本文以分子動力學結合火炎演算法建構二氧化鈦奈米氧化物團簇之結構，再應用密度泛函理論研究其結構與電子性質。密度泛函理論在處理火炎演算法所求得之小奈米團簇時可得結構穩定且立體之結構。對於尺寸較大之立體結構而言，對稱性高的團簇結構將維持原狀，對稱性不高的團簇(n=5,6)會變成大表面積、低配位數之結構。此外我們將用此平衡結構討論總電子態密度(Total Density of States, TDOS)、部份電子態密度(Partial Density of States, PDOS)及福井方程式(Fukui function)等電荷分佈情形。
最後我們將催化分子吸附於奈米團簇上討論團簇的尺寸變化對催化的影響，可觀察到團簇的變化對分子之碎片結構(fragments)有明顯的效應產生，對完整的分子則無顯著的影響，並且將此結果比對表面催化的性質。

In order to understand the structural and electronic properties of titanium oxide nanoparticles of different sizes, the FIRE algorithm combining the simulated annealing method is employed to find the structures of TinO2n (n=1－6) nanoparticles with the global minimum potential energy. To deeply understand electronic properties, the relaxation structures of TinO2n (n=1－6) nanoparticle from previous method will be recalculated by density functional theory (DFT) method. The Fukui function, Frontier Molecular Orbital and density of state of TinO2n (n=1－6) nanoparticles are discussed for understanding the size effect of TiO2 nanoparticles on chemical reactivity.
The adsorption and dissociation energy mechanism of the HN3 molecule and its fragments are also discussed and are compared with the mechanism about HN3 on the anatase surface.

目錄
目錄..……………………………………………………………………...I
圖目錄..………………………………………………………………...III
表目錄..………………………………………………………………….V
符號說明………………………………………………………………..VI
中文摘要……………………………………………………………...VIII
英文摘要………………………………………………………………..IX
第1章 緒論………….……………………………………………….....1
1.1 研究動機與目的 ……………………………………………………....1
1.2 二氧化鈦簡介 …………………………………………………………4
1.3 文獻回顧..………………………………………………………………5
1.4 本文架構..………………………………………………………………9
第2章 分子動力學理論方法..………………………………………..10
2.1 勢能函數..…………………………………………………………..11
2.1.1 白金漢勢能函數..……………………………………………...11
2.2 運動方程式..………………………………………………………..12
2.3 積分法則..…………………………………………………………..13
2.4 時間步階選取………………………………………………………14
2.5 溫度修正……………………………………………………………15
2.5.1 反正規化法(Rescaling method) ………………………………15
2.5.2 諾斯-胡佛?皕讀k(Nosé-Hoover thermostat) …………………16
2.6 週期性邊界…………………………………………………………18
2.7 數值方法……………………………………………………………19
2.7.1截斷半徑法(Cut-off method) …………………………………..20
2.7.2物理參數與無因次化…………………………………………..22
第3章 火炎演算法與密度泛函理論…………………………………25
3.1 火炎演算法理論……………………………………………………25
3.2 密度泛函理論………………………………………………………26
3.2.1電子密度..……………………………………………………….26
3.2.2 Thomas-Fermi model…………………………………………....27
3.2.3 Hohenberg-Kohn model ………………………………………..27
3.2.4 Kohn-Sham equation.........................…………………………...27
第4章 結果分析與討論………………………………………………31
4.1 二氧化鈦奈米團簇結構與電性分析………………………………31
4.1.1物理模型建構……………………………………………..……31
4.1.2 結構與能量分析………………………………………….……34
4.1.3 軌域混層分析………………………………………………….39
4.1.4 活化區域分析………………………………………………….47
4.2 催化分析………………………………………………….. ……….50
4.2.1氫疊氮酸吸附解離……………………………………………..50
4.2.2 催化結果比較………………………………………………….51
第5章 結論與建議……………………………………………………59
5.1 結論…………………………………………………………………59
5.2 建議與未來展望……………………………………………………61
參考文獻.……………………………………………………………….64

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