臺灣博碩士論文加值系統

　　本碩士論文共有三章，第一章我們探討 MC-DFT 方法應用於 Minnesota 系列密度泛函方法的計算表現，第二章我們測試 mixed functionals 方法於預測 70 個過渡金屬分子的鍵能之表現，第三章則是以理論計算鈍氣置換的反應速率常數以及分析穿隧效應 (tunneling effects) 對動力學同位素效應 (kinetic isotope effects, KIEs) 的影響。
　　
　　第一章我們將 MC-DFT 方法應用在近年來 Truhlar 團隊所開發的 Minnesota 系列密度泛函方法，包括 M06-2X，M08-HX，M11 與 MN12-SX，並且測試其在熱力學和動力學計算的表現。計算結果顯示，使用多個基底函數組合明顯比使用單一基底函數還要準確；結果亦顯示 M06-2X 搭配基底函數組合 [6-311+G(d,p)/6-311+G(2d,2p)] 是一種極有效率的計算方式，具有最高的 performance/cost ratio，針對 211 個準確能量的測試結果，其 MUE 為 1.58 kcal/mol，若加入 SCS-MP2 能量校正則可使 MUE 降至 1.22 kcal/mol。
　　
　　在第二章中我們結合兩種不同的 DFT 方法來預測 70 個過渡金屬分子的原子化能量 (實驗值誤差小於 2 kcal/mol)，期許能夠抵消方法本身造成的系統性預測誤差。表現最佳的混合式方法 (Mixed DFT) 是 τ-HCTHhyb/mPW2-PLYP，其 MUE 為 5.49 kcal/mol，而單一 τ-HCTHhyb 與 mPW2-PLYP 的 MUE 則分別為 6.14 kcal/mol 與 12.88 kcal/mol，使用 Mixed DFT 方法相較於單一方法可以減少約 0.5 kcal/mol 以上的誤差。若使用 MC-DFT 方法利用二個基底函數進行計算則可提升計算準確度至 4.94 kcal/mol。我們亦進一步加入 MP2 與 CCSD 方法的能量校正，可使其 MUE 分別下降至 4.77 kcal/mol 與 4.51 kcal/mol。
　　
　　第三章我們利用雙層 VTST/MT (dual-level dynamics approach with variational transition state theory including multidimensional tunneling) 理論來研究四種不同的氣態鈍氣分子置換反應之動力學性質，Ng’ + HNBNg+ (Ng, Ng’ = He, Ne, and Ar)。計算結果顯示，四個反應之反應能障都約在 5－9 kcal/mol 左右，且穿隧效應對反應速率的貢獻在室溫下仍然不可忽略，特別是 He + HNBHe+ 反應中穿隧效應的貢獻最顯著，但在低溫下這四種反應皆有明顯的穿隧效應。此外我們亦討論了 3He 的動力學同位素效應，即 3He + HNBHe+，He + HNB3He+ 與 3He + HNB3He+ 三種相異位置同位素取代的情形，發現此反應中 He 原子的穿隧效應對反應速率常數與 KIEs 的貢獻極為顯著，且在低溫下，HNBHe+ 上的 He 原子對穿隧效應的貢獻要比中性的 He 原子明顯。

　　This thesis consists of three chapters. In chapter 1, we applied the multi-coefficient density functional theory (MC-DFT) to a few recent Minnesota functionals. In chapter 2, we have developed a new method using mixed functionals and we tested it on 70 bond energies of 3d transition-metal-containing molecules. In chapter 3, we investigated the kinetic isotope effects and tunneling effects of noble-gas exchange reactions.
　　
　　In chapter 1, we have applied MC-DFT method to four recent Minnesota functionals, including M06-2X, M08-HX, M11, and MN12-SX on the performance of thermochemical kinetics. The results indicated that the accuracy can be improved significantly by using two or three basis sets. We further included the SCS-MP2 energies into MC-DFT, and the resulting mean unsigned errors (MUE) decreased by ~0.3 kcal/mol for the most accurate basis set combinations. The M06-2X functional with the simple [6-311+G(d,p)/6-311+G(2d,2p)] combination gave the best performance/cost ratios for the MC-DFT and MC-SCS-MP2 | MC-DFT methods with MUE of 1.58 and 1.22 kcal/mol, respectively.
　　
　　In chapter 2, we have developed a new method using mixed functionals for transition metals. This method was tested against a database including 70 bond energies of 3d transition-metal-containing molecules with small experimental uncertainties. The best mixed functional method was the τ-HCTHhyb/mPW2-PLYP combination, and it yielded an MUE of 5.49 kcal/mol. In comparison, the single τ-HCTHhyb and mPW2-PLYP functional gave MUEs of 6.14 and 12.88 kcal/mol, respectively. We also applied the MC-DFT approach into the mixed functional and it yielded an MUE of 4.94 kcal/mol. We further added the MP2 and CCSD energies into the new method, and obtained MUE of 4.75 kcal/mol and 4.51 kcal/mol, respectively.
　　
　　In chapter 3, we used VTST/MT method to investigate four noble-gas exchange reactions: Ng’ + HNBNg+ (Ng, Ng’ = He, Ne, and Ar). The barrier heights of these four reactions were predicted to be 5－9 kcal/mol. The calculated results showed significant tunneling effects even at room temperature, especially for the He + HNBHe+ reaction. All reactions showed very significant tunneling effects at low temperature. For helium exchange reactions, the internal helium atom (in the cation) contributed more in the tunneling effects than the external helium atom (the neutral reactant) at low temperature.

中文摘要 IV
Abstract VI

第一章 The MC-DFT Approach Including the SCS-MP2 Energies to the New Minnesota-type Functionals
摘要 1
1.1 前言 2
1.2 計算方法 6
1.3 結果與討論 10
1.3.1 MC-DFT 方法的計算表現 10
1.3.1.1 B3LYP 方法的結果 10
1.3.1.2 M06-2X 方法的結果 11
1.3.1.3 M08-HX 方法的結果 11
1.3.1.4 M11 與 MN12-SX 方法的結果 12
1.3.2 SCS-MP2 | MC-DFT 方法的計算表現 12
1.3.3 MC-SCS-MP2 | MC-DFT 方法的計算表現 14
1.3.4 計算時間 (Computational Cost) 與計算效率 (Performance/Cost Ratio) 17
1.4 結論 20
1.5 參考資料 21
1.6 Tables and Figures 25

第二章 Benchmark Study of the MC-DFT approach with Mixed Functionals on the Bond Energies of 3d Transition Metals
摘要 47
2.1 前言 49
2.2 計算方法 54
2.3 結果與討論 59
2.3.1各種 DFT 方法的計算表現 59
2.3.2 MC-DFT 方法的計算表現 60
2.3.3 Mixed DFT 與 Mixed | MC-DFT方法的計算表現 62
2.3.4 新型多層電子結構方法的計算表現 66
2.3.5 各方法預測主族元素原子化能量的計算表現 69
2.4 結論 71
2.5 參考資料 73
2.6 Tables and Figures 79

第三章 Reaction Dynamics Study of Ng’ + HNBNg+ → Ng + HNBNg’ + (Ng, Ng’ = He, Ne, and Ar)
摘要 101
3.1 前言 102
3.2 計算方法 106
3.2.1 靜態點的電子結構計算方法 106
3.2.2 速率常數計算 107
3.2.3 動力學同位素效應 108
3.3 結果與討論 111
3.3.1 結構比較 111
3.3.2 能量比較 113
3.3.3 反應速率常數 115
3.3.4 動力學同位素效應 119
3.3.4.1 分析 KIEs 的貢獻來源 121
3.3.4.2 穿隧效應對速率常數與 KIEs 的貢獻 125
3.4 結論 130
3.5 參考資料 132
3.6 Tables and Figures 138

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