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研究生： 法 瓦
wafa maftuhin
論文名稱： 利用密度泛函緊束縛和密度泛函理論以及改良版的能量谷跳躍方法來研究金奈米叢集的最佳化構形
Studying Au clusters by an efficient optimization algorithm that hybridizes DFTB and DFT theories with the modified basin hopping method
指導教授： 賴山強
San-Kiong Lai
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2017
畢業學年度： 105
語文別： 英文
論文頁數： 38
中文關鍵詞： 金屬簇 、密度泛函理論 、優化算法
外文關鍵詞： metallic cluster, density functional theory, optimization algorithm
相關次數： 點閱：14  下載：0 
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    • 我們將密度泛函緊束縛理論和密度泛函理論各別地和一個所謂的改良版的能量谷跳躍法做了結合，並且巧妙的將之變成了一個在計算上有強大功效的兩階段構形最佳化搜尋法並用它來搜尋了金奈米叢集( n=3-20)的最穩定結構。在第一個階段中，我們先利用了密度泛函緊束縛理論/改良版能量谷跳躍法作了一個初步概略的能量面上的搜尋，並以搜尋到的最低能量結果作為下一個階段–密度泛函理論/改良版能量谷跳躍法的候選結構的基礎。為了強化演算法的搜尋效率，我們特別針對了緊束縛理論中的排斥力能量項在一些不同的擬合參考系統中做了分析比較。這個部分之所以重要的理由在於奈米叢集的構形絕大部分都是由排斥力項所主導。我們使用了兩組不同的緊束縛擬合參數作為分析結果優劣的參考依據。這兩組參數都在上述所提的二階段構形搜尋方法中被應用。數據結果顯示，金奈米叢集的最穩定構形和第一階段方法所獲得的最低能量結構基本上是脫鉤的，只會和第二個階段方法所獲得的最穩定構形有相關。我們也和文獻上其他的理論工作以及實驗量測的結果作了交叉分析比較。我們的數值結果和他們的大致上都是符合的。

    The density functional tight-binding (DFTB) theory and density functional theory (DFT) are separately combined with the modified basin hopping (MBH) method, and they are hybridized into an efficient two-stage algorithm for finding the lowest energy structures of gold clusters Aun with the size n spanning 3≤n≤20. In the first-stage, the DFTB/MBH is conducted mainly to provide a speedy and yet semi-quantitative searching of the lowest energy structures so as to pave the way for the second-stage DFT/MBH for a more accurate and reliable sorting of them at the DFT level. To ensure a high efficiency search of the global energy minimum, we devote more attention to the repulsive part energy in the DFTB theory and examine the quality of the DFTB parameters fitted to different set of reference structures. This study is physically relevant since the structure of a cluster is basically entropic, being by and large determined by the repulsive potential. To test the elegance of the present method, we employ two different sets of DFTB parameters for performing the first-stage DFTB/MBH but continue the second-stage optimization applying the same DFT/MBH to both. We found that the lowest energy geometries of Aun obtained are independent of the use of the first-stage DFTB/MBH. On comparing further our calculated lowest energy gold structures with other theoretical calculations and selected experimental clusters, our predicted Aun are encouraging, being in very good agreement with both.

    Table of Contents Abstract ................................................. i 中文摘要 ................................................ ii Table of Contents ...................................... iii List of Tables .......................................... iv List of Figures .......................................... v I. INTRODUCTION ....................................... 1 II. THEORY AND COMPUTATIONAL METHOD .................... 3 A. DFTB theory ...................................... 3 B. DFTB parameters .................................. 4 C. EMBH optimization method: hybridized DFTB/MBH and DFT/MBH .................................................. 5 D. DFT optimization ................................. 7 III. NUMERICAL RESULTS AND DISCUSSIONS .................. 7 A. Evaluation of Erep for different reference isomers .................................................. 8 B. DFTB/MBH for Aun ................................ 9 C. EMBH for Aun .................................... 14 IV. CONCLUDING REMARKS ................................. 16 Appendix A: DFTB parametrization ....................... 17 Appendix B: Fitting the repulsive energy Erep in eq.(1) 19 ACKNOWLEDGMENTS ......................................... 25 REFERENCES .............................................. 25

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