此論文的第一部分我們提出了能夠非常有效率搜尋奈米粒子的最佳化構形的演算法。肇因於離子和價電子在半導體中的複雜偶合作用，我們必須提出一個能夠不預設前提下卻能夠有效搜尋系統的最優化構形的演算法。我們研究的系統為碳奈米粒子在顆數3~24這個範圍的構形變化。此外，我們和文獻上其他相關的理論工作結果做了比較和評論。論文的第二個部分首先我們使用了一個被公認為最好的構形演算法 (P. J. Hsu, S. K. Lai, J. Chem. Phys. 124 (2006) 0447110) 來得到銀銅合金奈米粒子 (粒子數為38) 的最穩定構形。緊接著我們在這個最佳化構形的基礎上，把電子間的交互作用透過一個更嚴謹的密度泛函理論來進一步分析。我們特別關注於系統的電性和磁性性質。數據結果顯示對於某些高度對稱的奈米粒子會意外地帶有靜磁矩。我們提出使用分子點群理論以及克萊門-尼爾森的模型來解釋靜磁矩之所以會出現其背後的物理機制為何。;In the first part, we proposed a modified basin hopping method which is very robust in searching the lowest energy structure of carbon clusters CN ( N=3-24). Due to the intricate coupling among ions and valence electrons in covalent systems, an unbiased optimization is necessary to locate the lowest energy structures. We have obtained the topological transition from a linear chain, a monocyclic ring to a polycyclic ring, and a fullerene/cage-like geometry and we also compared our structural findings with theoretical works in this field. In the second part of the thesis we first utilized a state-of-the-art algorithm that applies the empirical Gupta potential to search for the lowest energy structures of AgnCu38-n bimetallic clusters. We investigated from the results of DFT the charge density and spin charge density dispersions as well as magnetic properties of this system. It was found that the clusters at n=1-4, 24 as well as the two pure clusters Ag and Cu uncommonly carry net magnetic moments. We invoked the point group theory to explain these unexpected magnetism by analyzing the molecular orbital energy levels (MOELs) of these clusters. The MOELs were, however calculated by symmetry restricted DFT. and proposed to use point group theory for further explanation of these unexpected net magnetism.
