本論文利用密度泛函理論(DFT)模擬計算鎢奈米粒子(Wn, n=2-16)於不同尺寸下之結構特性及電子性質。首先利用basin-hopping method (BH)與big-bang method (BB)計算法配合tight-binding 多體勢能找出多筆初始的穩定結構。並利用DFT計算這些初始結構與能量並調配其之間的關係而獲得新的勢能參數，進而找出最穩定的結構。之後根據模擬計算出來的binding energy鍵結能 和 second-order energy difference，發現有跟其它尺寸的鎢奈米粒子有相對高的穩定性。另外也藉由計算vertical ionization potential (VIP)，adiabatic electron affinity (AEA)，最高占據軌域與最低未占據軌域能隙差 (HOMO-LUMO Gap) 和電荷分佈來分析各個顆數的鎢奈米粒子的電子性質及結構穩定度。

The structural and electronic properties of small tungsten nanoparticles Wn (n=2-16) were investigated by density functional theory (DFT) calculation. For the W10 nanoparticle, ten lowest-energy structures were first obtained by basin-hopping method (BH) and ten by big-bang method (BB) with the tight-binding many-body potential for bulk tungsten material. These fifty structures were further optimized by the DFT calculation in order to find the better parameters of tight-binding potential adquately for W nanoparticles. With these modified parameters of tight-binding potentials, several lowest-energy W nanoparticles of different sizes can be obtained by BH and BB methods and then further refined by DFT calculation. According to the values of binding energy and second-order energy difference, it reveals that the structure W12 has a relatively higher stability than those of other sizes. The vertical ionization potential (VIP), adiabatic electron affinity (AEA) and HOMO-LUMO Gap are also discussed for W nanoparticles of different sizes.

目錄
目錄 I
圖目錄 III
表目錄 IV
中文摘要 V
英文摘要 VI
第一章 緒論 1
1.1研究動機與目的 1
1.2 鎢奈米粒子簡介與文獻回顧 3
1.3 本文架構 6
第二章 理論介紹 7
2.1 密度泛函理論(Density Functional Theory) 7
2.1.1 密度泛函理論與電子密度 7
2.1.2 托馬斯-費米模型 8
2.1.3 霍恩貝格-科恩理論 9
2.1.4 科恩-軒姆方程式 9
2.1.5 交換-相關函數 11
2.1.6 基底 12
2.2 分子靜力學計算法介紹 13
2.2.1 Big-bang計算法 13
2.2.2 Basin-hopping計算法 15
2.3 緊束法(Tight-Binding) 16
2.3.1 緊束法多體勢能(Tight-binding potential)………….…….……16
2.3.2 鎢原子間作用勢能……………… . …………………….….…. 22
2.4 Force-matching method 介紹 23
第三章 結果與討論 25
3.1鎢奈米粒子結構分析 25
3.1.1 模擬模型建構 25
3.1.2 DFT模組參數設定 29
3.1.3 最穩定結構分析 29
3.1.4 二維與三維之結構探討 30
3.2 電性分析 34
3.2.1 鍵結能與平均鍵長分析 34
3.2.2 能量二階能量差分析 35
3.2.3 HOMO-LUMO Gap分析 35
3.2.4 VIP與AEA電性分析 35
3.2.5 電荷分佈分析 36

第四章 結論與建議 47
4.1 結論 47
4.2 建議與未來展望 48
參考文獻 49




圖目錄
圖2-1模擬Big-bang原理之示意圖 14
圖2-2 Basin-Hopping尋找穩定結構之示意圖 16
圖2-3 d軌域填充電子數與內聚能之關係 21
圖2-4 d軌域寬度W與狀態密度N(E)之關係 21
圖3-1找出鎢奈米粒子最穩定結構之流程圖 28
圖3-2 Wn (n=2-16)奈米粒子之最穩定結構與同分異構物 31
圖3-3不同尺寸下之鎢奈米粒子之平均鍵長與鍵結能的比較 35
圖3-4 Wn (n=2-16)奈米粒子之二階能量差(Δ2E) 39
圖3-5 Wn (n=2-16)奈米粒子之 HOMO-LUMO Gap 40
圖3-6 Wn (n=2-16)奈米粒子之The vertical ionization potential. 41
圖3-7 Wn (n=2-16)奈米粒子之adiabatic electron affinities . 42
圖3-8 Wn (n=2-16) 奈米粒子在5d, 6s與6p軌域上的電荷分佈 45







表目錄
表2-1各種元素的tight-binding勢能參數 ……………………………...23
表3-1修正過後的tight-binding參數 …….……………………….…….27
表3-2 利用PW91與BP91方法計算bulk材料之鎢奈米粒子的內聚能……………………………………………………………….……........32
表3-3比較PW91與BP91方法計算不同初始結構之W2奈米粒子的鍵長、振動頻率與分離能…………………………………………..….......32
表3-4比較2D平面與3D三維的Wn(n=3-8)奈米粒子的鍵結能….....34
表3-5 Wn (n=2-16)奈米粒子之最穩定結構單位原子之鍵結能..….…………………………………………………………………………….……38
表3-6 Wn (n=2-16)奈米粒子於價電子帶上的電荷分佈 ……….………38

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