本論文利用密度泛函理論(DFT)模擬計算鎢奈米粒子(Wn, n=2-16)於不同尺寸下之結構特性及電子性質。首先利用basin-hopping method (BH)與big-bang method (BB)計算法配合tight-binding 多體勢能找出多筆初始的穩定結構。並利用DFT計算這些初始結構與能量並調配其之間的關係而獲得新的勢能參數，進而找出最穩定的結構。之後根據模擬計算出來的binding energy鍵結能 和 second-order energy difference，發現有跟其它尺寸的鎢奈米粒子有相對高的穩定性。另外也藉由計算vertical ionization potential (VIP)，adiabatic electron affinity (AEA)，最高占據軌域與最低未占據軌域能隙差 (HOMO-LUMO Gap) 和電荷分佈來分析各個顆數的鎢奈米粒子的電子性質及結構穩定度。

The structural and electronic properties of small tungsten nanoparticles Wn (n=2-16) were investigated by density functional theory (DFT) calculation. For the W10 nanoparticle, ten lowest-energy structures were first obtained by basin-hopping method (BH) and ten by big-bang method (BB) with the tight-binding many-body potential for bulk tungsten material. These fifty structures were further optimized by the DFT calculation in order to find the better parameters of tight-binding potential adquately for W nanoparticles. With these modified parameters of tight-binding potentials, several lowest-energy W nanoparticles of different sizes can be obtained by BH and BB methods and then further refined by DFT calculation. According to the values of binding energy and second-order energy difference, it reveals that the structure W12 has a relatively higher stability than those of other sizes. The vertical ionization potential (VIP), adiabatic electron affinity (AEA) and HOMO-LUMO Gap are also discussed for W nanoparticles of different sizes.

目錄
目錄 I
圖目錄 III
表目錄 IV
中文摘要 V
英文摘要 VI
第一章 緒論 1
1.1研究動機與目的 1
1.2 鎢奈米粒子簡介與文獻回顧 3
1.3 本文架構 6
第二章 理論介紹 7
2.1 密度泛函理論(Density Functional Theory) 7
2.1.1 密度泛函理論與電子密度 7
2.1.2 托馬斯-費米模型 8
2.1.3 霍恩貝格-科恩理論 9
2.1.4 科恩-軒姆方程式 9
2.1.5 交換-相關函數 11
2.1.6 基底 12
2.2 分子靜力學計算法介紹 13
2.2.1 Big-bang計算法 13
2.2.2 Basin-hopping計算法 15
2.3 緊束法(Tight-Binding) 16
2.3.1 緊束法多體勢能(Tight-binding potential)………….…….……16
2.3.2 鎢原子間作用勢能……………… . …………………….….…. 22
2.4 Force-matching method 介紹 23
第三章 結果與討論 25
3.1鎢奈米粒子結構分析 25
3.1.1 模擬模型建構 25
3.1.2 DFT模組參數設定 29
3.1.3 最穩定結構分析 29
3.1.4 二維與三維之結構探討 30
3.2 電性分析 34
3.2.1 鍵結能與平均鍵長分析 34
3.2.2 能量二階能量差分析 35
3.2.3 HOMO-LUMO Gap分析 35
3.2.4 VIP與AEA電性分析 35
3.2.5 電荷分佈分析 36

第四章 結論與建議 47
4.1 結論 47
4.2 建議與未來展望 48
參考文獻 49




圖目錄
圖2-1模擬Big-bang原理之示意圖 14
圖2-2 Basin-Hopping尋找穩定結構之示意圖 16
圖2-3 d軌域填充電子數與內聚能之關係 21
圖2-4 d軌域寬度W與狀態密度N(E)之關係 21
圖3-1找出鎢奈米粒子最穩定結構之流程圖 28
圖3-2 Wn (n=2-16)奈米粒子之最穩定結構與同分異構物 31
圖3-3不同尺寸下之鎢奈米粒子之平均鍵長與鍵結能的比較 35
圖3-4 Wn (n=2-16)奈米粒子之二階能量差(Δ2E) 39
圖3-5 Wn (n=2-16)奈米粒子之 HOMO-LUMO Gap 40
圖3-6 Wn (n=2-16)奈米粒子之The vertical ionization potential. 41
圖3-7 Wn (n=2-16)奈米粒子之adiabatic electron affinities . 42
圖3-8 Wn (n=2-16) 奈米粒子在5d, 6s與6p軌域上的電荷分佈 45







表目錄
表2-1各種元素的tight-binding勢能參數 ……………………………...23
表3-1修正過後的tight-binding參數 …….……………………….…….27
表3-2 利用PW91與BP91方法計算bulk材料之鎢奈米粒子的內聚能……………………………………………………………….……........32
表3-3比較PW91與BP91方法計算不同初始結構之W2奈米粒子的鍵長、振動頻率與分離能…………………………………………..….......32
表3-4比較2D平面與3D三維的Wn(n=3-8)奈米粒子的鍵結能….....34
表3-5 Wn (n=2-16)奈米粒子之最穩定結構單位原子之鍵結能..….…………………………………………………………………………….……38
表3-6 Wn (n=2-16)奈米粒子於價電子帶上的電荷分佈 ……….………38

參考文獻
[1] P. Gao, Z. Z. Wang, K. H. Liu, Z. Xu, W. L. Wang, X. D. Bai, , "Photoconducting response on bending of individual zno nanowires", Journal of Materials Chemistry, vol. 19, p. 1002-1005, 2009.
[2] WangWang, J. Zhou, Song, J. Liu, N. Xu and Z. L. Wang, "Piezoelectric field effect transistor and nanoforce sensor based on a single zno nanowire", Nano Letters, vol. 6, p. 2768-2772, 2006.
[3] Z. L. Wang and J. Song, "Piezoelectric nanogenerators based on zinc oxide nanowire arrays", Science, vol. 312, p. 242-246, 2006.
[4] M. Haruta, "When gold is not noble: Catalysis by nanoparticle", Chem Record, vol. 3, p. 75, 2003.
[5] M. Haruta, T. Kobayashi, H. Sano and N. Yamada, "Novel gold catalysts for the oxidation of carbon-monoxide at a temperature far below 0-degrees-c", Chemistry Letters, vol. p. 405-408, 1987.
[6] M. Haruta, "Size- and support-dependency in the catalysis of gold", Catalysis Today, vol. 36, p. 153-166, 1997.
[7] M. E. Davis, J. E. Zuckerman, C. H. J. Choi, D. Seligson, A. Tolcher, C. A. Alabi, , "Evidence of rnai in humans from systemically administered sirna via targeted nanoparticles", Nature, vol. 464, p. 1067-1070,
[8] J.-g. Wang, Y.-a. Lv, X.-n. Li and M. Dong, "Point-defect mediated bonding of pt clusters on (5,5) carbon nanotubes", The Journal of Physical Chemistry C, vol. 113, p. 890-893, 2008.
[9] J. A. Rodri?guez, J. Evans, J. s. Graciani, J.-B. Park, P. Liu, J. Hrbek, , "High water?隠as shift activity in tio2(110) supported cu and au nanoparticles: Role of the oxide and metal particle size", The Journal of Physical Chemistry C, vol. 113, p. 7364-7370, 2009.
[10] V. Khatko, E. Llobet, X. Vilanova, J. Brezmes, J. Hubalek, K. Malysz, , "Gas sensing properties of nanoparticle indium-doped wo3 thick films", Sensors and Actuators B-Chemical, vol. 111, p. 45-51, 2005.
[11] Y. K. Chung, M. H. Kim, W. S. Um, H. S. Lee, J. K. Song, S. C. Choi, , "Gas sensing properties of wo3 thick film for no2 gas dependent on process condition", Sensors and Actuators B-Chemical, vol. 60, p. 49-56, 1999.
[12] D. S. Lee, S. D. Han, J. S. Huh and D. D. Lee, "Nitrogen oxides-sensing characteristics of wo3-based nanocrystalline thick film gas sensor", Sensors and Actuators B-Chemical, vol. 60, p. 57-63, 1999.
[13] H. H. Nersisyan, J. H. Lee and C. W. Won, "A study of tungsten nanopowder formation by self-propagating high-temperature synthesis", Combustion and Flame, vol. 142, p. 241-248, 2005.
[14] M. A. Butler, "Photoelectrolysis and physical-properties of semiconducting electrode wo3", Journal of Applied Physics, vol. 48, p. 1914-1920, 1977.
[15] S. J. Wang, C. H. Chen, S. C. Chang, K. M. Uang, C. P. Juan and H. C. Cheng, "Growth and characterization of tungsten carbide nanowires by thermal annealing of sputter-deposited wcx films", Applied Physics Letters, vol. 85, p. 2358-2360, 2004.
[16] B. S. Hobbs and A. C. C. Tseung, "Anodic-oxidation of hydrogen on platinized tungsten oxides .2. Mechanism of h2 oxidation on platinized lower tungsten oxide electrodes", Journal of the Electrochemical Society, vol. 122, p. 1174-1177, 1975.
[17] I. Jimenez, J. Arbiol, G. Dezanneau, A. Cornet and J. R. Morante, "Crystalline structure, defects and gas sensor response to no2 and h2s of tungsten trioxide nanopowders", Sensors and Actuators B-Chemical, vol. 93, p. 475-485, 2003.
[18] S. H. Wang, T. C. Chou and C. C. Liu, "Nano-crystalline tungsten oxide no2 sensor", Sensors and Actuators B-Chemical, vol. 94, p. 343-351, 2003.
[19] P. J. Shaver, "Activated tungsten oxide gas detectors", Applied Physics Letters, vol. 11, p. 255-&, 1967.
[20] D. J. Dwyer, "Surface-chemistry of gas sensors - h2s on wo3 films", Sensors and Actuators B-Chemical, vol. 5, p. 155-159, 1991.
[21] A. A. Tomchenko, V. V. Khatko and I. L. Emelianov, "Wo3 thick-film gas sensors", Sensors and Actuators B-Chemical, vol. 46, p. 8-14, 1998.
[22] A. A. Tomchenko, I. L. Emelianov and V. V. Khatko, "Tungsten trioxide-based thick-film no sensor: Design and investigation", Sensors and Actuators B-Chemical, vol. 57, p. 166-170, 1999.
[23] G. H. Ryu, S. C. Park and S. B. Lee, "Molecular orbital study of the interactions of co molecules adsorbed on a w(111) surface", Surface Science, vol. 428, p. 419-425, 1999.
[24] L. Chen, D. S. Sholl and J. K. Johnson, "First principles study of adsorption and dissociation of co on w(111)", Journal of Physical Chemistry B, vol. 110, p. 1344-1349, 2006.
[25] H. T. Chen, D. G. Musaev and M. C. Lin, "Adsorption and dissociation of h2o on a w(111) surface: A computational study", Journal of Physical Chemistry C, vol. 111, p. 17333-17339, 2007.
[26] H. L. Chen, S. P. Ju, H. T. Chen, D. G. Musaev and M. C. Lin, "Adsorption and dissociation of the hcl and cl-2 molecules on w(111) surface: A computational study", Journal of Physical Chemistry C, vol. 112, p. 12342-12348, 2008.
[27] H. T. Chen, D. G. Musaev and M. C. Lin, "Adsorption and dissociation of cox (x=1, 2) on w(111) surface : A computational study", Journal of Physical Chemistry C, vol. 112, p. 3341-3348, 2008.
[28] H. H. Hwu, B. D. Polizzotti and J. G. G. Chen, "Potential application of tungsten carbides as electrocatalysts. 2. Coadsorption of co and h2o on carbide-modified w(111)", Journal of Physical Chemistry B, vol. 105, p. 10045-10053, 2001.
[29] J. B. Benziger, E. I. Ko and R. J. Madix, "Characterization of surface carbides of tungsten", Journal of Catalysis, vol. 54, p. 414-425, 1978.
[30] C. M. Friend, J. G. Serafin, E. K. Baldwin, P. A. Stevens and R. J. Madix, "Bonding and adsorption structure of co on w(100)-(5x1)-c", Journal of Chemical Physics, vol. 87, p. 1847-1850, 1987.
[31] B. Fruhberger and J. G. Chen, "Reaction of ethylene with clean and carbide-modified mo(110): Converting surface reactivities of molybdenum to pt-group metals", Journal of the American Chemical Society, vol. 118, p. 11599-11609, 1996.
[32] B. Fruhberger and J. G. Chen, "Modification of the surface reactivity of mo(110) upon carbide formation", Surface Science, vol. 342, p. 38-46, 1995.
[33] P. Gruene, D. M. Rayner, B. Redlich, A. F. G. van der Meer, J. T. Lyon, G. Meijer, , "Structures of neutral au-7, au-19, and au-20 clusters in the gas phase", Science, vol. 321, p. 674-676, 2008.
[34] C. Lemire, R. Meyer, S. Shaikhutdinov and H. J. Freund, "Do quantum size effects control co adsorption on gold nanoparticles?", Angewandte Chemie-International Edition, vol. 43, p. 118-121, 2004.
[35] G. Mills, M. S. Gordon and H. Metiu, "Oxygen adsorption on au clusters and a rough au(111) surface: The role of surface flatness, electron confinement, excess electrons, and band gap", Journal of Chemical Physics, vol. 118, p. 4198-4205, 2003.
[36] G. G. Gaertner, Nanostruct Mater, vol. 4, p. 559, 1994.
[37] B. Hvolbaek, T. V. W. Janssens, B. S. Clausen, H. Falsig, C. H. Christensen and J. K. Norskov, "Catalytic activity of au nanoparticles", Nano Today, vol. 2, p. 14-18, 2007.
[38] H. Z. Zhang and J. F. Banfield, "Thermodynamic analysis of phase stability of nanocrystalline titania", Journal of Materials Chemistry, vol. 8, p. 2073-2076, 1998.
[39] Z. J. Wu, "Density functional study of w2 and w3 clusters ", Chem Phys Lett, vol. 370, p. 510, 2003.
[40] D. K. H. Weidele, E. Recknagel, "Thermionic emission from small clusters: Direct observation of the kinetic energy distribution of the electrons ", Chem Phys Lett, vol. 237, p. 425, 1995.
[41] X. D. Xiurong Zhang, Bing Dai, Jinlong Yang, "Density functional theory study of wn (n=2-4) clusters", Journal of Molecular Structure: THEOCHEM, vol. 757, p. 113, 2005.
[42] J. C. Slater, "A simplification of the hartree-fock method", Physical Review, vol. 81, p. 385, 1951.
[43] P. Hohenberg and W. Kohn, "Inhomogeneous electron gas", Physical Review, vol. 136, p. B864, 1964.
[44] W. Kohn and L. J. Sham, "Self-consistent equations including exchange and correlation effects", Physical Review, vol. 140, p. A1133, 1965.
[45] K. W. Hohenberg P., "Inhomogenerous electron gas", Physical Review B, vol. 136, p. 964, 1964.
[46] J. L. S. K.W., "Self-consistent equations including exchange and correlation effects", physical review A, vol. 140, p. 1133, 1965.
[47] D. M. Ceperley and B. J. Alder, "Ground-state of the electron-gas by a stochastic method", Physical Review Letters, vol. 45, p. 566-569, 1980.
[48] K. A. Jackson, M. Horoi, I. Chaudhuri, T. Frauenheim and A. A. Shvartsburg, "Unraveling the shape transformation in silicon clusters", Physical Review Letters, vol. 93, p. 013401, 2004.
[49] K. A. Jackson, M. Horoi, I. Chaudhuri, T. Frauenheim and A. A. Shvartsburg, "Statistical evaluation of the big bang search algorithm", Computational Materials Science, vol. 35, p. 232-237, 2006.
[50] S. S. Tripathi and K. S. Narendra, "Optimization using conjugate gradient methods", Ieee Transactions on Automatic Control, vol. AC15, p. 268-&, 1970.
[51] D. C. Liu and J. Nocedal, "On the limited memory bfgs method for large-scale optimization", Mathematical Programming, vol. 45, p. 503-528, 1989.
[52] J. C. Slater and G. F. Koster, "Simplified lcao method for the periodic potential problem", Physical Review, vol. 94, p. 1498, 1954.
[53] C. Kittle, "Introduction to solid state physics", vol. p., 1996.
[54] L. Colombo, "A source code for tight-binding molecular dynamics simulations", Computational Materials Science, vol. 12, p. 278-287, 1998.
[55] J. Z. H. Zhang, "Theory and application of quantum molecular dynamics", vol. p., 1999.
[56] C. H. Xu, C. Z. Wang, C. T. Chan and K. M. Ho, "A transferable tight-binding potential for carbon", Journal of Physics-Condensed Matter, vol. 4, p. 6047-6054, 1992.
[57] I. Kwon, R. Biswas, C. Z. Wang, K. M. Ho and C. M. Soukoulis, "Transferable tight-binding models for silicon", Physical Review B, vol. 49, p. 7242-7250, 1994.
[58] R. P. Gupta, "Lattice relaxation at a metal surface", Physical Review B, vol. 23, p. 6265, 1981.
[59] M. Meyer, "Computer simulation in material science", Series E: Applied Sciences, vol. 205, p., 1991.
[60] D. Tomanek, S. Mukherjee and K. H. Bennemann, "Simple theory for the electronic and atomic-structure of small clusters", Physical Review B, vol. 28, p. 665-673, 1983.
[61] D. Tomanek, A. A. Aligia and C. A. Balseiro, "Calculation of elastic strain and electronic effects on surface segregation", Physical Review B, vol. 32, p. 5051-5056, 1985.
[62] W. Zhong, Y. S. Li and D. Tomanek, "Effect of adsorbates on surface phonon modes - h on pd(001) and pd(110)", Physical Review B, vol. 44, p. 13053-13062, 1991.
[63] M. M. Sigalas and D. A. Papaconstantopoulos, "Transferable total-energy parametrizations for metals: Applications to elastic-constant determination", Physical Review B, vol. 49, p. 1574, 1994.
[64] G. C. Kallinteris, N. I. Papanicolaou, G. A. Evangelakis and D. A. Papaconstantopoulos, "Tight-binding interatomic potentials based on total-energy calculation: Application to noble metals using molecular-dynamics simulation", Physical Review B, vol. 55, p. 2150-2156, 1997.
[65] V. Rosato, M. Guillope and B. Legrand, "Thermodynamical and structural-properties of fcc transition-metals using a simple tight-binding model", Philosophical Magazine a-Physics of Condensed Matter Structure Defects and Mechanical Properties, vol. 59, p. 321-336, 1989.
[66] F. Cleri and V. Rosato, "Tight-binding potentials for transition-metals and alloys", Physical Review B, vol. 48, p. 22-33, 1993.
[67] F. Ercolessi and J. B. Adams, "Interatomic potentials from 1st-principles calculations - the force-matching method", Europhysics Letters, vol. 26, p. 583-588, 1994.
[68] M. S. Daw and M. I. Baskes, "Embedded-atom method - derivation and application to impurities, surfaces, and other defects in metals", Physical Review B, vol. 29, p. 6443-6453, 1984.
[69] S. M. Foiles, M. I. Baskes and M. S. Daw, "Embedded-atom-method functions for the fcc metals cu, ag, au, ni, pd, pt, and their alloys", Physical Review B, vol. 33, p. 7983-7991, 1986.
[70] M. Hou, "A molecular dynamics evidence for enhanced cluster beam epitaxy", Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, vol. 135, p. 501-506, 1998.
[71] M. Hou and Z. Y. Pan, "Cascade statistics in the binary collision approximation and in full molecular-dynamics", Nuclear Instruments & Methods in Physics Research Section B-Beam Interactions with Materials and Atoms, vol. 102, p. 93-102, 1995.
[72] G. Mazzone, V. Rosato and M. Pintore, "Molecular-dynamics calculations of thermodynamic properties of metastable alloys", Physical Review B, vol. 55, p. 837-842, 1997.
[73] I. Meunier, G. Treglia, B. Legrand, R. Tetot, B. Aufray and J. M. Gay, "Molecular dynamics simulations for the ag/cu (111) system: From segregated to constitutive interfacial vacancies", Applied Surface Science, vol. 162, p. 219-226, 2000.
[74] M. A. Karolewski, "Tight-binding potentials for sputtering simulations with fcc and bcc metals", Radiation Effects and Defects in Solids, vol. 153, p. 239-255, 2001.
[75] F. Y. Chen and R. L. Johnston, "Energetic, electronic, and thermal effects on structural properties of ag-au nanoalloys", Acs Nano, vol. 2, p. 165-175, 2008.
[76] S. P. Ju, Y. C. Lo, S. J. Sun and J. G. Chang, "Investigation on the structural variation of co-cu nanoparticles during the annealing process", Journal of Physical Chemistry B, vol. 109, p. 20805-20809, 2005.
[77] J. P. Perdew and W. Yue, "Accurate and simple density functional for the electronic exchange energy - generalized gradient approximation", Physical Review B, vol. 33, p. 8800-8802, 1986.
[78] J. P. Perdew and Y. Wang, "Accurate and simple analytic representation of the electron-gas correlation-energy", Physical Review B, vol. 45, p. 13244-13249, 1992.
[79] J. P. Perdew, K. Burke and M. Ernzerhof, "Generalized gradient approximation made simple (vol 77, pg 3865, 1996)", Physical Review Letters, vol. 78, p. 1396-1396, 1997.
[80] Z. Hu, J.-G. Dong, J. R. Lombardi and D. M. Lindsay, "Optical and raman spectroscopy of mass-selected tungsten dimers in argon matrices", The Journal of Chemical Physics, vol. 97, p. 8811-8812, 1992.
[81] M. D. Morse, "Clusters of transition-metal atoms", Chemical Reviews, vol. 86, p. 1049-1109, 1986.
[82] M.-S. Lee, S. Chacko and D. G. Kanhere, "First-principles investigation of finite-temperature behavior in small sodium clusters", The Journal of Chemical Physics, vol. 123, p. 164310-164317, 2005.
[83] S. M. Ghazi, M.-S. Lee and D. G. Kanhere, "The effects of electronic structure and charged state on thermodynamic properties: An ab initio molecular dynamics investigations on neutral and charged clusters of na[sub 39], na[sub 40], and na[sub 41]", The Journal of Chemical Physics, vol. 128, p. 104701-104707, 2008.
[84] W. Fa and J. Dong, "Possible ground-state structure of au[sub 26]: A highly symmetric tubelike cage", The Journal of Chemical Physics, vol. 124, p. 114310-114314, 2006.
[85] L. Xiao and L. C. Wang, "From planar to three-dimensional structural transition in gold clusters and the spin-orbit coupling effect", Chemical Physics Letters, vol. 392, p. 452-455, 2004.
[86] J. G. Du, X. Y. Sun, D. Q. Meng, P. C. Zhang and G. Jiang, "Geometrical and electronic structures of small w-n (n=2-16) clusters", Journal of Chemical Physics, vol. 131, p., 2009.
[87] P. Villars, L. D. Calvert and W. B. Pearson, "Handbook of crystallographic data for intermetallic phases", Acta Crystallographica Section A, vol. 40, p. C444-C444, 1984.
[88] M.-X. Chen and X. H. Yan, "A new magic titanium-doped gold cluster and orientation dependent cluster-cluster interaction", The Journal of Chemical Physics, vol. 128, p. 174305-174306, 2008.
[89] F. Chen and R. L. Johnston, "Charge transfer driven surface segregation of gold atoms in 13-atom au-ag nanoalloys and its relevance to their structural, optical and electronic properties", Acta Materialia, vol. 56, p. 2374-2380, 2008.
[90] R. S. Mulliken, "Electronic population analysis on lcao[single bond]mo molecular wave functions. I", The Journal of Chemical Physics, vol. 23, p. 1833-1840, 1955.