以第一原理計算矽化銀原子團(AgSin, n=1,16)，結果指出在這一系列的AgSin原子團中， n = 7, 10 以及15 時為相對穩定的結構，並且所有的結構 (n <17) 都傾向將銀原子吸附在矽原子團的外面。再者，經由裂解能(fragmentation energy)分析的結果指出，此系列的原子團簇傾向優先裂解成單一的銀原子和剩下純矽的原子團， n>7的原子團(除了 n= 11和16)時，次要的裂解方式為分解成穩定的Si7以及甚餘的AgSi(n-7)，而AgSi11和AgSi16則是傾向分裂成穩定的Si10。分析最高填滿軌道(HOMO)以及最低未填滿軌道(LUMO)發現，當吸附銀原子之後，這兩者之間的差距(HOMO-LUMO gap)明顯的縮小。

The structures of AgSin (n = 1 – 16) clusters are investigated using first-principles calculations.
Our studies suggest that AgSin clusters with n = 7, 10, and 15 are relatively
stable isomers and that these clusters prefer to be exohedral rather than endohedral.
Moreover, doping leaves the inner core structure of the clusters largely intact. Additionally,
the plot of fragmentation energies as a function of silicon atoms shows
that the AgSin are favored to dissociate into one Ag atom and Sin clusters. Alternative
pathways exist for n > 7 (except n = 11 and 16) in which the AgSin cluster dissociates
into a stable Si7 and a smaller fragment AgSin&#1048576;7. The AgSi11 and AgSi16 cluster dissociates
into a stable Si10 and a small fragment AgSi. Lastly, our analysis indicates that
doping of Ag atom significantly decreases the gaps between the highest occupied
molecular orbital and the lowest unoccupied molecular orbital for n > 7.

ACKNOWLEDGMENT i
ABSTRACT iii
LIST OF FIGURES vi
1 Introduction 1
2 Theory 3
2.1 Density functional theory (DFT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 The Hohenberg-Kohn theorem . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.2 The Kohn-Sham equation with local spin density approximation
(LSDA) and generalized gradient approximation (GGA) . . . 4
2.2 The pseudopotential method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2.1 Norm-conserving pseudopotential . . . . . . . . . . . . . . . . . . . . . 6
2.2.2 Efficient formfor the model pseudopotentials . . . . . . . . . . . . . 9
2.2.3 Projector augmented waves (PAW) . . . . . . . . . . . . . . . . . . . . . 11
2.3 Geometry optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.1 Hellmann-Feynman theorem . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.2 Steepest descent method and conjugate gradient method . . . . 13
2.3.3 Simulated annealing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.3.4 Generating initial structure by cluster growth method . . . . . . . 13
2.4 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Results and discussions 15
3.1 Structures of AgSin ( n = 1 – 16) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.1 Structures of AgSin ( n = 1 – 5) . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.2 Structures of AgSin ( n = 6 – 8) . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1.3 Structures of AgSin ( n = 9) . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.4 Structures of AgSin ( n = 10) . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.1.5 Structures of AgSin ( n = 11) . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.6 Structures of AgSin ( n = 12) . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.7 Structures of AgSin ( n = 13) . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.8 Structures of AgSin ( n = 14) . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.9 Structures of AgSin ( n = 15) . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.1.10 Structures of AgSin ( n = 16) . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Relative stability of AgSin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Electronic properties of AgSin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.1 HOMO-LUMO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3.2 Charge transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4 Conclusions 36

[1] Steven M. Beck, J. Chem. Phys. 87, 4233 (1987).
[2] Hidefumi Hiura, Takehide Miyazaki, and Toshihiko Kanayama, Phys. Rev. Lett.
86, 1733 (2001).
[3] Vijay Kumar and Yoshiyuki Kawazoe, Phys. Rev. Lett. 87 045503 (2001).
[4] Abhishek Kumar Singh, Tina M. Briere, Vijay Kumar, and Yoshiyuki Kawazoe,
Phys. Rev. Lett. 91, 146802 (2003); Hiroaki Kawamura, Vijay Kumar, and
Yoshiyuki Kawazoe, Phys. Rev. B 70, 245433 (2004); Hiroaki Kawamura, Vijay
Kumar, and Yoshiyuki Kawazoe, Phys. Rev. B 71, 075423 (2005).
[5] Vijay Kumar, Abhishek Kumar Singh, and Yoshiyuki Kawazoe, Phys. Rev. B 74,
125411 (2006).
[6] J.B. Jaeber, T.D. Haeger, and M.A. Duncan, Journal of Physical Chemistry A 110,
9310 (2006).
[7] P.-F. Zhang, J.-G. Han and Q.-R.Pu, THEOCHEM 634, 25 (2003).
[8] G.K. Gueorguiev, J.M. Pacheco, S. Stafstrom and L. Hultman, Thin Solid films,
515 1192 (2006); G.K. Gueorguie and J. M. Pacheco, J. Chem. Phys. 119, 10313
(2003).
[9] J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).
[10] P. Hohenberg andW. Kohn, Phys. Rev. 136, B864 (1964);W. Kohn and L. J. Sham,
Phys. Rev. 140, A1135 (1965).
[11] G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).
[12] G. Kresse and J.Hafner, Phys. Rev. B 47, 558 (1993); G. Kresse and J. Furthmuller,
Phys. Rev. B 54, 11169 (1996).
[13] K. M. Ho, A. A. Shvartsburg, B. Pan, Z. Y. Lu, C. Z. Wang, J. G. Wacker, J. L. Eye,
and M. F. Jarrold, Nature 392, 582 (1998).
[14] Bei Liu, Zhong-Yi Lu, Bicai Pan, Cai-Zhuang Wang, Kai-Ming Ho, Alexandre A.
Shvartsburg andMartin F. Jarrold, J. Chem. Phys. 109, 9401 (1998).
[15] Zhong-Yi Lu, Cai-ZhuangWang, and Kai-Ming Ho, Phys. Rev. B 61 2329 (2005).
[16] J. G. Han, Z. Y. Ren, and B. Z. Lu, J. Phys. Chem. A, 108, 5100 (2004).
[17] Ping Huo, Zhao-Yu Ren, Fan Wang, Jiang Bian, Ju-Guang Han, and Guang-Hou
Wang, J. Chem. Phys. 121 12265 (2004).
[18] JimWang and Ju-Guang Han, J. Chem. Phys. 123, 064306 (2005).
[19] Vijay Kumar, Abhishek Kumar Singh, and Yoshiyuki Kawazoe, Nano Letters 4,
677 (2004).
[20] S. N. Khanna, B. K. Rao, P. Jena, and S.K.Nayak, Chem. Phy. Lett. 373, 433 (2003).
[21] S. N. Khanna, B. K. Rao, and P. Jena, Phys. Rev. Lett. 89 016803 (2002).
[22] Noriyuki Uchida, TakehideMiyazaki, and Toshihiko Kanayama, Phys. Rev. B 74,
205427 (2006).
[23] D. M. Deaven and K. M. Ho, Phys. Rev. Lett. 75, 288 (1995).
[24] P. Turski, Chemical Physics Lett. 325, 115 (1999).
[25] J. J. Scherer, J. B. Paul, C. P. Collier, and R. J. Saykally, J. Chem. Phys. 103, 113
(1995).
[26] Alexandre A. Shvartsburg, Martin F. Jarrold, Bei Liu, Zhong-Yi Lu, Cai-Zhuang
Wang, and Kai-Ming Ho, Phys. Rev. Lett. 81, 4616 (1999).
[27] P. E. Blochl, Phy. Rev. B. 50, 17 953 (1994).
[28] D. R. Hamann, M. Schluter, and C. Chiang, Phys. Rev. Lett. 43 1494 (1979).
[29] L. Kleinman and D. M. Bylander, Phys. Rev. Lett. 48 1425 (1982).
[30] S. Kirkpatrick, C. D. Gelatt, Jr., and M. P. Vecchi, Science 220 4598 (1983).
[31] M. C. Payn, M. P. Teter, D. C. Allan T. A. Arias, and J. D. Joannopoulos, Rev.Mod.
Phys. 64 1045 (1992).