提高氫氣儲存量是發展氫經濟的關鍵之一，為了有效提升氫能的使用效率，材料儲氫是現今公認最為安全且具潛力的儲氫方法。石墨烯具備高比表面積、重量輕、成本低、低壓吸附氫、常溫脫附氫等材料特性，可視為一個非常有潛力的儲氫材料。但由於材料表面對氫氣的吸附較弱，其儲氫量有限。氫溢流機制被視為一個提高石墨烯等吸附型材料儲氫量的有效方法，其透用摻雜金屬團簇在石墨烯表面來增強石墨烯對氫氣的吸附，然而金屬團簇本身內聚能相對於與石墨烯的結合能較強，因此催化劑在石墨烯表面有脫附的趨勢，並使氫溢流機制無法進行。本研究利用石墨烯之單空位缺陷來增強金屬團簇與石墨烯表面的結合能力，並研究氫溢流機制是否能在此系統上進行。
本論文利用密度泛函理論並考慮凡德瓦力進行計算，根據氫的吸附現象來設計合適的鉑金屬修飾單空位缺陷石墨烯材料。首先我們發現Pt原子與單空位缺陷石墨烯表面能夠更強地結合，結合能 -7.89 eV，相較於原始石墨烯，結合能-1.93 eV。接著計算了Pt4在單空位缺陷石墨烯上之結合能，尋找出其在表面上的最穩定構型。最後，我們使用了三組Pt4金屬團簇結合於單空位缺陷石墨烯，去觀察金屬團簇與表面的結合能是否會影響系統之氫吸附能的變化，並確認氫溢流機制是否在材料上能夠進行。

Increasing hydrogen storage is one of the keys to the development of hydrogen economy. In order to effectively improve the efficiency of hydrogen energy, hydrogen storage is the safest and most promising hydrogen storage method. Graphene has high specific surface area, light weight, low cost, low pressure adsorption of hydrogen, hydrogen desorption at room temperature and other material properties, which can be regarded as a very potential hydrogen storage material. However, due to the weak adsorption of hydrogen on the surface of the material, its hydrogen storage capacity is limited. The hydrogen overflow mechanism is considered as an effective method to increase the hydrogen storage capacity of adsorbent materials such as graphene. It uses a doped metal cluster on the surface of graphene to enhance the adsorption of hydrogen by graphene. However, the metal cluster itself cohesive. The binding energy with respect to the stone millene is strong, so the catalyst has a tendency to desorb on the surface of the graphene, and the hydrogen overflow mechanism cannot be performed. This study utilized the single vacancy defects of graphene to enhance the binding ability of metal clusters to the surface of graphene, and to study whether the hydrogen overflow mechanism can be carried out on this system.
In this thesis, we use density functional theory and consider Van der Waals force to calculate the appropriate platinum metal modified single vacancy defect graphene material according to the adsorption phenomenon of hydrogen. First, we found that the Pt atom and the single vacancy-deficient graphene surface can bind more strongly, and the binding energy is -7.89 eV, which is -1.93 eV compared to the original graphene. Next, the binding energy of Pt4 on single-vacancy-deficient graphene was calculated to find the most stable configuration on the surface. Finally, we use the structure of the Pt4 metal cluster on the surface to establish a hydrogen overflow model and observe the change of hydrogen adsorption energy of the system to confirm whether the hydrogen overflow mechanism can be carried out on the material.

摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 vii
表目錄 ix
第一章 緒論 1
1.1前言 1
1.2研究動機與要點 4
1.3文章架構 7
第二章 文獻回顧 8
2.1缺陷對於石墨烯的影響 8
2.1.1 Stone-Wales缺陷石墨烯 8
2.1.2單空位缺陷石墨烯 8
2.1.3雙空位缺陷石墨烯 9
2.1.4線缺陷石墨烯 10
2.2鉑金屬團簇與缺陷石墨烯之結合 11
2.3氫溢流現象 14
第三章 計算方法 16
3.1薛丁格方程式（Schrödinger equation）[35, 36] 16
3.1.1波恩–歐本海默近似法(Born-Oppenheimer approximation)[36, 37] 17
3.2密度泛函理論(Density functional theory, DFT)[37, 38] 18
3.2.1科恩－沈方程(Kohn–Sham equation) [38] 18
3.3.1局部密度近似(Local Density Approximation, LDA)[39] 19
3.3.2廣義梯度近似(Generalized Gradient Approximation, GGA)[38] 20
3.4.1平面波(Plane wave)[38] 21
3.6.1凡得瓦力的三種型式 23
3.6.2密度泛函理論的色散校正 23
3.7.1位能面(Potential energy surface) 24
3.7.2最小化(Minimization) 24
3.8.1建立原始石墨烯與相關測試 26
3.8.2結合能(binding energy)與吸附能(adsoption energy) 28
第四章 結果與討論 30
4.1Pt及Pt4.修飾於單空位缺陷石墨烯表面. 30
4.1.1Pt修飾於單空位缺陷石墨烯表面之模擬結果 30
4.1.2文獻之Pt4構型結合單空位缺陷石墨烯表面之模擬結果 32
4.2Pt4結合單空位缺陷石墨烯表面之模擬結果 33
4.3氫原子吸附於單空位缺陷石墨烯表面的位置及現象 35
4.4氫分子吸附於單空位缺陷石墨烯表面之模擬結果 37
4.5氫原子吸附Pt4在石墨烯表面 39
4.6多顆氫原子吸附倒金字塔型Pt4於單空位缺陷石墨烯表面之模擬結果 45
4.7多顆氫原子吸附正金字塔型Pt4於單空位缺陷石墨烯表面模擬結果 59
第五章 結論 65
第六章 未來工作 70
參考資料 71
附錄 75
摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 vii
表目錄 ix
第一章 緒論 1
1.1前言 1
1.2研究動機與要點 4
1.3文章架構 7
第二章 文獻回顧 8
2.1缺陷對於石墨烯的影響 8
2.1.1 Stone-Wales缺陷石墨烯 8
2.1.2單空位缺陷石墨烯 8
2.1.3雙空位缺陷石墨烯 9
2.1.4線缺陷石墨烯 10
2.2鉑金屬團簇與缺陷石墨烯之結合 11
2.3氫溢流現象 14
第三章 計算方法 16
3.1薛丁格方程式（Schrödinger equation）[35, 36] 16
3.1.1波恩–歐本海默近似法(Born-Oppenheimer approximation)[36, 37] 17
3.2密度泛函理論(Density functional theory, DFT)[37, 38] 18
3.2.1科恩－沈方程(Kohn–Sham equation) [38] 18
3.3.1局部密度近似(Local Density Approximation, LDA)[39] 19
3.3.2廣義梯度近似(Generalized Gradient Approximation, GGA)[38] 20
3.4.1平面波(Plane wave)[38] 21
3.6.1凡得瓦力的三種型式 23
3.6.2密度泛函理論的色散校正 23
3.7.1位能面(Potential energy surface) 24
3.7.2最小化(Minimization) 24
3.8.1建立原始石墨烯與相關測試 26
3.8.2結合能(binding energy)與吸附能(adsoption energy) 28
第四章 結果與討論 30
4.1Pt及Pt4.修飾於單空位缺陷石墨烯表面. 30
4.1.1Pt修飾於單空位缺陷石墨烯表面之模擬結果 30
4.1.2文獻之Pt4構型結合單空位缺陷石墨烯表面之模擬結果 32
4.2Pt4結合單空位缺陷石墨烯表面之模擬結果 33
4.3氫原子吸附於單空位缺陷石墨烯表面的位置及現象 35
4.4氫分子吸附於單空位缺陷石墨烯表面之模擬結果 37
4.5氫原子吸附Pt4在單空位缺陷石墨烯表面 39
4.6氫原子吸附在單空位缺陷石墨烯表面並結合Pt4 45
4.7多顆氫原子吸附倒金字塔型Pt4於單空位缺陷石墨烯表面之模擬結果 46
4.8多顆氫原子吸附正金字塔型Pt4於單空位缺陷石墨烯表面模擬結果 59
4.9多顆氫原子吸附倒金字塔型Pt4於兩個單空位缺陷石墨烯表面模擬結果 65
第五章 結論 69
第六章 未來工作 70
參考資料 71
附錄 75
附錄一 氫吸附於雙層石墨烯表面之模擬結果 75

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