以往分子動力模擬對於有帶電粒子系統較不易處理，主要是因為靜電力的收斂緩慢，若強制使用截斷半徑則會對力的計算上產生相當大的誤差。所幸藉由Ewald sum來處理靜電力，可得到合理的計算結果。但是Ewald sum方程式複雜，因此須先得到正確的作用力處理式才能夠運用於分子動力模擬中。

本研究可分為三個部份：
I.首先推導出Ewald sum以得到正確的計算式，接著驗證Ewald sum程式
化過程無誤。
II.將成功得到的計算式運用於分子動力模擬-建立純水系統。
III.最後建立鹽類水溶液。

研究最後探討各種離子對與不同的濃度對於水分子間氫鍵的影響，結果發現離子對於水分子間氫鍵的破壞與離子的水合能力是成正比關係。

Because of the slow convergence of static electricity, a molecular dynamic simulated system for charged particles is difficult to handle. If we force to use the truncation radius, the calculation of forces will generate considerable errors. However, by using Ewald sum which deals with static electricity, we are entitled to get reasonable results. But, Ewald sum formula is too complex to use. The force should be gotten first, so the correct address type can be applied in molecular dynamic simulation.

The research can be divided into three parts:

I. Get the right formula by derived Ewald sum, then verify if the Ewald sum
program process is correct or not.

II. Apply the formula into molecular dynamics simulation - the established water
system.

III. Establish salt solution.

Finally, the research is discussing about the effect of hydrogen bonds between water molecules and ions in different concentrations. The result shows that the destruction of hydrogen bonds between water molecules and ions is proportional to hydration.

謝誌 I
中文摘要 II
Abstract III
目錄 IV
圖目錄 V
表目錄 IX
符號表 XI
第一章 序論 1
1.1 前言 1
1.2 研究動機 3
第二章 文獻回顧 5
2.1 純水分子文獻回顧 5
2.2鹽類水溶液的文獻回顧 7
第三章 研究方法 9
3.1 分子動力學基本理論 9
3.1.1分子動力學的基本假設與模擬流程 9
3.1.2運動方程式的數值方法 12
3.1.3週期性邊界 14
3.2 分子勢能 17
3.2.1分子內作用力 17
3.2.2分子間作用力 18
3.3 系統的控制 20
3.4 程式加速方法 22
3.4.1.牛頓第三運動定律 22
3.4.2分子截斷半徑法 22
3.4.3.Verlet鄰近列表法(Neighbor list) 24
3.5 性質統計 25
第四章 水分子勢能介紹 31
4.1水分子勢能介紹 31
4.2靜電力的介紹 35
4.2.1 截斷勢能的介紹 36
4.2.2 Ewald sum的介紹 38
第五章 Ewald sum驗證與模擬系統 42
5.1Ewald sum驗證 42
5.1.1 Ewald sum 數學式之驗證 42
5.1.2Ewald sum於多粒子系統的驗證 45
5.2模擬系統 47
5.2.1純水系統 47
5.2.3 鹽類水溶液系統 49
第六章 結果與討論 51
6.1 Ewald sum簡單系統驗證 51
6.2 純水系統 57
6.2.1.SPC/Fw勢能模型之分子結構 57
6.2.2 SPC/Fw模型平衡鍵長與結構 60
6.3鹽類水溶液系統 63
6.3.1單離子系統之結構性質 63
6.3.2多離子系統對氫鍵影響 73
第七章 結論與未來展望 79
7.1結論 79
7.2未來展望 81
附錄A 82
附錄B 89
參考文獻 90

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