利用第一原理整體性探討AuSin(n=1-16)原子團之結構。而在n=1-16 中，同樣大小的原子團裡，其最低能量結構表現出一種趨勢-- 傾向把金原子擺在結構外圍勝於用矽原子來包覆。我們的研究表示在AuSin 原子團n=5 與10 時，是相對其他尺度更為穩定的結構。在n=6、7、10、11、12、14、15 尺度下，我們發現即使參雜了金原子，矽原子團仍然維持了穩定時的結構。此外，也詳細地分析了裂解能(Fragmentation energy)。研究更進一步指出對於n>7 的尺度，金原子的參雜會縮小最高填滿與最低未填滿分子軌道間的能量差距。再者，我們在CuSin(n=1-16)與AgSin(n=14、15、16)呈現了類似的分析，也將其與AuSin 原子團之結果做一個比較。接著，在特定尺度(n=10-16)的CuSin 原子團中，選定一些較低能量的同分異構物，讓其在Gaussian03 package 下做進一步的最佳化。我們發現對於CuSin(n=12-16)，包覆金屬粒子的結構比金屬粒子依附在外的結構擁有更低的能量，而此種趨勢也跟Janssens et al. Phys. Rev. Lett. 99, 063401 (2007)最近的研究相符。

The structures of AuSin (n = 1 - 16) clusters are investigated systematically using first-principles calculations. The lowest energy isomers exhibit preference toward exohedral rather than endohedral structure. Our studies suggest that AuSin clusters with n = 5 and 10 are relatively stable isomers. We found no significant alteration in the cluster’s inner core structure for sizes n= 6, 7, 10, 11, 12, 14, and 15 even in the presence of doping. Moreover, analysis of fragmentation energies is presented in detail. Our studies further indicate that doping of Au atom significantly decreases the gaps between the highest occupied molecular orbital and the lowest unoccupied molecular orbital for n > 7. Additionally, we report on similar results obtained for CuSin (n = 1 - 16) and AgSin (n = 14, 15, and 16) and compared them with those on AuSin clusters. Next, the low energy isomers for certain sizes of CuSin (n = 10 -16 ) clusters are selected for further optimizations using Gaussian 03 package. We found that for CuSin (n = 12 - 16 ), the endohedral isomers have lower energies than their exohedral counterparts, consistent with a recent study by Janssens et al. [15] in which a similar trend was observed.

ACKNOWLEDGMENT i
ABSTRACT iii
LIST OF FIGURES vi
LIST OF TABLES vii
1 Introduction 1
2 Theory 3
2.1 Density functional theory (DFT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 Thomas-Fermi model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 The Hohenberg-Kohn theorem . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.3 The Kohn-Sham equation with local spin density approximation
(LSDA) and generalized gradient approximation (GGA) . . . 5
2.2 The pseudopotential method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Norm-conserving pseudopotential . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Efficient formfor the model pseudopotentials . . . . . . . . . . . . . 11
2.2.3 Projector augmented waves (PAW) . . . . . . . . . . . . . . . . . . . . . 13
2.3 Geometry optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.1 Hellmann-Feynman theorem . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3.2 Steepest descent method and conjugate gradient method . . . . 14
2.3.3 Simulated annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.3.4 Generating initial structure by cluster growth method . . . . . . . 15
2.4 Details of Computational Packages . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.4.1 Vienna Ab initio Simulation Package . . . . . . . . . . . . . . . . . . . 16
2.4.2 Gaussian 03 package . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3 Results and discussions 18
3.1 Structures of AuSin ( n = 1 to 16) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.1 Structures of AuSin ( n = 1 to 5) . . . . . . . . . . . . . . . . . . . . . . . . 18
3.1.2 Structures of AuSin ( n = 6 to 8) . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1.3 Structures of AuSin ( n = 9, 10) . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.4 Structures of AuSin ( n = 11) . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.5 Structures of AuSin ( n = 12, 13) . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.6 Structures of AuSin ( n = 14) . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.1.7 Structures of AuSin ( n = 15) . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.8 Structures of AuSin ( n = 16) . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.2 Exohedral versus endohedral structures . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Relative Stability of AuSin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.4 Embedding energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.5 Electronic properties of MSin (M = Au, Ag, and Cu) . . . . . . . . . . . . . . 38
3.5.1 HOMO and LUMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.5.2 Charge transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
4 Conclusion 41

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