本篇論文共分為兩個部分，第一部分是以第一原理計算方法探討魔術尺寸之奈米團簇(CdSe)13之結構與物理性質。第二部分是以理論計算方法探討單分子電子傳輸中的衰退係數。
在第一部份中，我們希望能以理論計算的方式了解劉沂欣教授研究團隊實驗觀察之CdSe奈米團簇的真實構型。由於目前的實驗技術僅能觀察到奈米團簇的外觀及大小，並無法確定實際原子的幾何結構。我們參考過去的文獻，選定C3-球殼、C1-籠狀及C3V-柱狀結構作為我們研究的對象，並在裸核加上甲胺及乙胺模擬實驗所用的正辛胺及油胺。和實驗比對後，我們提出柱狀結構的二聚體模型，顛覆了過去文獻中一致的C3-球殼模型。我們提出的CdSe奈米團簇構型不僅最為符合SAXS實驗觀察的尺寸，也符合吸收光譜與CD光譜的結果。也提出CdSe奈米團簇為何會形成二聚體的物理原因。
第二部分中我們對於不同的分子骨架在量子傳輸中的衰退係數進行探討。在單分子量子傳輸中，導電度隨分子長度呈指數遞減，遞減之速度由「衰退係數」（decay constant）而定。先前有文獻以Hückel Model提出，衰退係數可由長鏈分子骨架的基本重複單元求出，不受電極或連接基團的影響，但尚未獲得第一原理計算之驗證。本研究選用了單鍵、雙鍵及三鍵的分子骨架，以不同層級的電子傳導方法進行分子導電度的計算與研究。在計算方法上，分別使用了正交基底函數(orthogonal basis set)的瓦尼爾軌域方法(Wannier orbital, WO)配合虛擬電極針對分子部分，使用格林函數方法（Green’s Function Method）進行包含左右電極之系統，以及以模組近似法（Modular Approach）對分子骨架之重複單元，計算出衰退係數。

This study includes two parts. The first-part is a first-principles investigation on the structure and physical properties of the magic-size (CdSe)13 nanoclusters, and the second part is a theoretical study on the decay constant in quantum transport through single molecular junctions.
In first part, we investigated the structure and configuration of the experimentally synthesized CdSe nanoclusters using computational approaches. Based on previous literatures, we examined the C3-cage-core, the C1-cage, and the C3V-tubular structure for the (CdSe)13 nanoclusters. Both the bare and the ligated clusters were considered, using the methylamine and ethylamine to mimic the octylamine and oleylamine used in the experiment. Based on our calculation results, we propose a dimerized tubular model for the CdSe clusters, which is drastically different from the previous C3-cage-core model. This model not only matches well with the experimental SAXS result for the size and shape of the nanoclusters, but also shows a good correspondence to the absorbance and CD spectra. The underlying physical reason for the dimerization is also proposed.
In second part, several theoretical methods were used to study the attenuation factor in the quantum transport of different molecular frameworks. In electron transport through single molecules, it is known that the quantum conductance decreases exponentially with increasing molecular length, and the extent of decrease is determined by the decay constant. Previous Hückel Model studies, suggested that the decay constant may be determined solely by the repeating unit of the molecular framework, and is not affected by the electrode or the linkage group, but a first-principles validation has not yet been performed. Here we investigated different molecules consisted of single, double, and triple-bond frameworks, and adopted three theoretical methods of different levels to calculate the molecular conductance. In the first method, an orthogonal Wannier basis set and a virtual electrode was adopted to study the central molecules. In the second method, we use the Green’s Function method to study the molecule linked to a nanographene electrode. In the third one, we apply the modular approach to the Hamiltonian of the repeating unit derived ab initially, and calculate the decay constant.

(一)以第一原理計算方法探討魔術尺寸奈米團簇(CdSe)13之結構與性質
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(二) 單分子電子傳輸中的衰退係數之理論研究
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