奈米貴金屬團簇，如Au、Ag、Cu，由於具有d10s1的電子殼層結構，而呈現出不同於單一原子或分子的特性。為了進一步地瞭解銀原子團簇的結構與性質，本論文將根據第一原理的密度泛函理論來計算銀原子團簇(Agn-cluster，n=2~8)的電子特性及響應函數。

為了比較團簇與塊材間的特性差異，本論文一開始針對銀原子的週期性結構進行計算，經由收斂測試得知銀原子原始晶胞的穩定結構，利用此原始晶胞來模擬週期性結構的電子特性。

接下來，同樣地藉由收斂測試得到各銀原子團簇的穩定結構，並計算其狀態密度，以觀察其電子特性與銀原子週期性結構的不同。結果發現銀原子團簇的特性會隨著原子顆數的增加而改變，由近似分子的特性逐漸轉變為與銀原子週期性結構相同的金屬材料特性。

在了解銀原子團簇的電子特性後，本論文根據密度泛函微擾理論，給予銀原子團簇不同方向的靜電場微擾，觀測電子密度的變化情形。另外利用與時間有關密度泛函理論來計算銀原子團簇的電子躍遷能量與振盪強度，藉以求得其光學吸收頻譜，並加以分析。

Noble metal nanoclusters (Au, Ag and Cu) show some properties which are different from single particle and molecule caused by their single valence s-electron shell and filled d-shell. In order to realize the structure and properties of the clusters, we will compute the electronic properties and response functions of Agn clusters (n = 2-8) according to the first principle method.

We find the lowest energy structure of the primitive cell of silver by the convergence calculation and use the primitive cell to investigating the electronic properties of the periodic structure of silver., we find the lowest energy structure of Agn clusters by the convergence calculation, and calculate the density of states of silver clusters to comparing the different with the periodic structure of silver. In this work, we also discuss the size dependence of electronic properties such as density of states, fermi energy and HOMO-LUMO gap.

Finally, we analyze the response functions of Agn clusters. First, we compute the response of clusters to an homogeneous electric field in different direction to observing the distribution of charge density. Next, in order to find the optic absorption spectrum, we must compute the electronic excitations and oscillator strengths by Time-Dependent Density Functional Theory (TDDFT).

[1] M. Schmidt, R. Kusche, T. Hippler, J. Donges, and W. Kronmullter,Phys.Rev. Lett. 86, 1191 (2001).
[2] A. J. Cox, J. G. Louderback, and L. A. Bloomfield, Phys. Rev. Lett. 71, 923 (1993)
[3] Masatake Haruta, Catal. Today, 36,153 (1997).
[4] R. G. Parr, and W. Yang, “Density-Functional Theory of Atom and Molecules”, by Oxford University Press (1989).
[5] Giovanni Onida, Lucia Reining, and Angel Rubio, Review of Modern Physics, 74, 601 (2002)
[6] J. P. Perdew, and A. Zunger, Phys. Rev. B 23, 5048 (1981).
[7] A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, Phys. Rev. B 52, R5467 (1995).
[8] M. Petersilka, U. J. Gossmann, and E. K. U. Gross, Phys. Rev. Lett. 76, 1212 (1996).
[9] Vasiliev, I., Ogut, S., and Chelikowsky, J. R., Phys. Rev. B 65, 115416 (2002).
[10] P. Hohenberg and W. Kohn, Phys.Rev. 136, pp. B864−Β871 (1964).
[11] W. Kohn and L. J. Sham, Phys.Rev.,140,A1133 (1965)
[12] J. P. Perdew, Y. Wang, Phys. Rev. B, 33, 8800 (1986).
[13] J. P. Perdew, Y. Wang, Phys. Rev. B, 46, 6671 (1992).
[14] G. P. Kerker, Phys. Rev. B, 23, 3802 (1981).
[15] H. J. Monkhorst and J. D. Pack, Phys. Rev. B 13, 5188 (1976).
[16] J. D. Pack and H. J. Monkhorst, Phys. Rev. B 16, 1748 (1977).
[17] D. R. Hamann, M. Schlüter and C. Chiang, Phys. Rev. Lett. 43, pp. 1494−1497 (1979).
[18] G. B. Bachelet, D. R. Hamann and M. Schluter, Phys. Rev. B 26, pp. 4199−4228 (1982).
[19] A. Zangwill and Paul Soven, Phys. Rev. A 21, pp.1561-1572 (1980).
[20] ABINIT, http://www.abinit.org/ (2006)
[21] National Center for High-Performance Computing,
http://www.nchc.org.tw (2006).
[22] V. Bonačić-Koutecký, J. Pittner, M. Boiron, and P. Fantucci, J. Chem. Phys. 110, 3876 (1999)
[23] V. Bonačić-Koutecký, V. Veyret, and R. Mitrić,J. Chem. Phys.115, 10450 (2001)
[24] J.P.K. Doye and D.J. Wales, New J. Chem., 22, pp. 733-744 (1998)
[25] V. Bonačić-Koutecký, L. Češpiva, P. Fantucci, and J. Koutecký, J.Chem. Phys. 98, 7981 (1993)
[26] J. Zhao, Y. Luo, and G. Wang,Eur. Phys. J. D 14,pp. 309-316 (2001)
[27] Rene´ Fournier, J. Chem. Phys. 115,2165(2001)
[28] X. Gonze, Phys. Rev. B 55, 10337 (1997)
[29] X. Gonze and C. Lee, Phys. Rev. B 55, 10355 (1997).
[30] M. E. Casida, C. Jamorski, K. C. Casida, and D. R. Salahub, J. Chem. Phys. 108, 4439 (1998).
[31] S. Fedrigo, W. Harbich, and J. Buttet, Phys. Rev. B 47, 10706(1993)
[32] I. Rabin, W. Schulze, G. Ertl, C. Félix, C. Sieber, W. Harbich, and J. Buttet, Chem. Phys. Lett. 320, 59 (2000)
[33] C. Félix, C. Sieber, W. Harbich, J. Buttet, I. Rabin, W. Schulze,and G. Ertl, Chem. Phys. Lett. 313, 105 (1999)