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Molecular Dynamics Simulations of Methane Fluids using Quantum Chemistry Calculated Intermolecular Interactions
No full text我們使用HF、MP2和DFT來計算甲烷與矽烷雙體作用力，HF會產生純排斥的位能曲線，且基底對HF影響並不大。在MP2的計算中，基底會影響排斥指數項(Repulsion exponent)、平衡鍵長(Equilibrium bond length)、束縛能(Binding energy)與漸進行為(Asymptotic behavior)。比較加了BSSE與未加BSSE的結果，發現加了BSSE的計算其漸進行為會隨著基底增大而逐漸收斂至實驗值，而未加BSSE的計算則不規則的產生位能曲線，顯示BSSE對MP2方法來模擬漸近行為的重要性。我們使用大範圍的exchange-correlation functionals配對的DFT計算，並比較哪種配對較接近MP2結果。
我們接下來將量子化學計算出的位能曲線利用Lennard-Jones potentials fitting出鍵距與束縛能的參數，帶進牛頓方程式，模擬甲烷液體的平衡性質與動態性質並與實驗比較，發現模擬結果與實驗比較已經相當精確，這可說明量子力學對分子間勢能計算相當具精確性。接著利用三種位能模型去模擬甲烷實驗三相圖的氣化曲線與溶化曲線，幫助我們了解氣化曲線與溶化曲線的平衡性質與動態性質。We have calculated the intermolecular interaction potentials of the methane dimer at the minimum-energy D3d conformation using the Hartree-Fock (HF) self-consistent theory, the correlation-corrected second-order Møller-Plesset (MP2) perturbation theory and the density functional theory (DFT). The HF calculations yield unbound potentials largely due to the exchange-repulsion interaction. In the MP2 calculations, the basis set effects on the repulsion exponent, the equilibrium bond length, the binding energy, and the asymptotic behavior of the calculated intermolecular potentials have been thoroughly studied. Up to the largest basis set used, the asymptotic dispersion coefficient has not converged to the destined C6 value from molecular polarizability calculations. The slow convergence could indicate the inefficacy of using the MP2 calculations with Gaussian-type functions to model the asymptotic behavior. Both the basis set superposition error (BSSE) corrected and uncorrected results are presented to emphasize the importance of including such corrections. Only the BSSE corrected results systematically converge to the destined potential curve with increasing basis size. The DFT calculations generate a wide range of interaction patterns, and compare with MP2 results.
Next, we use a curve fitting method to fit the results of quantum chemistry calculation. We can get the force parameters of bond lengths and binding energies and then input them to solve Newton’s equations. To simulate the equilibrium properties and dynamics properties of methane liquid, we perform NVT ensemble molecular dynamics simulations. Our results well reproduce the experimental data. It demonstrates that quantum chemistry calculated intermolecular interaction is very good. Beside we simulate the equilibrium properties and dynamics properties along the vapor-liquid curve and solid-liquid curve in the phase diagram using three potential models.目 錄
口試委員會審定書…………………………………………………………………………..i
致謝…………………………………………………………………………….....................ii
摘要……………………………………………………………………………………..…..iii
目錄………………………………………………………………………………………....vi
圖目錄……...…………………………………………………….........................................ix
表目錄…...……..……………………………………………………………………..…...xiii
第一章 緒論……………………………………………………………………….……1
第二章 基本理論介紹……………………………………………………………….…2
Part I 量子力學部份………………………………………………………..……….……....7
2.1 多電子問題的薛丁格方程式……………………………………………………….….7
2.1.1 單電子的薛丁格方程式……………………………………………………….…7
2.1.2 歐本-海默近似法(Born-Oppenheimer Approximation)…………….…………....8
2.1.3 庖立不相容原理(Pauli exclusion principle)…………………………………….11
2.1.4 Hartree-Fock Approximation……………………………………………………..12
2.2 Møller-Plesset微擾理論(Møller-Plesset perturbation theory)…………………….....17
2.2.1 基本數學概念……………………………………………………………....…...17
2.2.2 時間無關的微擾理論……………………………………………………….......18
2.2.3 Møller-Plesset微擾理論(Time Independent Perturbation Theory)……………....20
2.3密度泛函理論(Density Functional theory)………………………………………….….22
2.3.1 密度泛函理論的基本概念………………………………………………….......22
2.3.2 Kohn-Sham模型……………………………………………………………….…22
Part II 量子力學部份……………………………………………………..………....….....25
2.4 分子動力學的基本理論…………………………………….……………...…...….…25
2.4.1 牛頓方程式(Newton’s equation)……………………………………….......…...25
2.4.2 勢能函數(Potential energy function)………………………………..………......25
2.4.3 時步(Time step)………………………………………………………….…..…..28
2.4.4 運動方程式(Equation of motion)……………………………………………......29
2.4.5 週期性邊界條件(Periodic boundary condition)……………………………..….31
2.4.6 量測 (Measurement)…………………………………………………..………….....31
2.4.7 All-Pair method……………………………………………………………..….....…..33
2.4.8 積分演算法………………………………………………………………..…….......33
2.4.9 溫度微調(Temperature adjustment)……………..……………………….…….....…36
2.5 分子動力學的平衡性質與動態性質………………………………………………....37
2.5.1 徑向分布函數(Radial distribution function)….……………………..…………...…37
2.5.2 速度自相關函數(Velocity autocorrelation function)………...……………….....39
2.5.3 擴散係數(Diffusion coefficient)……………………………...……………........41
第三章 計算方法………………………………………………………………….…..44
Part I 量子力學部份………………………………………………………..………..........44
3.1 甲烷與矽烷的計算方法…………………………………………………………..…..44
Part II 分子動力學部份..…………………………………………………..…………..….44
3.2 分子動力學的計算詳細-2D…………………………………………………….….…45
3.2.1 二維系統……………………………………………………………………..….45
3.2.2 三維系統………………………………………………………………….……..46
第四章 計算結果與模擬結果…………………………………………………..…….51
Part I 量子力學部份………………………………………………………..……......…….51
4.1 甲烷與矽烷的計算結果…………………………………………………………..…..51
4.1.1 甲烷HF的計算結果…………………………………………………….….…..51
4.1.2 甲烷MP2的計算結果…………………………………………………..….…..52
4.1.3 甲烷DFT的計算結果………………………………………………….……....55
4.1.4 矽烷HF的計算結果………………………………………………….………...63
4.1.5 矽烷MP2的計算結果………………………………………………….….…...64
4.1.6 矽烷DFT的計算結果……………………………………………………….....66
Part II 分子動力學部份..…………………………………………………..…………..….74
4.2 二維溶化模擬…………………………………………………………………….…...74
4.3 剛性分子的分子動力學模擬-平衡性質……………………...………………..…….77
4.3.1 徑向分布函數與實驗比較…………………………………………….…….….77
4.3.2徑向分布函數－模擬沿著氣化曲線與溶化曲線……………….……….……..79
4.4剛性分子的分子動力學模擬-動態性質…………………………………….…….….90
4.4.1速度自相關函數與擴散係數－模擬沿著氣化曲線與溶化曲線……….….…..90
4.4.2擴散係數－與實驗比較……………………………………………………..…..94
第五章 結論與未來展望………………………………………………………..…….96
5.1 量子力學結論…………………………………………………………………..……..96
5.2 分子動力學結論……………………………………………………………….…...…97
5.3 未來展望……………………………………………………………………….….…..98
圖目錄
圖1 跨尺度模擬的示意圖－在不同尺度下都有與之對應的學科，這些學科經過 連接，即完成跨尺度研究。...............................................................................................2
圖2 從位能曲線出發，了解系統的平衡性質與動態性質。…………………..………...6
圖3 薛丁格方程式解出的能量曲線圖。…………………………………….…...……….10
圖4 電子在空間某點出現的機率示意圖。………………………………….…................11
圖5 hole自旋軌道數與virtual自旋軌道數示意圖。………………….…….……..…..16
圖6 Hard sphere位能曲線，在位置rc時，有一個無限高的位能障礙。…….…..............26
圖7 Shifted Lennard-Jones Potential，為Lennard-Jones Potential加上ε。…………........27
圖8 Shifted Lennard-Jones Potential且中斷點在rc。…………………………….....…..28
圖9 週期性邊界條件示意圖－中間粗黑線的框框為真實模擬的格子，其他地方為假想的格子，目的是為了讓真實格子在每一時刻都保有相同的粒子數。………….32
圖10 All-pairs method－每ㄧ個原子都必須與模擬空間中所有的原子作用。.….........33
圖11 徑向分布函數－在ㄧ球殼中所包圍的粒子數總數，在與系統的平均密度做比值，即為在此球殼的徑向分布函數值。………………………………...……........38
圖12 甲烷的D3d構型。…………………………………………………………..…...…45
圖13 4C模型－4C模型只有氫(H)參與力的計算。……………………………….....…46
圖14 4C模型fit結果。…………………………………………………………...…..…..47
圖15 5C模型fit結果。……………………………………………………………….…..48
圖16 5C模型－每個原子間都參與力的計算，故稱5C模型。……………...….............48
圖17 H構型與I構型。…………………………………………………………..…..…...49
圖18 H+I 兩種構型的fit結果。………………………………………………….….......50
圖19 甲烷的HF計算結果－可發現除了STO-3G外，其餘幾乎都已達到收斂。…..…..52
圖20 甲烷的MP2計算結果－MP2的計算呈現了鍵長、束縛能與漸近行為，其中實心為未加BSSE修正量的曲線，其曲線未隨著基底增大而系統性收斂，反之有
加BSSE修正量則有系統性的收斂。………………………………………..…….53
圖21 甲烷遠處色散能比較－發現C6+C8項的結果比C6項精確。…………………….55
圖22 (a) 固定PBE correlaion functional(甲烷)。………………………………….…..…..56
圖22 (b) 固定PW91 correlaion functional(甲烷)。…………………………………...…...57
圖22 (c) 固定VWN correlaion functional(甲烷)。…………………………………...…...57
圖22 (d) 固定VP86 correlaion functional(甲烷)。………………………………….…......58
圖22 (e) 固定LYP correlaion functional(甲烷)。………………………………….….…...58
圖23 甲烷的漸近行為分析－除了MP2外，DFT在遠處誤差較大。……….............…...59
圖24 矽烷的HF計算結果－可發現除了STO-3G外，其餘幾乎都已達到收 斂。………………………………………………………………………………….63
圖25 矽烷的MP2計算結果－MP2的計算呈現了鍵長、束縛能與漸近行為，其中實心為未加BSSE修正量的曲線，其曲線未隨著基底增大而系統性收斂，反之有
加BSSE修正量則有系統性的收斂。………………………………………….....65
圖26 矽烷遠處色散能比較發現C6+C8項的結果比C6項精確。…………………….…66
圖27 (a) 固定PBE correlaion functional(矽烷)。……………………………………….....67
圖27 (b) 固定PBE correlaion functional(矽烷)。……………………………………..…..68
圖27 (c) 固定PBE correlaion functional(矽烷)。……………………………………….....68
圖27 (d) 固定PBE correlaion functional(矽烷)。………………………………………....69
圖27 (e) 固定PBE correlaion functional(矽烷)。……………………………………….....69
圖28 矽烷的漸近行為分析除了MP2外，DFT在遠處誤差較大。……………….……...70
圖29 First order van der Waals loop。…………………………………………...…….….75
圖30 在49000-50000△t連續曝光結果，發現有相轉移存在。……………….............…75
圖31 二維溶化－在某一時間點河流現象。…………………………………………..….76
圖32 甲烷為一個似金字塔的架構，中間是碳原子，旁邊有四個氫原子與碳連接。……………………………………………………………………………….....76
圖33 不同位能曲線所計算出的徑向分布函數 與實驗比較。……….………......78
圖34 不同位能曲線所計算出的徑向分布函數 與實驗比較。………………..…78
圖35 不同位能曲線所計算出的徑向分布函數 與實驗比較。……………...…...79
圖36 甲烷的三相實驗圖[75]。………………………………………………….………...80
圖37 (a) 模擬沿著氣化曲線的徑向分布函數 圖(4C模型)。……………...……..81
圖37 (b) 模擬沿著氣化曲線的徑向分布函數 圖(4C模型)。…………………….81
圖37 (c) 模擬沿著氣化曲線的徑向分布函數 圖(4C模型)。………………...…..82
圖37 (d) 模擬沿著氣化曲線的徑向分布函數 圖(5C模型)。……………….....…82
圖37 (e) 模擬沿著氣化曲線的徑向分布函數 圖(5C模型)。………………...…..83
圖37 (f) 模擬沿著氣化曲線的徑向分布函數 圖(5C模型)。…………………….83
圖37 (g) 模擬沿著氣化曲線的徑向分布函數 圖(H+I-4C模型)。……..........…...84
圖37 (h) 模擬沿著氣化曲線的徑向分布函數 圖(H+I-4C模型)。…………….....84
圖37 (i) 模擬沿著氣化曲線的徑向分布函數 圖(H+I-4C模型)。…………...…...85
圖38 (a) 模擬沿著溶化曲線的徑向分布函數 圖(4C模型)。………………..…...85
圖38 (b) 模擬沿著溶化曲線的徑向分布函數 圖(4C模型)。………………...…..86
圖38 (c) 模擬沿著溶化曲線的徑向分布函數 圖(4C模型)。………………….....86
圖38 (d) 模擬沿著溶化曲線的徑向分布函數 圖(5C模型)。………………..…...87
圖38 (e) 模擬沿著溶化曲線的徑向分布函數 圖(5C模型)。………………..…...87
圖38 (f) 模擬沿著溶化曲線的徑向分布函數 圖(5C模型)。……………..……...88
圖38 (g) 模擬沿著溶化曲線的徑向分布函數 圖(H+I-4C模型)。.........................88
圖38 (h) 模擬沿著溶化曲線的徑向分布函數 圖(H+I-4C模型)。…………...…..89
圖38 (i) 模擬沿著溶化曲線的徑向分布函數 圖(H+I-4C模型)。……………......89
圖39 (a) 模擬沿著氣化曲線的速度自相關函數(4C模型)。………………………...…...91
圖39 (b) 模擬沿著氣化曲線的速度自相關函數(5C模型)。…………………..……..….91
圖39 (c) 模擬沿著氣化曲線的速度自相關函數(H+I-4C模型)。…………………….….92
圖40 (a) 模擬沿著溶化曲線的速度自相關函數(4C模型)。…………………..……...….92
圖40 (b) 模擬沿著氣化曲線的速度自相關函數(5C模型)。…………………..………...93
圖40 (c) 模擬沿著溶化曲線的速度自相關函數(H+I-4C模型)。……………………......93
圖41 甲烷與矽烷12個不同構型示意圖，這12個構型幾何皆對稱。………………....104
圖42 H和I方向之構型。………………………………………………………..….….105
表目錄
Table 1 利用HF和MP2的方法計算甲烷雙體的位能模型，R0為位能為0時候的距離、Rm為平衡鍵長、Eb為束縛能、ω為振動頻率，其餘為fitting的參數。…….60
Table 2 比較6-311++G(3df,3pd)的基底計算甲烷90個exchange-correlation functional的組合，MP2計算平衡鍵長的結果為3.73 ，粗黑斜線的值為誤差在10%以內的組合。…………………………………………………………………….....61
Table3 比較6-311++G(3df,3pd)的基底計算甲烷90個exchange-correlation functionals 的組合，MP2計算束縛能的結果為-0.415 kcal/mol，粗黑斜線
的值為誤差在10%以內的組合。………………..……………………………....62
Table 4 利用HF和MP2的方法計算矽烷雙體的位能模型，R0為位能為0時候的距離、Rm為平衡鍵長、Eb為束縛能、ω為振動頻率，其餘為fitting的參數。…….....71
Table 5 比較6-311++G(3df,3pd)的基底計算矽烷108個exchange-correlation functionals 的組合，MP2計算平衡鍵長的結果為4.25 ，粗黑斜線的值為誤差在10%以內的組合。………………………………………….............................................72
Table 6 比較6-311++G(3df,3pd)的基底計算矽烷108個exchange-correlation functionals 的組合，MP2計算束縛能的結果為-0.454kcal/mol，粗黑斜線的值為誤差在10%以內的組合。……………………………………………………………......73
Table 7 隨著粒子數的增加，河流出現的時間也增加，增加二為溶化假設的論證。…………………………………………………………………….………....74
Table 8 使用三種位能模型計算沿著氣化曲線與溶化曲線的擴散係數，可以討論物質存在的相。……………………………………………………….……………....94
Table 9 使用三種位能模型計算不同溫度與密度下的擴散係數，並與實驗比較。…....95
Table 10沿著氣化曲線的熱力學資料。……………………………………………….....109
Table 11沿著溶化曲線的熱力學資料。……………………………………………..……109
參考文獻………………………………………………………………………….………..99
附錄A…………………………………………………………………………………......104
附錄B………………………………………………………………………………..…....105
附錄C…………………………………………………………………………………..…10
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No full textAuthor-wise bibliometric analysis based on entropy.</p
Author Under Sail The Imagination of Jack London, 1893-1902
No full textIn Author Under Sail, Jay Williams offers the first complete literary biography of Jack London as a professional writer engaged in the labor of writing. It examines the authorial imagination in London's work, the use of imagination in both his fiction and nonfiction, and the ways he defined imagination in the creative process in his business dealings with his publishers, editors, and agents. In this first volume of a two-volume biography, Williams traverses the years 1893 to 1902, from London's "Story of a Typhoon" to The People of the Abyss. The Jack London who emerges in the pages of Author Under Sail is a writer whose partnership with publishers, most notably his productive alliance with George Brett of Macmillan, was one of the most formative in American literary history. London pioneered many author models during the heyday of realism and naturalism, blurring the boundaries of these popular genres by focusing on absorption and theatricality and the representation of the seen and unseen. London created an impassioned, sincere, and extremely personal realism unlike that of other American writers of the time. Author Under Sail is a literary tour de force that reveals the full range of London as writer, creative citizen, and entrepreneur at the same time it sheds light on the maverick side of machine-age literature.Intro -- Title Page -- Copyright Page -- Dedication -- Contents -- Acknowledgments -- Introduction -- 1. Spirit Truth -- 2. From Absorption to Theatricality and Back Again -- 3. "I Will Build a New Present" -- 4. Sons as Authors -- 5. Fathers as Publishers -- 6. The Daughter as Author -- 7. Lovers as Authors -- 8. At Sea with the Family -- 9. Yellow News, Yellow Stories -- 10. The Return Home -- Notes -- Bibliography -- Index -- About Jay WilliamsIn Author Under Sail, Jay Williams offers the first complete literary biography of Jack London as a professional writer engaged in the labor of writing. It examines the authorial imagination in London's work, the use of imagination in both his fiction and nonfiction, and the ways he defined imagination in the creative process in his business dealings with his publishers, editors, and agents. In this first volume of a two-volume biography, Williams traverses the years 1893 to 1902, from London's "Story of a Typhoon" to The People of the Abyss. The Jack London who emerges in the pages of Author Under Sail is a writer whose partnership with publishers, most notably his productive alliance with George Brett of Macmillan, was one of the most formative in American literary history. London pioneered many author models during the heyday of realism and naturalism, blurring the boundaries of these popular genres by focusing on absorption and theatricality and the representation of the seen and unseen. London created an impassioned, sincere, and extremely personal realism unlike that of other American writers of the time. Author Under Sail is a literary tour de force that reveals the full range of London as writer, creative citizen, and entrepreneur at the same time it sheds light on the maverick side of machine-age literature.Description based on publisher supplied metadata and other sources.Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, YYYY. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
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