採用以DFT為基底之理論計算金、銀叢集之最低能量結構並由所得的金原子組態計算及比較量子與古典物理理論的價電子分佈

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姓名

努魯莉亞(Nurulia Shinta Rahmani) 查詢紙本館藏

畢業系所

物理學系

論文名稱

採用以DFT為基底之理論計算金、銀叢集之最低能量結構並由所得的金原子組態計算及比較量子與古典物理理論的價電子分佈
(Calculate the lowest energy structures of Au and Ag clusters by the DFT-based theory and using the Au conformations obtained compare classically and quantum-mechanically their valence electron charge distributions)

相關論文

★ 金屬叢集的融化現象	★ 帶電膠體系統之液態-液態/固態相變研究
★ 低濃度電解質在奈米管內異常的擴散和導電性	★ 一價和多價叢集原子的熱穩定現象
★ 金屬與合金分子叢集的結構	★ 物理系統之能量與焓分佈之統計力學研究
★ 膠體系統平衡相域與動態凝聚之研究	★ 合金金屬叢集的溫度效應
★ 介面膠體叢聚現象的理論研究	★ 帶電膠體懸浮液的相圖與液態-玻璃相變研究
★ 膠體相圖之理論計算	★ 膠體、棒狀粒子混合系統之相圖的理論分析
★ 利用時間序列的統計方法研究金屬叢集的動力學	★ 由分子動力學模擬探討層狀石墨烯的成長與碳化矽基板上多層石墨烯的熱穩定性
★ 金銅合金金屬叢集(N=38)的磁性性質研究	★ 膠體、盤狀粒子混合系統的兩階段動態相變區域

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摘要(中)

新修飾之泛密度函數化的緊密結合（DFTB）參數 [Oliveira et al., J. Phys. Chem. A 120, 8469 (2016) ] 用於計算能量函數，並和質優改良後的盆地跳躍式（MBH）演算法結合，研究金屬叢集體金和銀, 其原子數目 n 為 3,...,20。計算結果發現，使用DFTB/MBH方法，可依據最低能量值之幾何結構預測二維（2D）到三維（3D）的維度轉換 n；對於金叢集，其維度轉換自 n = 8（2D）至 n = 9（3D），而對於銀叢集則是 n = 5（ 2D）到 n = 6（3D）。對於金叢集 n 範圍 3-8，19 及 20，本計算（i）確認由 Oliveira 等人幾個能量接近，但形狀尚未給予明確定位的計算，特別是原子數目 n 在 8-11 範圍的金叢集結構，以及（ii）給出足於比較可從遠紅外光譜實驗中獲得的穩定叢集的其他證據。在與銀叢集的早期和最近的理論計算相比較，不管是第一原理或和DFT相關所建立的理論，我們可以看出，計算出的最佳化能量結構與本論文專研的金叢集所預測的各個幾何形狀都具有同等的品質。另外，由於 DFTB/MBH 最佳化演算法對金和銀叢集所預測得到最低能量結構的信心，我們續深入探討在量子力學 DFTB 理論跟在古典物理電荷平衡模型兩架構下，價電子之分佈。從比較此二方法所得到的電荷分散結果，我們可以進一步揭示 DFTB 理論的各種近似，以及其和古典物理的相似處。或許更有趣的是，我們發現金與銀叢集體其各別在等最低能量值的鏡子影像對稱性，後者對稱性發生在金叢集中為 Au15 和 Au18，而銀則為 Ag14 和 Ag20。這個意想不到的發現，猜想歸功於我們在 MBH 能量佳化過程中，引入了剪切再拼接之遺傳算子樣操作。

摘要(英)

New modified density functional tight-binding (DFTB) parameters [Oliveira et al., J. Phys. Chem. A 120, 8469 (2016)] are used to calculate the energy function and combined it with an elegant modified basin hopping (MBH) optimization algorithm to systematically study the coinage metal clusters Aun and Agn, n=3,…,20. It is found that the lowest energy geometries predicted by the DFTB/MBH method yield reasonable bidimensional (2D) to tridimensional (3D) transition which are n=8 (2D) to n=9 (3D) for Au cluster and n=5 (2D) to n=6 (3D) for Ag cluster. The calculated individual Au isomers in the size range n=3-8, 19 and 20 (i) confirm the shapes of several iso-energetic structures Au8-Au11 left unsettled in their locating these stable clusters by Oliveira et al. and (ii) give additional evidences to those stable clusters that are available from far-IR spectra experiments. Comparisons with early and more recent theoretical calculations for the Ag clusters, both ab initio methods and DFT-based theory, show that our calculated optimized energy structures are of comparable good quality of the predicted shapes as those of Au clusters studied here. Given that the DFTB/MBH algorithm lends great credence to the predicted lowest energy structures of Aun and Agn, we delve further into the valence electron charge distribution in clusters both at the quantum mechanical DFTB theory level and at a classical level appealing to a charge equilibration model. The comparison of the charge dispersion results from these two methods would shed light on the various approximations made in the DFTB theory and their classical analogues. Perhaps more interesting is our findings of lowest energy clusters showing mirror-image symmetry and these chiral clusters are Au15 and Au18 in Aun, and Ag14 and Ag20 in Agn. This unexpected discovery in this work is attributed to our introduced cut-and-splice genetic-operator-like operation in the MBH energy optimization.

關鍵字(中)

★ -金屬叢集
★ 電荷分佈
★ 密度泛函理論
★ 電荷轉移
★ 拓樸構形

關鍵字(英)

★ metallic clusters
★ charge distribution
★ density functional theory
★ charge transfer
★ topological structure

論文目次

Table of Contents

Abstract …….……...…………………………………………………………………………. i
中文摘要 ….….……………………………………………………………………………… ii
Acknowledgments………..………………………………………………………................. iii
Table of Contents …………………………………………………………….…………….. iv
List of Tables ...……………………………………..………………………….……………..v
List of Figures ...……………………………………… …………………….……………… vi
I. INTRODUCTION ..……………………………………………………...…………..... 1
II. THEORY AND COMPUTATIONAL DETAILS……………………...……………... 3
A. DFTB theory .....………………………………………………...………………. 3
B. DFTB parameters ………………………………………………...…………....... 6
C. MBH optimization algorithm …………………………………………………… 9
D. Electronic distribution: DFTB→DFT ….…………..………………………..… 10
E. Classical Charge Equilibration Model ….…………..……...………………..… 11
III. NUMERICAL RESULTS AND DISCUSSIONS ………………………..………… 18
A. Aun clusters: n = 3-20……………………………………….….….…….………... 19
B. Electronic charge distribution for Au clusters ……….….……..…………………. 20
C. Ag clusters: n=3-20……………………………..………………..……………….. 28
IV. CONCLUSIONS…………………………………….………………………..……… 33
Appendix A: Matlab and Fortran Codes………….……………………………………. 33
REFERENCES ………………………………………………………..………...…………. 40

參考文獻

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指導教授

賴山強(San-Kiong, Lai)

審核日期

2017-9-26

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