本研究主要利用量子化學模擬探討人工光合作用中陰極催化二氧化碳
(CO2)還原成甲醇燃料的過程，希望能詳盡了解整個反應步驟，並藉由建構
完整的反應流程求得當中各步驟的反應速率常數，並探尋過程中會遇到的
問題，找出可能的改善方案。選用的陰極材料是中心原子為鈷的紫質(CoPP)，
此類摻有過渡金屬的紫質化合物已被廣泛運用於二氧化碳還原，其不僅結
構穩定，可最大化實現金屬原子利用率，且產物選擇性佳；本研究主要使用
工具為計算量子化學的 Gaussian09，由密度泛函理論評估各反應勢能函數；
次要的模擬軟體則是 Adsorption Locator，後者基於蒙地卡羅理論快速估計
各反應物空間位置。

本研究首先透過蒙地卡羅法預測加入的二氧化碳分子與氫離子(H+)的
可能位置，透過最低能量做結構最佳化、過渡態計算、內反應座標等一系列
流程逐步建立可能的反應路徑，藉此瞭解 CoPP 催化二氧化碳還原的反應發
生步驟及計算各步驟反應速率常數，模擬結果催化劑CoPP 的最佳化結構誤
差與實驗值相比平均約為 1.84%，最大不超過5%；二氧化碳在催化初期會
被折彎成具有120.82o 的結構，對於降低結構穩定性並與氫離子生成COOH*
增加催化發生的可能性有重要的影響；最終找尋到了催化還原二氧化碳並
析出最終產物甲醇的反應路徑，全部過程需提供 1.33eV 的能量，且整個反
應過程能量共下降了 65.80eV 的能量；在形成CO*中間體後的接續步驟中，
找到了兩個可能的過渡態結構與反應路徑，依據∆𝐺‡與速率常數來評估出形
成 CHO*中間體為較可能的反應路徑；整個模擬中反應速率較低的步驟出現
在第二步形成CO*中間體並釋出一個水分子的過程(k=4.226×10-6s-1)。

本研究結論為尋找有效的助催化劑提升形成 CO*中間體的反應速率將
可大幅提升催化的效率，並可與其他過渡金屬官能化紫質比較找出效率最
佳的金屬原子與觸媒框架，此外改善模擬流程中的溶劑效應有助於更貼近
實際的實驗過程。

This thesis aims to use quantum simulation to investigate the process of CO2 reduction to Methanol fuel at the cathode in the artificial photosynthesis. The selected cathode catalyst is Cobalt Porphyrin(CoPP). The main simulation software uses Gaussian09, which is designed according to the computational quantum chemistry. The potential energy function of each reaction is evaluated through the density functional theory. In addition, the secondary simulation software is Adsorption Locator, which rapidly estimates the spatial position of each reactant based on the Monte Carlo algorithm.

Firstly, the Monte Carlo method was programmed to predict possible
positions of the added carbon dioxide molecules and those hydrogen ions (H+) from the anode. In order to calculate the reaction rate constant of each step, the possible reaction pathways are established through a series of processes such as the lowest energy for structural optimization, transition state calculations, and internal reaction coordinates step by step. The geometric error of the CoPP model is 1.84% on average compared with the experimental results. In addition, CO2 was bent into a structure with an angle of 120.82o at the initial stage of catalysis, which
has an important influence on reducing structural stability and generating COOH* with hydrogen ions to increase the possibility of the catalytic reaction. The entire process is exergonic, when producing methanol, 1.333eV is required and 65.80eV will be released. In the subsequent steps after the formation of the CO*
intermediate, two possible transition state structures and reaction paths were found. According to ∆𝐺‡ and the rate constant, the formation of the CHO* intermediate was evaluated as a more likely reaction pathway. In the whole simulation, the rate-controlled step with the lowest reaction rate occurred at the
second step of forming a CO* intermediate and producing a water molecule (k=4.226×10-6 s-1).

摘要 I
Abstract II
誌謝 III
圖目錄 VI
表目錄 IX
符號表 XII
第一章 緒論 1
1.1 前言 1
1.2 人工光合作用 2
1.2.1 光陽極 3
1.2.2 陰極 4
1.3 過渡金屬官能化紫質 5
1.3.1 過渡金屬官能化紫質與二氧化碳還原 6
1.4 文獻回顧 7
1.5研究動機與目的 9
第二章 計算理論與研究方法 12
2.1 分子力學 12
2.2 蒙地卡羅法 13
2.2.1 蒙地卡羅模擬退火法 14
2.2.1 模擬退火法計算過程 16
2.3 量子力學 18
2.3.1 薛丁格方程式 19
2.3.2 波恩-歐本海默近似 19
2.3.3 密度泛函理論 20
2.3.4 局部密度近似法 23
2.3.4 廣義梯度近似法 24
2.3.5 自洽場迭代 24
2.4 混合泛函 26
2.4.1 交換相關理論－B3LYP 28
2.4.2 計算基底函數－6-31G(d,p) 29
2.5 過渡態理論 32
2.5.1 過渡態搜索 35
2.5.2 內反應座標計算 37
第三章 計算與模擬方法 41
3.1 Adsorption Locator 41
3.2 Gaussian09 43
3.2.1 TS指令 44
3.2.2 IRC計算注意事項 45
3.3 研究方法與流程 46
第四章 結果與討論 49
4.1 二氧化碳催化還原計算結果 49
4.1.1 CoPP結構建立與基本性質計算 49
4.1.2 CoPP吸附二氧化碳與氫離子之計算 51
4.1.3 CoPP催化還原二氧化碳－H2 53
4.1.4 CoPP催化還原二氧化碳－H3 56
4.1.5 CoPP催化還原二氧化碳－H4 61
4.1.6 CoPP催化還原二氧化碳－H5 64
4.1.7 CoPP催化還原二氧化碳－H6 67
4.2 二氧化碳催化還原總結 71
4.2.1還原產物：甲醇 71
第五章 結論與未來研究計畫 74
5.1結論 74
5.2 未來研究建議 74
參考文獻 76

 

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