我們利用密度泛函理論為基礎，搭配ultrasoft pseudopotential以及自旋極化的GGSA處理電子相關交換能來模擬銅金屬表面上不同碳烯分子間的耦合催化反應以及進行不同架橋基應用在太陽能光電材料上對於光電轉換效率差異的研究探討。在碳烯耦合催化反應方面，我們藉由部分結構限制法的方式來獲得不同碳烯耦合反應的反應途徑與反應相關的活化能，計算結果顯示，生成不同耦合產物的反應活化能分別為：CH2=CH2、CH2=CF2、CF2=CF2分別為：0.201eV、0.204eV與0.310eV。相較於實驗所測得的去吸附溫度：160K、163K與250K獲得一致的趨勢。此外我們發現反應過程中碳烯分子會透過擴散(diffusion)方式在表面進行游移，待達到合適的反應中心會快速生成碳碳雙鍵完成耦合反應。進一步由態密度與電荷密度的分析結果顯示，反應接近過渡態時會產生C-Cu的部分鍵結，使反應活化能得以下降。最後，我們順利利用碳烯分子在反應發生前混成軌域的差異解釋CH2得以透過sp3 coupling的方式來獲得較低的反應活化能。
 　在太陽能光電材料方面，我們使用不同的架橋基(H3PO3、H3BO3)吸附於InN/Anatase(101)1x2。計算結果顯示，不同的linkage與表面的鍵結方式不同，在HPO3會呈現角型、HBO3則呈現平面型的結構。進一步透過能態密度的分析顯示，InN/Linkage/Anatase(101)1x2的可吸收光波長分別紅位移為InN/PO3的596nm與InN/BO3的794nm，均落在可見光的波長範圍內。但在InN/BO3方面其導帶上的InN、B-O與Ti在能態分佈上的能態交互作用較高。最後，我們透過軌域密度的分析法，發現BO3的結構可以提供較好的橋梁使表面Ti原子及InN之間可以透過π軌域的方式鍵結，大幅提升光電轉換的效率。

Total energy calculations based on density functional theory (DFT) in connection with ultrasoft pseudopotential (USP) and generalized gradient spin-polarized approximation (GGSA) are used to simulate the coupling reaction of two absorbed CF2(ads) and CH2(ads) on the Cu(111) surface and the different photocurrent effect by linkage group treatment on adsorbed InN on the TiO2 anatase(101) surface. For the coupling reaction, we used partial structural constraint path minimization (PSCPM) method to study the reaction mechanism on the surface and their activation barrier. Our calculated energy barriers for CH2=CH2, CH2=CF2 and CF2=CF2 are 0.198eV, 0.204eV and 0.712eV, respectively. These calculated results are qualitatively in good agreement with the experimental observations. According to the reaction pathway we proposed, the two carbenes will diffuse to the top site of Cu surface and the coupling reaction occurs immediately. To study the electronic structure, we applied the partial density of states (PDOS) method and charge slice diagram to investigate the energetic profile for different carbenes, and we successfully explain the lower activation barrier due to the fact that there is a stronger interaction between carbon atom and the d-orbital of the top-site Cu atom at transition state. Finally, we also found that the hybrid orbital for CH2 self-coupling is like the sp3 character and CF2 is like sp2 and that is the reason why the CH2 self-coupling is easier than CF2. 
     In the part 2 section, we used boric acid and phosphorous acid on adsorbed InN on the TiO2 anatase(101)1x2 surface. According our calculation results, we found that there is a significant different structural geometry on anchoring group, that is pyramid for PO3 vs. planer for BO3. Our calculated band gaps for InN/PO3/Anatase(101) and InN/BO3/Anatase(101) are red-shift to 596nm and 794nm. Moreover, we noticed that there is a suitable energy matching within visible range (1.5eV~3.1eV) between InN、BO3 and surface on their conduction band by using BO3 anchoring group. Finally, according to our collected orbital density at conduction band, there is a favourable electron injection pathway from InN thought BO3 to TiO2 surface by using π delocalized orbital.

第一章	前言                                            1 

第二章  計算模擬方法簡介   
  2-1 電子結構理論簡介                                    5
    2-1-1 密度泛函理論(Density Functional Theory)         6
    2-1-2 LDA與GGA                                       10
    2-1-3 週期系統之建立                                 12
    2-1-4 贗位勢(pseudopotential)的引進                  15
  2-2 量子模擬計算軟體介紹                   　　　      17
    2-2-1  CASTEP計算程式介紹                            
  2-3 態密度(Density of state : DOS)簡介                 18
    2-3-1 原子軌道簡介                                   18
    2-3-2 態密度(DOS)                                    19
    2-3-3 部份態密度的分析(PDOS)與應用                   20
                       
第三章 碳烯分子在Cu(111)金屬表面的耦合(coupling)反應
                                  
  3-1過渡金屬表面上的催化反應簡介                        22
    3-1-1 過渡金屬上的費托(Fischer-Tropsch)合成反應      23
    3-1-2 碳烯分子在過渡金屬上的耦合(coupling)反應       25
  3-2 模型建立與反應途徑設計                             27
      3-2-1 Cu金屬表面簡介                               28
      3-2-2 計算參數的使用                               31
      3-2-3 碳烯分子coupling反應之途徑選擇               32
      3-2-4 碳烯分子coupling反應之幾何結構與能量探       43
      3-2-5 碳烯分子coupling反應之態密度分析             51
  3-3 分析與結論                                         62
                     
 第四章  (InN)-XO3/TiO2 (x=P,B)太陽能電池光電轉換理論研究
  4-1 太陽能電池的演進與簡介                             65
      4-1-1太陽能電池的理論研究                          66
      4-1-2架橋基應用於太陽能電池之研究                  70
  4-2 TiO2表面模型之建立                                 72
      4-2-1 TiO2 表面之電子結構性質                      75
      4-2-2 計算參數的使用                               78
  4-3 InN透過linkage在TiO2表面上吸附結構與電子結構       81
      4-3-1 H3XO3在Anatase(101)1x2表面上的吸附結構       82
      4-3-2 (InN)–XO32-在Anatase(101)1x2表面上的電子    85
             結構及光電流轉換效率之研究
      4-3-3 InN/TiO2、InN-XO3/TiO2綜合光電流效率比較     93
  4-4 本章綜合分析與結論                                 96

第五章 論文總結                                         99
參考資料                                               101

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