本研究主要利用量子力學的時間獨立密度泛函理論(time-independent density functional theory, TI-DFT)來模擬粒線體中的細胞色素C氧化酶活性中心的結構模擬物進行氧氣還原反應，利用微觀分析了解細胞色素C氧化酶活性中心的材料性質與其電子轉移的特性。
細胞色素C氧化酶(cytochrome c oxidase)是粒線體內膜上所鑲嵌的酵素，是細胞呼吸鏈上的第四個複合物，為一種跨膜蛋白，細胞色素C氧化酶可以進行氧氣還原變成水，氧氣還原是將電子移轉給電子載體如細胞色素C可以被氧化，維持電子的傳遞並且儲存能量。氧化還原酵素含有數個金屬中心，因此可以進行多個電子的移轉，然而實際的反應機制並不清楚，只知道金屬中心在酵素的活化位置扮演著重要的角色，特別是做為氧化還原發生的的地方。本論文從微觀的角度研究簡化的細胞色素C氧化酶活化中心結構，及不同金屬中心(由銅代替鐵)對氧氣還原反應的影響，分別建立兩種不同金屬中心的簡化結構，進行幾何結構最佳化後，利用第一原理的密度泛函理論進行計算，獲得各結構的鍵長(bond length)、能隙(band gap)、分子軌域(molecular orbital)、紅外線光譜圖(IR spectrum)、結構總能(structure energy)等資訊。再建立兩種不同中心金屬結構進行氧氣還原反應後可能的結構圖，進行幾何結構最佳化後，再次利用密度泛函理論計算取得產物的總能，將此能量和初始結構的總能量做比較，分析進行氧氣還原反應的反應能。

Cytochrome c oxidase is a mitochondrial membrane bounded enzyme which is the fourth complex of the respiratory electron transport chain. Cytochrome c oxidase catalyzes the respiratory reduction reaction of O2 to water. Reduction of O2 takes places at the metallic center of the cytochrome c oxidase.
This thesis intensively studies the oxygen reduction reaction using the first principles calculations based on the time-independent density functional theory (TI-DFT) with the B3LYP /6-31G (d, p) method in the Gaussian09 program. It is generally agreed that DFT methods give accurate results for the geometries and vibrational frequencies of transition metals. In this study, the functional model of the metallic active site in the respiratory enzyme cytochrome c oxidase is simulated and the output data are used to analyze the bond length, band gaps, molecular orbitals, IR spectra, the structure energy and the reaction energy of the oxygen reduction reaction (ORR). The metallic active center was calculated with three different multiplicities, which are singlet, triplet, and quintet. According to the results of geometric energy of different multiplicities, we can sum up the reaction center of cytochrome c oxidase to be quintet. Finally, the total energy of the reaction product is calculated and the reaction energy of the ORR is discussed in this thesis.

摘要 I
Abstract II
目錄 III
圖目錄 V
表目錄 VIII
符號表 IX
第一章 緒論 1
1.1 前言 1
1.2 粒線體(mitochondrion)簡介 7
1.3 細胞色素 (Cytochrome) 9
1.4 氧氣還原反應(Oxygen Reduction Reaction) 12
1.5 文獻回顧 14
1.5.1 Mitochondrion (複數形：mitochondria) 14
1.5.2 Cytochrome 16
1.5.3 Oxygen Reduction Reaction on Cytochrome C oxidase 16
1.6 研究動機與目的 19
第二章 量子力學理論與計算 21
2.1 前言 21
2.2 密度泛函理論 (Density Functional Theory) 23
2.2.1 Hohenberg-Kohn理論 23
2.2.2 Kohn-Sham方法 26
2.2.3 Self-Consistent Field ( SCF,自洽場)計算 28
2.3 交換─相關泛函理論 30
2.3.1 交換─相關泛函理論B3LYP簡介 30
2.4 基底函數組 (Basis set)理論 31
2.4.1基底函數6-31G簡介 33
第三章 模型建構與模擬方法 34
3.1 模擬流程 34
3.2 模擬模型建構 35
3.3 密度泛函理論(DFT)模擬 38
3.3.1 Gaussian 輸入(input)檔及輸出(output)檔 38
3.3.2 模擬設定 38
3.3.3 能隙(Band Gap, Eg) 40
3.3.4 結合能(Binding Energy, Eb) 40
3.3.5 紅外光譜(IR Spectrum)與拉曼光譜(Raman Spectrum) 41
第四章 結果與討論 43
4.1 細胞色素C(cytochrome C)之幾何結構最佳化 43
4.2 氧氣分子的幾何結構最佳化 51
4.3 細胞色素C(cytochrome C)進行氧氣還原反應之產物的幾何結構最佳化 52
4.4 細胞色素C氧化酶(cytochrome C oxidase)進行氧氣還原反應之吸附能 55
第五章 結論與未來工作 56
5.1 結論 56
5.2 未來工作建議 57
參考文獻 59

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