn–Sham equation) [14] [15] [23] 16
3.3交換相關能量(exchange correlation energy) [14] [15] 17
3.3.1 局部密度近似(Local Density Approximation, LDA) [14] [15] [24] 18
3.3.2 廣義梯度近似(Generalized Gradient Approximation, GGA) [15] [21] 18
3.4 基底函數組(Basic set) [14] [15] [21] 19
3.4.1平面波(Plane wave) [14] [15] [21] 19
3.5膺勢(Pseudopotentials) [14] [15] [21] [38] 20
3.6凡得瓦力(van der Waals' force）[15] 21
3.6.1凡得瓦力的三種型式 21
3.6.2密度泛函理論的色散校正 21
3.7優化(Optimization) [14] [15] 22
3.7.1位能面(Potential energy surface) [14] [39] 22
3.7.2最小化(Minimization) [14] [15] 22
3.8 實驗設計與規劃 23
3.8.1建立石墨烯與相關測試 24
3.8.2建立Bulk的二氧化鈦與相關測試 26
3.8.3凝聚力(cohesive energy)結合能(binding energy)與吸附能(adsoption energy) 29
第四章 結果與討論 30
4.1氣相穩定之Pt4構型 30
4.2 Pt1和Pt4修飾於石墨烯/anatase二氧化鈦(101)表面上的穩定結構 31
4.2.1 Pt1修飾於石墨烯表面 31
4.2.2 Pt1修飾於anatase二氧化鈦(101)表面 33
4.2.3 Pt4修飾於石墨烯表面 34
4.2.4 Pt4修飾於anatase二氧化鈦(101)表面 35
4.3氫原子和氫分子吸附於石墨烯/anatase二氧化鈦(101)表面的吸附位置與現象 37
4.3.1氫原子吸附於石墨烯表面的吸附位置與現象 37
4.3.2氫分子吸附於石墨烯表面的吸附位置與現象 39
4.3.3氫原子吸附於anatase二氧化鈦(101)表面三個不同吸附位置與現象 40
4.3.4氫分子吸附於anatase二氧化鈦(101)表面吸附位置與現象 42
4.4氫原子和氫分子吸附於Pt1和Pt4 43
4.4.1一顆到八顆氫原子吸附於Pt1 43
4.4.2一顆到二十顆氫原子吸附於Pt4 44
4.5 氫原子吸附於Pt4在石墨烯/anatase二氧化鈦(101)表面吸附位置 46
4.5.1氫原子吸附Pt4在石墨烯表面 47
4.5.2:氫原子吸附Pt4在anatase二氧化鈦(101)表面 49
4.5.3一到二十四顆的氫原子吸附於Pt4在石墨烯表面 51
4.5.4一到二十四顆氫原子吸附Pt4於石墨烯表面的氫溢流機制 55
4.5.5九組二十四顆氫原子吸附Pt4於石墨烯表面氫溢流機制模型討論 59
4.5.6一到十六顆氫原子吸附於Pt4在anatase二氧化鈦(101)表面 62
4.5.7一到十六顆氫原子吸附於Pt4於anatase二氧化鈦(101)表面的氫溢流機制 64
第五章 結論 68
第六章 研究挑戰及未來展望 70
參考資料 71
附錄 75
附錄一 密度泛函理論的色散校正 75
本研究相關之發表 77

[1] "CHEMISTRY（THE CHINESE CHEM. SOC., TAIPEI）December. 2003 Vol. 61, No. 4, pp.585~597 ".
[2] 經濟部能源局. (2007). 我國重點能源科技研發動向與策略.
[3] J. Rubio, S. Zurita, J. Barthelat, and F. Illas, "Electronic and geometrical structures of Pt3 and Pt4. An ab initio one-electron proposal," Chemical physics letters, vol. 217, pp. 283-287, 1994.
[4] K. Okazaki-Maeda, Y. Morikawa, S. Tanaka, and M. Kohyama, "Structures of Pt clusters on graphene by first-principles calculations," Surface Science, vol. 604, pp. 144-154, 2010.
[5] Y. Han, C.-j. Liu, and Q. Ge, "Interaction of Pt clusters with the anatase TiO2 (101) surface: A first principles study," The Journal of Physical Chemistry B, vol. 110, pp. 7463-7472, 2006.
[6] K. Nakada and A. Ishii, "DFT calculation for adatom adsorption on graphene," in Graphene Simulation, ed: InTech, 2011.
[7] D. Henwood and J. D. Carey, "Ab initio investigation of molecular hydrogen physisorption on graphene and carbon nanotubes," Physical Review B, vol. 75, p. 245413, 2007.
[8] M. M. Islam, M. Calatayud, and G. Pacchioni, "Hydrogen adsorption and diffusion on the anatase TiO2 (101) surface: a first-principles investigation," The Journal of Physical Chemistry C, vol. 115, pp. 6809-6814, 2011.
[9] C. Ramos-Castillo, J. Reveles, R. Zope, and R. De Coss, "Palladium clusters supported on graphene monovacancies for hydrogen storage," The Journal of Physical Chemistry C, vol. 119, pp. 8402-8409, 2015.
[10] H.-Y. T. Chen, S. Tosoni, and G. Pacchioni, "Hydrogen adsorption, dissociation, and spillover on Ru10 clusters supported on anatase TiO2 and tetragonal ZrO2 (101) surfaces," ACS Catalysis, vol. 5, pp. 5486-5495, 2015.
[11] S. Khoobiar, "Particle to particle migration of hydrogen atoms on platinum—alumina catalysts from particle to neighboring particles," The Journal of Physical Chemistry, vol. 68, pp. 411-412, 1964.
[12] W. Karim, C. Spreafico, A. Kleibert, J. Gobrecht, J. VandeVondele, Y. Ekinci, et al., "Catalyst support effects on hydrogen spillover," Nature, vol. 541, p. 68, 01/04/online 2017.
[13] A. J. Lachawiec, G. Qi, and R. T. Yang, "Hydrogen Storage in Nanostructured Carbons by Spillover:  Bridge-Building Enhancement," Langmuir, vol. 21, pp. 11418-11424, 2005/11/01 2005.
[14] H.-Y. T. Chen, "Hydrogenation Reaction Catalysed by Organometallic Complexs." University College London Ph D 2011
[15] "Hands-on tutorial course on VASP. Available from: https://www.vasp.at/vasp-workshop/.".
[16] "Fermi, E., "Un metodo statistico per la determinazione di alcune priorietà dell'atome." Rend. Accad. Naz. Lincei. 6, 1927, p. 602-607.."
[17] "Thomas, L., "The calculation of atomic fields." Proceedings of the Cambridge Philosophical Society. 23, 1927, p. 542-548.."
[18] "Hohenberg, P. and W. Kohn, "Inhomogeneous Electron Gas." Physical Review. 136, 1964, p. B864-B871.."
[19] "Born-Oppenheimer approximation. Available from: https://en.wikipedia.org/wiki/Born%E2%80%93Oppenheimer_approximation."
[20] "M., B. and O. R., "Zur Quantentheorie der Molekeln." Annalen der Physik. 389, 1927, p. 457–484. ."
[21] "Density functional theory. Available from: https://en.wikipedia.org/wiki/Density_functional_theory."
[22] "Kohn, W. and L.J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects." Physical Review. 140, 1965, p. A1133-A1138."
[23] "Kohn–Sham equation. Available from: https://en.wikipedia.org/wiki/Kohn%E2%80%93Sham_equations."
[24] "Local-density approximation. Available from: https://en.wikipedia.org/wiki/Local-density_approximation."
[25] "Perdew, J.P. and A. Zunger, "Self-interaction correction to density-functional approximations for many-electron systems." Physical Review B. 23, 1981, p. 5048-5079. ."
[26] "Cole, L.A. and J.P. Perdew, "Calculated electron affinities of the elements." Physical Review A. 25, 1982, p. 1265-1271.."
[27] "Gell-Mann, M. and K.A. Brueckner, "Correlation Energy of an Electron Gas at High Density." Physical Review. 106, 1957, p. 364-368. ."
[28] "Dirac, P., "Note on exchange phenomena in the Thomas atom." Proceedings of the Cambridge Philosophical Society. 26, 1930, p. 376-385.."
[29] "Parr, R.G. and W. Yang, "Density-Functional Theory of Atoms and Molecules." 1994.."
[30] "Ceperley, D.M. and B.J. Alder, "Ground State of the Electron Gas by a Stochastic Method." Physical Review Letters. 45, 1980, p. 566-569.."
[31] "Perdew, J.P., K. Burke, and Y. Wang, "Generalized gradient approximation for the exchange-correlation hole of a many-electron system." Physical Review B. 54, 1996, p. 16533-16539.."
[32] "Perdew, J.P., "Density-functional approximation for the correlation energy of the inhomogeneous electron gas." Physical Review B. 33, 1986, p. 8822-8824.."
[33] "Perdew, J.P. and Y. Wang, "Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation." Physical Review B. 33, 1986, p. 8800-8802.."
[34] "Becke, A.D., "Density-functional exchange-energy approximation with correct asymptotic behavior." Physical Review A. 38, 1988, p. 3098-3100.."
[35] "Langreth, D.C. and M.J. Mehl, "Beyond the local-density approximation in calculations of ground-state electronic properties." Physical Review B. 28, 1983, p. 1809-1834.."
[36] "Perdew, J.P., et al., "Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation." Physical Review B. 46, 1992, p. 6671-6687.."
[37] "Perdew, J.P., K. Burke, and M. Ermzerhof, "Generalized Gradient Approximation Made Simple." Physical Review Letters. 77, 1996, p. 3865-3868.."
[38] "Pseudopotential. Available from: https://en.wikipedia.org/wiki/Pseudopotential."
[39] "Potential energy surface. Available from: https://en.wikipedia.org/wiki/Potential_energy_surface.."
[40] "Hessian matrix. Available from: https://en.wikipedia.org/wiki/Hessian_matrix."
[41] C. R. Rêgo, P. Tereshchuk, L. N. Oliveira, and J. L. Da Silva, "Graphene-supported small transition-metal clusters: a density functional theory investigation within van der Waals corrections," Physical Review B, vol. 95, p. 235422, 2017.
[42] C. I. Morgade, C. I. Vignatti, M. S. Avila, and G. F. Cabeza, "Theoretical and experimental analysis of the oxidation of CO on Pt catalysts supported on modified TiO2 (101)," Journal of Molecular Catalysis A: Chemical, vol. 407, pp. 102-112, 2015.
[43] D. Boukhvalov, M. Katsnelson, and A. Lichtenstein, "Hydrogen on graphene: Electronic structure, total energy, structural distortions and magnetism from first-principles calculations," Physical Review B, vol. 77, p. 035427, 2008.
[44] F. Costanzo, P. Silvestrelli, and F. Ancilotto, "Physisorption, Diffusion, and Chemisorption Pathways of H2 Molecule on Graphene and on (2, 2) Carbon Nanotube by First Principles Calculations," Journal of chemical theory and computation, vol. 8, pp. 1288-1294, 2012.
[45] I. López-Corral, S. Piriz, R. Faccio, A. Juan, and M. Avena, "A van der Waals DFT study of PtH2 systems absorbed on pristine and defective graphene," Applied Surface Science, vol. 382, pp. 80-87, 2016.