金、硼纳米管和内包金属硅富勒烯的结构与性能预测
|
摘要
C60和碳纳米管以其独特的结构和新颖的特性引起了人们广泛的关注。它们在场发射、传感器、复合增强材料、储氢材料等众多领域展现出的广泛的应用前景,激发了人们对纳米笼和纳米管的研究热情。
本文基于密度泛函理论,对3d过渡金属原子和贵金属Au原子掺杂的硅团簇的结构演化和电子性质进行了分析;预测了新的金纳米管、硼纳米管的结构稳定性和电子结构。
纯硅团簇由于其化学键的特性,不能形成碳团簇那样稳定的笼状结构。众多的实验和理论研究都表明,掺杂一些寄宿原子可以稳定硅的笼状结构。本文系统研究了3d过渡金属原子对硅笼状结构稳定性和电子特性的影响,发现了笼状Si15和Si16团簇的理想宿主----Ti元素;计算结果表明,Ti@Si15和Ti@Si16团簇均具有较高的结构稳定性和较好的化学稳定性。
基于密度泛函理论对内包金属Si20富勒烯的稳定结构进行了广泛搜索,发现了一个迄今为止最为稳定、Ih对称性的中性Eu@Si20富勒烯;在Eu@Si20中,中心Eu原子具有较大的自旋磁矩;以Ih-Eu@Si20为结构单元构造了一类能稳定存在的项链状准一维链,计算结果表明,该链具有半导体特性,中心Eu原子仍具有较大的自旋磁矩。
对过渡金属Ni原子和贵金属Au原子掺杂的硅小团簇,NiSin (n=1-14)和AuSin (n=1-16)的基态结构随尺寸的演化进行了计算。计算结果显示:当团簇原子数目较小时,不论Ni原子还是Au原子都倾向于占据表面格点的位置;随着团簇原子数目的增加,当n=9时Ni原子开始占据中心格点的位置,而当n=12时,形成内包Au原子的硅笼状结构Au@Si12;进一步分析表明,Ni原子的加入增强了硅团簇的稳定性,而Au原子的加入没有明显地改善硅团簇的稳定性;键能的二阶差分和HOMO-LUMO能隙表明,Au@Si12是幻数团簇,其基态结构具有较高的结构稳定性和较好的化学活性;以Au@Si12团簇为结构单元得到了一类稳定的Au-Cored硅纳米管,计算结果显示,这类内包金线硅纳米管具有较小的能隙和良好的电子传输特性。
论文基于稳定的二十面体Au32富勒烯和由Au (1 1 1)面卷曲而成的(5, 5)金纳米管,构建了一类新的中空金纳米管状结构Aun (n=37, 42, 47, 52,…, ?n =5);采用密度泛函理论,对该类中空金纳米管的结构稳定性和电子性质进行了广泛的探索,研究发现Au37、Au42、Au47纳米管状结构具有较高的结构稳定性;首次预言了42个金原子组成的大的、中空纳米管结构是具有比密积结构更强稳定性的基态结构。
基于Yakobson等人对B80富勒烯笼稳定结构的理论预测,构建了两类新的、稳定的金属性的硼片结构,进而得到两类新的稳定的硼纳米管,计算结果表明:在我们的研究范围内除第一类(4, 0)超细硼纳米管表现出半导体特性并伴随有0.441 eV的直接带隙以外,其它硼纳米管均表现出金属性。
硼掺杂过渡金属晶态和非晶态合金表现出优异的铁磁性能和良好的抗氧化、耐腐蚀、耐磨损等性能,成为理想的磁记录介质和薄膜磁头候选材料。本文对硼掺杂过渡金属铁、钴、镍混合团簇的电子结构和性能进行了系统的分析研究,找到了FenB、ConB、NinB (n=1-12, 14, 18)体系的最稳定几何构型,计算结果表明B原子的掺入大大提高了过渡金属团簇的稳定性,改变了团簇的磁特性。在我们的研究范围内,B原子的加入未能明显地改善过渡金属团簇的自旋磁矩;NinB混合团簇的自旋磁矩在n=5-13的范围内存在一个由量子限制效应引起的平台。
Since the discovery of C60 and carbon nanotubes, these molecules have have attracted wide attention due to their novel electronic properties and great potential of applications. Especilly, the unique structures and novel mechanical, themal, electronic and chemical properties have revealed potential applicantions on field emission, nanoelectronics, sensing probe, superconductivity, and chemistry. Recently, great attentions have addressed on the studies of nanocages and nanotubes.
In this project, the density functional theory is employed to investigate the stabilities, properties and performances of the transition metal-encapsulated silicon fullerenes, gold nanotubes, and boron nanotubes, as well as the growth behaviors and electronic properties of Ni-doped and Au-doped silicon clusters.
Unlike fullerene cages, a hollow Si cage is unstable because sp2 hybridization is highly unfavorable in silicon. By introducing metal atoms, the silicon clusters can be dramatically stabilized, and the choice of the central metal atom becomes a key point in the design of cage clusters and in their resultant chemical behavior. In this work, we have focused on Si15 and Si16 cage clusters with encapsulated 3d TM atoms and systematically investigated the effects of the encapsulated metal atoms on the configurations, stability, and magnetic properties of the clusters at two different all-electron DFT levels. The results show that Ti@Si16 and Ti@Si15 have the largest embedding energies and relative large HOMO-LUMO gaps in this series. It suggests that titanium atom is an ideal guest for Sin (n=15, 16) cages as far as stability is concerned.
Furthermore, a metal-encapsulated silicon fullerene, Eu@Si20, has been predicted by density function theory to be by far the most stable fullerene-like silicon structure. The Eu@Si20 structure is a regular dodecahedron with Ih symmetry in which the europium atom occupies the center site. The calculated results show that the europium atom has a large magnetic moment of nearly 7.0 Bohr magnetons. In addition, it was found that a stable“pearl necklace”nanowire, constructed by concatenating a series of Ih-Eu@Si20 units, each with a central europium atom retains the high spin moment.
The configurations, stability, and electronic structure of NiSin (n=1-14) and AuSin (n=1-16) clusters have been investigated within the framework of the density functional theory. The calculated results of NiSin clusters reveal that the Ni atom prefers to occupy the surface site when n < 9 and for the clusters with n≥9, the Ni atom starts to encapsulate in the cage. The results of AuSin clusters show that the Au atom begins to occupy the interior site from Si11 and for Si12 the Au atom completely falls into the interior site forming Au@Si12 cage. Furthermore, the doping of the Ni atom enhances the stability of silicon clusters while the doping of the Au atom does not enhance the stability of pure Sin clusters, similar to the case of Ag-doped silicon clusters. Relatively large embedding energy and small HOMO-LUMO gap are also found for this Au@Si12 structure indicating the enhanced chemical activity and good electronic transfer property. In addition, stable Au-cored Si nanotube is also found to be formed by Au@Si12 unit and it has relatively small energy gap making it attractive for electron transport device.
A series of Aun (n=37, 42, 47, 52,…, ?n =5) hollow tubelike structures have been constructed by capping the nanotube with halves of the icosahedral Au32 cage at both ends of the (5,5) single-wall gold nanotube, rolled from the (1 1 1) Au crystal plane, repeated unit cell. Based on the scalar relativistic density functional theory, the stablity and electronic properties of tubelike Aun structures have been investigated. The results indicate that tubelike structures of Au37、Au42、Au47 are relatively stable. At the same time, a large hollow tubelike ground state Au42 is predicted as a new ground-state configuration.
The recent prediction of the boron buckyball B80 cage has stimulated intensive studies on boron sheets and boron nanotubes. Here, two new classes of flat stable boron sheets have been constructed. Rolled from them, two series of boron nanotubes are obtained. Within the framework of density functional theory, the configurations, stability and electronic structures of new classes of boron sheet and related boron nanotubes have been predicted. The theoretic results show that within the scope of our research, the nanotubes rolled from the stable sheets with various diameters and chiral vectors are stable, and they are all metallic except for the thin (4, 0) tube with a band gap of 0.441 eV.
Boron is known to be an important additive to magnetic materials. It can affect the magnetic properties substantially and improve the magnetostrictive characteristics of transition-metal thin films. Within the framework of all-electron density functional theory, the configurations, electronic structure and magnetic properties of MnB (M = Fe, Co, Ni; n=1-12, 14, 18) clusters have been calculated. The ground-state structures of the MnB clusters were determined. The results reveal that the doping of a B atom enhances the stabilities significantly and has a slight effect on the spin magnetic moments at the scope of our study. In addition, the size dependence of the spin moments in NinB clusters exists one terrace from n = 5 to n = 13, which is mostly due to the quantum confinement.
本文基于密度泛函理论,对3d过渡金属原子和贵金属Au原子掺杂的硅团簇的结构演化和电子性质进行了分析;预测了新的金纳米管、硼纳米管的结构稳定性和电子结构。
纯硅团簇由于其化学键的特性,不能形成碳团簇那样稳定的笼状结构。众多的实验和理论研究都表明,掺杂一些寄宿原子可以稳定硅的笼状结构。本文系统研究了3d过渡金属原子对硅笼状结构稳定性和电子特性的影响,发现了笼状Si15和Si16团簇的理想宿主----Ti元素;计算结果表明,Ti@Si15和Ti@Si16团簇均具有较高的结构稳定性和较好的化学稳定性。
基于密度泛函理论对内包金属Si20富勒烯的稳定结构进行了广泛搜索,发现了一个迄今为止最为稳定、Ih对称性的中性Eu@Si20富勒烯;在Eu@Si20中,中心Eu原子具有较大的自旋磁矩;以Ih-Eu@Si20为结构单元构造了一类能稳定存在的项链状准一维链,计算结果表明,该链具有半导体特性,中心Eu原子仍具有较大的自旋磁矩。
对过渡金属Ni原子和贵金属Au原子掺杂的硅小团簇,NiSin (n=1-14)和AuSin (n=1-16)的基态结构随尺寸的演化进行了计算。计算结果显示:当团簇原子数目较小时,不论Ni原子还是Au原子都倾向于占据表面格点的位置;随着团簇原子数目的增加,当n=9时Ni原子开始占据中心格点的位置,而当n=12时,形成内包Au原子的硅笼状结构Au@Si12;进一步分析表明,Ni原子的加入增强了硅团簇的稳定性,而Au原子的加入没有明显地改善硅团簇的稳定性;键能的二阶差分和HOMO-LUMO能隙表明,Au@Si12是幻数团簇,其基态结构具有较高的结构稳定性和较好的化学活性;以Au@Si12团簇为结构单元得到了一类稳定的Au-Cored硅纳米管,计算结果显示,这类内包金线硅纳米管具有较小的能隙和良好的电子传输特性。
论文基于稳定的二十面体Au32富勒烯和由Au (1 1 1)面卷曲而成的(5, 5)金纳米管,构建了一类新的中空金纳米管状结构Aun (n=37, 42, 47, 52,…, ?n =5);采用密度泛函理论,对该类中空金纳米管的结构稳定性和电子性质进行了广泛的探索,研究发现Au37、Au42、Au47纳米管状结构具有较高的结构稳定性;首次预言了42个金原子组成的大的、中空纳米管结构是具有比密积结构更强稳定性的基态结构。
基于Yakobson等人对B80富勒烯笼稳定结构的理论预测,构建了两类新的、稳定的金属性的硼片结构,进而得到两类新的稳定的硼纳米管,计算结果表明:在我们的研究范围内除第一类(4, 0)超细硼纳米管表现出半导体特性并伴随有0.441 eV的直接带隙以外,其它硼纳米管均表现出金属性。
硼掺杂过渡金属晶态和非晶态合金表现出优异的铁磁性能和良好的抗氧化、耐腐蚀、耐磨损等性能,成为理想的磁记录介质和薄膜磁头候选材料。本文对硼掺杂过渡金属铁、钴、镍混合团簇的电子结构和性能进行了系统的分析研究,找到了FenB、ConB、NinB (n=1-12, 14, 18)体系的最稳定几何构型,计算结果表明B原子的掺入大大提高了过渡金属团簇的稳定性,改变了团簇的磁特性。在我们的研究范围内,B原子的加入未能明显地改善过渡金属团簇的自旋磁矩;NinB混合团簇的自旋磁矩在n=5-13的范围内存在一个由量子限制效应引起的平台。
Since the discovery of C60 and carbon nanotubes, these molecules have have attracted wide attention due to their novel electronic properties and great potential of applications. Especilly, the unique structures and novel mechanical, themal, electronic and chemical properties have revealed potential applicantions on field emission, nanoelectronics, sensing probe, superconductivity, and chemistry. Recently, great attentions have addressed on the studies of nanocages and nanotubes.
In this project, the density functional theory is employed to investigate the stabilities, properties and performances of the transition metal-encapsulated silicon fullerenes, gold nanotubes, and boron nanotubes, as well as the growth behaviors and electronic properties of Ni-doped and Au-doped silicon clusters.
Unlike fullerene cages, a hollow Si cage is unstable because sp2 hybridization is highly unfavorable in silicon. By introducing metal atoms, the silicon clusters can be dramatically stabilized, and the choice of the central metal atom becomes a key point in the design of cage clusters and in their resultant chemical behavior. In this work, we have focused on Si15 and Si16 cage clusters with encapsulated 3d TM atoms and systematically investigated the effects of the encapsulated metal atoms on the configurations, stability, and magnetic properties of the clusters at two different all-electron DFT levels. The results show that Ti@Si16 and Ti@Si15 have the largest embedding energies and relative large HOMO-LUMO gaps in this series. It suggests that titanium atom is an ideal guest for Sin (n=15, 16) cages as far as stability is concerned.
Furthermore, a metal-encapsulated silicon fullerene, Eu@Si20, has been predicted by density function theory to be by far the most stable fullerene-like silicon structure. The Eu@Si20 structure is a regular dodecahedron with Ih symmetry in which the europium atom occupies the center site. The calculated results show that the europium atom has a large magnetic moment of nearly 7.0 Bohr magnetons. In addition, it was found that a stable“pearl necklace”nanowire, constructed by concatenating a series of Ih-Eu@Si20 units, each with a central europium atom retains the high spin moment.
The configurations, stability, and electronic structure of NiSin (n=1-14) and AuSin (n=1-16) clusters have been investigated within the framework of the density functional theory. The calculated results of NiSin clusters reveal that the Ni atom prefers to occupy the surface site when n < 9 and for the clusters with n≥9, the Ni atom starts to encapsulate in the cage. The results of AuSin clusters show that the Au atom begins to occupy the interior site from Si11 and for Si12 the Au atom completely falls into the interior site forming Au@Si12 cage. Furthermore, the doping of the Ni atom enhances the stability of silicon clusters while the doping of the Au atom does not enhance the stability of pure Sin clusters, similar to the case of Ag-doped silicon clusters. Relatively large embedding energy and small HOMO-LUMO gap are also found for this Au@Si12 structure indicating the enhanced chemical activity and good electronic transfer property. In addition, stable Au-cored Si nanotube is also found to be formed by Au@Si12 unit and it has relatively small energy gap making it attractive for electron transport device.
A series of Aun (n=37, 42, 47, 52,…, ?n =5) hollow tubelike structures have been constructed by capping the nanotube with halves of the icosahedral Au32 cage at both ends of the (5,5) single-wall gold nanotube, rolled from the (1 1 1) Au crystal plane, repeated unit cell. Based on the scalar relativistic density functional theory, the stablity and electronic properties of tubelike Aun structures have been investigated. The results indicate that tubelike structures of Au37、Au42、Au47 are relatively stable. At the same time, a large hollow tubelike ground state Au42 is predicted as a new ground-state configuration.
The recent prediction of the boron buckyball B80 cage has stimulated intensive studies on boron sheets and boron nanotubes. Here, two new classes of flat stable boron sheets have been constructed. Rolled from them, two series of boron nanotubes are obtained. Within the framework of density functional theory, the configurations, stability and electronic structures of new classes of boron sheet and related boron nanotubes have been predicted. The theoretic results show that within the scope of our research, the nanotubes rolled from the stable sheets with various diameters and chiral vectors are stable, and they are all metallic except for the thin (4, 0) tube with a band gap of 0.441 eV.
Boron is known to be an important additive to magnetic materials. It can affect the magnetic properties substantially and improve the magnetostrictive characteristics of transition-metal thin films. Within the framework of all-electron density functional theory, the configurations, electronic structure and magnetic properties of MnB (M = Fe, Co, Ni; n=1-12, 14, 18) clusters have been calculated. The ground-state structures of the MnB clusters were determined. The results reveal that the doping of a B atom enhances the stabilities significantly and has a slight effect on the spin magnetic moments at the scope of our study. In addition, the size dependence of the spin moments in NinB clusters exists one terrace from n = 5 to n = 13, which is mostly due to the quantum confinement.
引文
[1]王广厚,团簇物理学,上海科学技术出版社出版发行,第一版,2003: 1.
[2] G. D. Stein, Atoms and molecules in small aggregates, Phys. Teach., 1997, 17: 503-512.
[3]王广厚,离子簇的奇异性质,物理学进展, 1987, 7: 1.
[4] E. W. Becker, Strahlen aus kondensierten Atomen und Molekeln im Hochvakuum, Z. Phys. 1956, 146(3): 333-338.
[5] W. D. Knight, K. Clemenger, W. A. de Heer, W. A. Saunders, M. Y. Chou, and M. L. Cohen, Electronic Shell Structure and Abundances of Sodium Clusters.Phys. Rev. Lett., 1984, 52(24): 2141-2143.
[6] H. W. Kroto, J. R. Heath, S. C. O'Brien, R. F. Curl,and R. E. Smaller, C60: Buckminsterfullerene, Nature, 1985, 318: 162-163.
[7] I .A. Harris, R. S. Kidwell,and J. A. Northby, Structure of Charged Argon Clusters Formed in a Free Jet Expansion, 1984, Phys. Rev. Lett., 53: 2390-2393.
[8] K. Rademann, B. Kaiser, U. Even, and F. Hensel,Size dependence of the gradual transition to metallic properties in isolated mercury clusters, Phys. Rev. Lett., 1987, 59: 2319-2321.
[9] O. Cheshnovsky, K. J. Taylor, J. Conceicao, and R. E. Smalley, Ultraviolet photoelectron spectra of mass-selected copper clusters: Evolution of the 3d band, Phys. Rev. Lett., 1990, 64: 1785-1788.
[10] J. Ho, K. M. Ervin, and W. C. Lineberger, Photoelectron spectroscopy of metal cluster anions: Cun-, Agn-, and Aun-, J. Chem. Phys., 1990, 93: 6987-7002.
[11] B. Kaiser and K. Rademann, Photoelectron spectroscopy of neutral mercury clusters Hgx (x≤109) in a molecular beam, Phys. Rev. Lett., 1992, 69: 3204-3207.
[12] J. Sinfelt, Structure of metal catalysts, Rev. Mod. Phys., 1979, 51: 569-589, and the references therein.
[13] S. N. Khanna and S. Linderoth, Magnetic behavior of clusters of ferromagnetic transition metals, Phys. Rev. Lett., 1991, 67: 742-745.
[14] D. M. Cox, D. J. Trevor, R. L. Whetten, E. A. Rohlfing, and A. Kaldor, Magnetic behavior of free-iron and iron oxide clusters, Phys. Rev. B, 1985, 32: 7290-7298.
[15] J. G. Louderback, A. J. Cox, L. J. Lising, D. C. Douglass, and L. A. Bloomfield, Magnetic properties of nickel clusters, Z. Phys. D, 1993, 26: 301-303.
[16] J. P. Bucher, D. C. Douglass, and L. A. Bloomfield, Magnetic properties of free cobalt clusters, Phys. Rev. Lett., 1991, 66: 3052-3055.
[17] D. C. Douglass, A. J. Cox, J. P. Bucher, and L. A. Bloomfield, Magnetic properties of free cobalt and gadolinium clusters, Phys. Rev. B, 1993, 47: 12874-12889.
[18] I. M. L. Billas,J. A. Becker, A. Chatelain, and W. A. de Heer, Magnetic moments of iron clusters with 25 to 700 atoms and their dependence on temperature, Phys. Rev. Lett., 1993, 71: 4067-4070.
[19] I. M. L. Billas, A. Chatelain, and W. A. de Heer, Magnetism in transition-metal clusters from the atom to the bulk, Surf. Rev. Lett., 1996, 3: 429-434.
[20] J. Zhao, M. Han, and G. Wang, Ionization potentials of transition-metal clusters, Phys. Rev. B, 1993, 48: 15297-15300, and the references therein.
[21] F. Liu, S. N. Khanna, and P. Jena, Magnetism in small vanadium clusters, Phys. Rev. B, 1991, 43: 8179-8182.
[22] K. Lee and J. Callaway, Electronic structure and magnetism of small V and Cr clusters, Phys. Rev. B, 1993, 48: 15358-15364.
[23] J. Dorantes-Dávila, and H. Dreysse, Magnetic behavior of small vanadium clusters, Phys. Rev. B, 1993, 47: 3857-3863.
[24] P. Alvarado, J. Dorantes-Dávila, and H. Dreysse, Structural effects on the magnetism of small vanadium clusters, Phys. Rev. B, 1994, 50: 1039-1045.
[25] G. M. Pastor, J. Dorantes-Dávila, and K. H. Bennemann, Size and structural dependence of the magnetic properties of small 3d-transition-metal clusters, Phys. Rev. B, 1989, 40: 7642-7654.
[26] H. Cheng and L. S. Wang, Dimer growth, structural transition, and antiferromagnetic ordering of small chromium clusters, Phys. Rev. Lett., 1996, 77: 51-54.
[27] D. C. Douglass, J. P. Bucher, and L. A. Bloomfield, Magnetic studies of free nonferromagnetic clusters, Phys. Rev. B, 1992, 45: 6341-6344.
[28] A. J. Cox, J. G. Louderback, and L. A. Bloomfield, Experimental observation of magnetism in rhodium clusters, Phys. Rev. Lett., 1993, 71: 923-926.
[29] A. J. Cox, J. G. Louderback, S. E. Aspel,and L. A. Bloomfield, Magnetism in 4d-transition metal clusters, Phys. Rev. B, 1994, 49: 12295-12298.
[30] Kreibig and M. Vollmer, Optical properties of metal c1usters, Springer-Verlag, Berlin Herdelberg, 1995.
[31] K. Selby, M. Vollmer, J. Masui,V. Kresin, W. A. de Heer, and W. D. Knight, Surface plasma resonances in free metal clusters, Phys. Rev. B, 1989, 40: 5417-5427.
[32] M. Brack, Multipole vibrations of small alkali-metal spheres in a semiclassical description, Phys. Rev. B, 1989, 39: 3533-3542.
[33] V. Kresin, Surface and volume collective modes in small clusters and their interaction with single-particle levels, Z. Phys. D, 1991, 19: 105-107.
[34] L. D. Landau and E. M. Lifshits, Quantum Mechanics, 3rd ed.,Pergamon, Oxford, 1977.
[35] L. Genzel,T. P. Martin, and U. Kreibig, Dielectric function and plasma resonances of small metal particles, Z. Phys. B, 1975, 21(4): 339-346.
[36] U. Kreibig and L. Genzel, Optical absorption of small metallic particles, Surf. Sci., 1985, 156: 678-700.
[37] X. Chen, J. Zhao, and G. Wang, Conductance resonance of metal-insulator-metal junction with embedded metal cluster, Appl. Phys. Lett., 1994, 65(19): 2419-21.
[38] J. X. Ma, M. Han, H. Q. Zhang, Y. C. Gong, and G. H. Wang, Dense randompacking formation of gold cluster-based film characterized by scanning tunneling microscope, Appl. Phys. Lett., 1994, 65: 1513-1515.
[39]王广厚,原子团簇科学,科技导报, 1994, 10: 9-11.
[40] S. Bjornholm, Clusters, condensed matter in embryonic form, Contemp. Phys., 1990, 31(5): 309-324.
[41]冯瑞,金国钧,凝聚态物理学的新进展Ⅲ,物理学进展, 1991, 11: 373.
[42]王金兰,半导体团体结构和性质及金纳米线热力学稳定性的理论研究,南京大学博士论文, 2001.
[43] K. Rademann, B. Kaiser, U. Even, and F. Hensel, Size dependence of the gradual transition to metallic properties in isolated mercury clusters, Phys. Rev. Lett., 1987, 59: 2319-2321.
[44] J. Ho, K. M. Ervin, and W. C. Lineberger, Photoelectron spectroscopy of metal cluster anions: Cun-, Agn-, and Aun-, J. Chem. Phys., 1990, 93: 6987-7002.
[45] K. Rademann, B. Kaiser, U. Even, and F. Hensel, Size dependence of the gradual transition to metallic properties in isolated mercury clusters, Phys. Rev. Lett., 1987, 59: 2319-22.
[46] J. L. Wang, G. H. Wang, and J. J. Zhao, Nonmetal-metal transition in Znn (n=2–20) clusters, Phys. Rev. A, 2003, 68: 013201-1-6.
[47] J. L. Wang, G. H. Wang, and J. J. Zhao, Density functional study of beryllium clusters, with gradient correction, J. Phys. Condens. Matter, 2001, 13: L753-L758.
[48] J. G. Louderback, A. J. Cox, L. J. Lising, D. C. Douglass, and L. A. Bloomfield, Magnetic properties of nickel clusters, Z. Phys. D, 1993, 26: 301-303.
[49] J. P. Bucher, D. C. Douglass, and L. A. Bloomfield, Magnetic properties of free cobalt clusters, Phys. Rev. Lett., 1991, 66: 3052-3055.
[50] J. Zhao, M. Han, and G. Wang, Ionization potentials of transition-metal clusters, Phys. Rev. B, 1993, 48: 15297-15300, and the references therein.
[51] S. N. Khanna and S. Linderoth, Magnetic behavior of clusters of ferromagnetic transition metals, Phys. Rev. Lett., 1991, 67: 742-745.
[52] D. M. Cox, D. J. Trevor, R. L. Whetten, E. A. Rohlfing, and A. Kaldor,Magnetic behavior of free-iron and iron oxide clusters, Phys. Rev. B, 1985, 32: 7290-7298.
[53] J. L. Wang, J. J. Zhao, F. Ding, W. F. Shen, H. Lee and G. H. Wang, Thermal properties of medium-sized Ge clusters, Solid State Commun., 2001, 117: 593-598.
[54] J. L. Wang, F. Ding, W. F. Shen, T. X. Li, G. H. Wang, and J. J. Zhao, Thermal behavior of Cu-Co bimetallic clusters, Solid State Commun., 2001, 119: 13-18.
[55] C. Binns, Nanoclusters deposited on surfaces, Surf. Sci. Rep., 2001, 44: 1-49.
[56]王远,徐东升,纳米尺度分子工程研究,新世纪的物理化/学科前沿与展望,科学出版社出版, 2004: 31.
[57] M. D. Ventra, S. T. Pantelides, and N. D. Lang, First-Principles calculation of transport properties of a molecular device, Phys. Rev. Lett., 2000, 84: 979-982.
[58] Y. Q. Xue, S. Datta, and M. A. Ratner, Charge transfer and "band lineup" in molecular electronic devices: A chemical and numerical interpretation, J. Chem. Phys., 2001, 115(9): 4292-4299.
[59] N. D. Lang, and P. Avouris, Electrical conductance of parallel atomic wires, Phys. Rev. B, 2000, 62: 7325-7392.
[60] R. N. Barnett, and U. Landman, Cluster-derived structures and fluctuations in nanowires, Nature, 1997, 387: 788-791.
[61] J. Lu, X. W. Zhang, and X. G. Zhao, Metal-cage hybridization in endohedral La@C60, Y@C60 and Sc@C60, Chem. Phys. Lett., 2000, 332: 51-57.
[62] C. Zybill, Structure and reactivity of silicon clusters in the gas phase, Angew. Chem. Int. Ed. Engl., 1992, 31: 173-174.
[63] Z. Slanina, S. L. Lee, K. Kobayashi, and S. Nagase, C61 clusters: AM1 computations, J. Mol. Struct.: THEOCHEM, 1994, 312: 173-179.
[64] K. M. Ho, A. A. Shvartsburg, B. Pan, Z. Y. Lu, C. Z. Wang, J. G. Wacker, J. L. Fye, and M. F. Jarrold, Structures of medium-sized silicon clusters, Nature, 1998, 392: 582-585.
[65] F. Hagelberg, J. Leszczynski, V. Murashov, Theoretical investigations on small closed-shell siliconN clusters, J. Mol. Struct.: THEOCHEM, 1998, 454: 209-216.
[66] I. Rata, A. A. Shvartsburg, M. Horoi, T. Frauenheim, K. W. M. Siu, and K. A. Jackson, Single-Parent Evolution Algorithm and the optimization of Si clusters, Phys. Rev. Lett., 2000, 85: 546-549.
[67] J. G. Han, Z. Y. Ren, L. S. Sheng, Y. W. Zhang, J. A. Morales, F. Hagelberg, The formation of new silicon cages: a semiempirical theoretical investigation, J. Mol. Struct.: THEOCHEM, 2003, 625: 47-58.
[68] K. Jackson, B. Nellemore, Zr@Si20: a strongly bound Si endohedral system, Chem. Phys. Lett., 1996, 254: 249-256.
[69] J. G. Han and F. Hagelberg, A density functional theory investigation on CrSin (n=1-6) Clusters, Chem. Phys., 2001, 263: 255-263.
[70] J. G. Han, A computational study on electronic structures of GenF? and GenF (n=3–6) clusters by density functional theory, Chem. Phys. Lett., 2000, 324: 143-148.
[71] J. G. Han, Density functional studies on the molecular geometries, vibrational frequencies, electron affinities of X2F? (X=C, Si, Ge) cluster, J. Mol. Struct.: THEOCHEM, 1999, 491: 41-47.
[72] J. G. Han and Y. Y. Shi, A computational study on geometries, electronic structures and ionization potentials of MSi15 (M=Cr, Mo, W) clusters by density functional method, Chem. Phys., 2001, 266(1): 33-40.
[73] J. J. Scherer, J. B. Paul,C. P. Collier, R. J. Saykally, Cavity ringdown laser absorption spectroscopy and time-of-flight mass spectroscopy of jet-cooled copper silicides, J. Chem. Phys., 1995, 102(13): 5190-5199.
[74] Y. M. Harrick, W. Jr. Weltner, Quenching of angular momentum in the ground states of VC, NbC, VSi, and NbSi molecules, J. Chem. Phys., 1991, 94(5): 3371-3380.
[75] H. Hiura, T. Miyazaki, and T. Kanayama, Formation of Metal-Encapsulating Si Cage Clusters, Phys. Rev. Lett., 2001, 86(9): 1733-1736.
[76] M. Ohara, K. Koyasu, A. Nakajima, and K. Kaya, Geometric and electronic structures of metal (M)-doped silicon clusters (M=Ti, Hf, Mo and W), Chem. Phys.Lett., 2003, 371: 490-497.
[77] K. Koyasu, M. Akutsu, M. Mitsui, and A. Nakajima, Selective Formation of MSi16 (M = Sc, Ti, and V), J. Am. Chem. Soc., 2005, 127(14): 4998-4999.
[78] V. Kumar and Y. Kawazoe, Metal-encapsulated fullerenelike and cubic caged clusters of silicon, Phys. Rev. Lett., 2001, 87: 045503-1-4.
[79] J. Lu and S. Nagase, Structural and electronic properties of metal-encapsulated silicon clusters in a large size range, Phys. Rev. Lett., 2003, 90: 115506-1-4.
[80] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth behavior of metal-doped silicon clusters SinM(M= Ti, Zr, Hf; n= 8-16), Phys. Rev. B, 2005, 71: 075423-1-12.
[81] J. U. Reveles and S. N. Khanna, Electronic counting rules for the stability of metal-silicon clusters, Phys. Rev. B, 2006, 74: 035435-1-6.
[82] M. B. Torres, E. M. Fernández, L. C. Balbás, Theoretical study of isoelectronic SinM clusters (M=Sc-, Ti, V+; n=14–18), Phys. Rev. B, 2007, 75: 205425-1-14.
[83] C. Xiao, J. Blundell, F. Hagelberg, and W. A. Lester, Silicon clusters doped with an yttrium metal atom impurity, Jr., Int. J. Quantum Chem., 2004, 96: 416-425.
[84] L. J. Guo, X. Liu, G. F. Zhao, and Y. H. Luo, Computational investigation of TiSin (n=2–15) clusters by the density-functional theory, J. Chem. Phys., 2007, 126(23): 234704-1-7.
[85] J. Wang and J. G. Han, Geometries, stabilities, and electronic properties of different-sized ZrSin (n=1–16) clusters: A density-functional investigation, J. Chem. Phys., 2005, 123(6): 064306-1-16.
[86] P. Guo, Z. Y. Ren, F.Wang, J. Bian, J. G. Han, and G. H.Wang, Structural and electronic properties of TaSin (n=1–13) clusters: A relativistic density functional investigation, J. Chem. Phys., 2004, 121(24): 12265-75.
[87] J. G. Han and F. Hagelberg, A density functional theory investigation of CrSin (n=1–6) clusters, Chem. Phys., 2001, 263: 255-262.
[88] J. G. Han and F. Hagelberg, A density functional investigation of MoSin (n=1–6) clusters, J. Mol. Struct.: THEOCHEM, 2001, 549: 165-180.
[89] J. G. Han, C. Xiao, and F. Hagelberg, Geometric and electronic structure ofWSin (n=1-6, 12) clusters, Struct. Chem., 2002, 13: 173-191.
[90] J. G. Han, Z. Y. Ren, and B. Z. Lu, Geometries and stabilities of re-doped Si-n (n=1-12) clusters: a density functional investigation, J. Phys. Chem. A, 2004, 108(23): 5100-5110.
[91] L. Ma, J. J. Zhao, J. G. Wang, B. L. Wang, Q. L. Lu, and G. H. Wang, Growth behavior and magnetic properties of SinFe (n=2–14) clusters, Phys. Rev. B, 2006, 73(12): 125439-1-8.
[92] L. Ma, J. J. Zhao, J. G. Wang, Q. L. Lu, L. Z. Zhu, and G. H. Wang, Structure and electronic properties of cobalt atoms encapsulated in Sin(n=1–13) clusters, Chem. Phys. Lett., 2005, 411: 279-284.
[93] J. G. Han, A theoretical investigation on electronic properties and stability of IrSix (x=1–6) clusters, Chem. Phys., 2003, 286: 181-192.
[94] J. Wang, Q. M. Ma, Y. Liu, and Y. C. Li, From SinNi to Ni@Sin: An investigation of configurations and electronic structure, Phys. Rev. B, 2007, 76(3): 035406-1-8.
[95] C. Y. Xiao, F. Hagelberg, and W. A. Lester, Jr., Geometric, energetic, and bonding properties of neutral and charged copper-doped silicon clusters, Phys. Rev. B, 2002, 66(7): 075425-1-23.
[96] P. F. Zhang, J. G. Hana, and Q. R. Pu, A density functional investigation of AgSin (n=1?5) clusters, J. Mol. Struct.: THEOCHE, 2003, 635: 25-35.
[97] F. C. Chuang, Y. Y. Hsieh, C. C. Hsu, and M. A. Albao, Geometries and stabilities of Ag-doped Sin (n=1–13) clusters: A first-principles study, J. Chem. Phys., 2007, 127(14): 144313-1-6.
[1] B. J. Alder and T. E. Wainwright, Phase Transition for a Hard Sphere System, J. Chem. Phys., 1957, 27(5): 1208.
[2] J. B. Gibson, A. N. Goland, M. Milgram, and G. H. Vmeyard, Dynamics of Radiation Damage, Phys. Rev., 1960, 120: 1229-1253.
[3] D. W. Heermann著,秦克诚译,理论物理中的计算机模拟方法,北京:北京大学出版社, 1996.
[4][德] K. Binder, D. W. Heermann,秦克诚译,统计物理学中的蒙特卡罗模拟方法,北京:北京大学出版社, 1994.
[5]张孝泽,蒙特卡罗方法在统计物理中的应用,河南:科学技术出社, 1991.
[6] Y. H. Luo, J. J. Zhao, S. T. Qiu, and G. H. Wang, Genetic-algorithm prediction of the magic-number structure of (C60)N clusters with a first-principles interaction potential, Phys. Rev. B, 1999, 59(23): 14903-14906.
[7]王广厚,遗传算法研究原子团簇,物理学进展, 2000, 20(3): 252-275.
[8]徐光宪,黎乐民,王德民,量子化学(中册),科学出版社,1999: 678.
[9] D. R. Hartree, Proc. Combidge, The wave mechanics of an atom with a non-coulomb central field. I. Theory and methods, Phil. Soc., 1928, 24: 89-110.
[10] V. Fock, N?herungsmethode zur L?sung des quantenmechanischen Mehrk?rperproblems, Z. Physik, 1930, 61: 126-148.
[11] W. J. Hehre, L. Radom, P. R. Schleyer, et al., Ab initio molecular orbital theory. New York: John Wiley&Sons, 1996.
[12] P. R. Schleyer, Encyclopaedia of computational chemistry. New York: John Wiley &Sons, 1998.
[13] R. G. Parr, W. Yang, Density-functional theory of atoms and molecules. Oxford: Oxford Science, 1989.
[14] H. Thomas, The calculation of atomic fields, Proc. Camb. Phil. Soc., 1927, 23: 542-548.
[15] E. Fermi, Un Metodo Statistico per la Determinazione di alcune Priorieta dell'Atome", Rend. Accad. Naz. Lincei, 1927, 6: 602-607.
[16] P. Hohnberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. B, 1964, 136: 864-871.
[17] W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. A, 1965, 140: 1133-1138.
[18] A. S. Joseph and A. C. Thorsen, De Haas-van Alphen effect and fermi surface in rhenium, Phys. Rev. A, 1964, 133: 1546-1552.
[19] C. F. Weiszacker, Zur Theorie der Kernmassen, Z. Phys., 1935, 96: 431-458.
[20] F. Perrot, Hydrogen-hydrogen interaction in an electron gas, J. Phys. Condens. Matter, 1994, 6: 431-446.
[21] L. W. Wang and M. P. Teter, Kinetic-energy functional of the electron density, Phys. Rev. B, 1992, 45(23): 1319 -13220.
[22] E. Smargiassi and P. A. Madden, Orbital-free kinetic-energy functionals for first-principles molecular dynamics, Phys. Rev. B, 1994, 49(8): 5220-5226.
[23] J. Callaway and N. H. March, Density functional methods: theory and applications, Solid State Phys., 1984, 38: 135-221.
[24] J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Chem. B, 1992, 45: 13244-49.
[25] J. C. Slater, A simplification of the Hartree-Fock method, Phys. Rev., 1951, 81(3): 385-390.
[26] J. C. Slater, T. M. Wilson, and J. H. Wood, Comparison of several exchange potentials for electrons in the Cu+ Ion, Phys. Rev., 1969, 179(1): 28-38.
[27] E. Wigner, On the interaction of electrons in metals, Phys. Rev., 1934, 46(11): 1002-1011.
[28] D. M. Ceperley and B. J. Alder, Ground state of the electron gas by a stochastic method, Phys. Rev. Lett., 1980, 45(7): 566-569.
[29] S. H. Vosko, L. Wilk, and M. Nusair, Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis, Canadian J.Phys., 1980, 58(8): 1200-1211.
[30] J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B, 1981, 23: 5048-5079.
[31] L. A. Cole and J. P. Perdew, Calculated electron affinities of the elements, Phys. Rev. A, 1982, 25(3): 1265-1271.
[32] A. D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Chem. A, 1988, 38: 3098-3100.
[33] J. P. Perdew, J. A. Chevary, S. H. Vosko, et al., Atomic, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation, Phys. Chem. B, 1992, 46: 6671-6687.
[34] J. P. Perdew, K. Burke, and Y. Wang, Generalized gradient approximation for the exchange-correlation hole of a many-electron system, Phys. Chem. B, 1996, 54: 16533-16539.
[35] M. Filatov and W. Thiel, A new gradient-corrected exchange-correlation density functional, Mol. Phys. 1997, 91(5): 847-859.
[36] G. J. Laming, V. Termath, and N. C. Handy, A general purpose exchange-correlation energy functional, J. Chem. Phys., 1993, 99: 8765-8773.
[37] A. D. Becke, Density functional calculations of molecular-bond energies, J. Chem. Phys., 1986, 84: 4524-4529.
[38] J. P. Perdew and Y. Wang, Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation, Phys. Rev. B, 1986, 33: 8800-8802.
[39] D. J. Lacks and R. G. Gordon, Pair interactions of rare-gas atoms as a test of exchange-energy-density functionals in regions of large density gradients, Phys. Rev. A, 1993, 47: 4681-4690.
[40] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1986, 77: 3865-3868.
[41] J. P. Perdew, Denstity-functional approximation for the correlation energy of the inhomogeneous electron gas, Phys. Rev. B, 1986, 33: 8822-8824.
[42] C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[43] A. D. Becke, A new mixing of Hartree-Fock and local density-functional theories, J. Chem. Phys., 1993, 98: 1372-1377.
[44] A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys., 1993, 98(7): 5648-5652.
[45] P. J. Stevens, J. F. Devlin, C. F. Chabalowski, and M. J. Frisch, Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields, J. Chem. Phys., 1994, 98(45): 11623-11627.
[46] A. D. Becke, A new dynamical correlation functional and implications for exact-exchange mixing, J. Chem. Phys., 1995, 104: 1040-1046.
[47] A. D. Becke, Systematic optimization of exchange-correlation functionals, J. Chem. Phys., 1997, 107: 8554-8560.
[48] A. D. Becke, A new inhomogeneity parameter in density-functional theory, J. Chem. Phys., 1998, 109: 2092-2098.
[49] C. Adamo and V. Barone, Toward reliable density functional methods without adjustable parameters: The PBE0 model, J. Chem. Phys., 1999, 110: 6158-6170.
[50] G. Kresse and J. Hafner, Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements, J. Phys.: Condens. Matter, 1994, 6(40): 9245-8257.
[51] G. Kresse and J. Furthmiiller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B, 1996, 54(16): 11169-86.
[52] G. Kresse and J. Furthmuller, VASP the GUIDE [EB/01]. http://flcms.mpi.univie.ac.atlvasp/vasp/vasp.html
[53] G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B, 1999, 59(3): 1758-1775.
[54] E. Polak, Computational Methods in Optimization, New York: Academic, 1971.
[55] E. R. Davidson, In G. H. F Diercksen, and S. Wilson, eds., Methods inComputational Molecular Physics, NATO Advanced Study Institute, Series C: Mathematical and Physical Sciences, Plenum, New York, 113: 95.
[56] P Pulay, Convergence acceleration of iterative sequences: the case of scf iteration, Chem. Phys. Lett., 1980, 73(2): 393-398.
[57] H. J. Monkhorst and D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B, 1976, 13(12): 5188-5192.
[58] O. Jepsen and O. K. Andersen, The electronic structure of h.c.p. Ytterbium, Solid State Commun., 1971, 9(20): 1763-1767.
[59] P. E. Bltichl, O. Jepsen and O. K. Andersen, Improved tetrahedron method for Brillouin-zone Integrations, Phys. Rev. B, 1994, 49(23): 16223-16233.
[60] C. L. Fu and K. M. Ho, First-principles calculation of the equilibrium ground-state properties of transition metals: Applications to Nb and Mo, Phys. Rev. B, 1983, 28(10): 5480-5486.
[61] M. Methfessel and A. T. Paxton, High-precision sampling for Brillouin-zone integration in metals, Phys. Rev. B, 1989, 40(6): 3616-3621.
[1] S. Li, R. J. Van Zee, W. Weltner, Jr., and K. Raghavachari, Si3-Si7: Experimental and theoretical infrared spectra, Chem. Phys. Lett., 1995, 243: 275-280.
[2] E. Kaxiras and K. Jackson, Shape of small silicon clusters, Phys. Rev. Lett., 1993, 71(5): 727-730.
[3] U. Rothlisberger, W. Andreoni, and M. Parrinello, Structure of nanoscale silicon clusters, Phys. Rev. Lett., 1994, 72: 665-668.
[4] K. M. Ho, A. A. Shvartsburg, B. Pan, Z. Y. Lu, C. Z. Wang, J. G. Wacker, J. Fye, and M. F. Jarrold, Structures of medium-sized silicon clusters, Nature (London), 1998, 392: 582-585.
[5] I. Rata, A. A. Shvartsburg, M. Horoi, T. Frauenheim, K. W. Michael Siu, and K. A. Jackson, Single-parent evolution algorithm and the optimization of Si clusters, Phys. Rev. Lett., 2000, 85(3): 546-549.
[6] M. F. Jarrold and J. E. Bower, Mobilities of silicon cluster ions: The reactivity of silicon sausages and spheres, J. Chem. Phys., 1992, 96(12): 9180-9190.
[7] S. M. Beck, Studies of silicon cluster-metal atom compound formation in a supersonic molecular beam, J. Chem. Phys., 1987, 87: 4233-4234.
[8] S. M. Beck, Mixed metal-silicon clusters formed by chemical reaction in a supersonic molecular beam: Implications for reactions at the metal/silicon interface, J. Chem. Phys., 1989, 90: 6306-6312.
[9] S. M. Beck, Photophysical studies of bare and metal-containing silicon clusters, Advances in Metal and Semiconductor Clusters, 1993, 1: 241-265.
[10] H. Hiura, T. Miyazaki,T. Kanayama, Formation of metal-encapsulating Si cage clusters, Phys. Rev. Lett., 2001, 86(9): 1733-1736.
[11] M. Ohara, K. Miyajima, A. Pramann, A. Nakajima, K. Kaya, Geometric and electronic structures of terbium?silicon mixed clusters (TbSin; 6≤n≤16), J. Phys. Chem. A, 2002, 106(15): 3702-3705.
[12] M. Ohara, K. Koyasu, A. Nakajima, K. Kaya, Geometric and electronic structures of metal (M)-doped silicon clusters (M=Ti, Hf, Mo, and W), Chem. Phys. Lett., 2003, 371: 490-497.
[13] K. Koyasu, M. Akutsu, M. Mitsui, and A. Nakajima, Selective formation of MSi16 (M = Sc, Ti, and V), J. Am. Chem. Soc., 2005, 127(14): 4998-4999.
[14] J. J. Scherer, J. B. Paul,C. P. Collier, R. J. Saykally, Cavity ringdown laser absorption spectroscopy and time-of-flight mass spectroscopy of jet-cooled copper silicides, J. Chem. Phys., 1995, 102(13): 5190-5199.
[15] Y. M. Harrick, W. Jr. Weltner, Quenching of angular momentum in the ground states of VC, NbC, VSP, and NbSi molecules, J. Chem. Phys., 1991, 94(5): 3371-3380.
[16] V. Kumar and Y. Kawazoe, Metal-encapsulated fullerenelike and cubic caged clusters of silicon, Phys. Rev. Lett., 2001, 87(4): 045503-1-4.
[17] V. Kumar and Y. Kawazoe, Magic behavior of Si15M and Si16M (M=Cr, Mo, and W) clusters, Phys. Rev. B, 2002, 65(7): 073404-1-4.
[18] V. Kumar and Y. Kawazoe, Metal-doped magic clusters of Si, Ge, and Sn: The finding of a magnetic superatom, Appl. Phys. Lett., 2003, 83(13): 2677-2679.
[19] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth, magic behavior, and electronic and vibrational properties of Cr-doped Si clusters, Phys. Rev. B, 2004, 70(24): 245433-1-10.
[20] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth behavior of metal-doped silicon clusters SinM (M=Ti, Zr, Hf; n=8–16), Phys. Rev. B, 2005, 71(7): 075423-1-12.
[21] J. Lu and S. Nagase, Structural and electronic properties of metal-encapsulated silicon clusters in a large size range, Phys. Rev. Lett., 2003, 90(11): 115506-1-4.
[22] G. Mpourmpakis, G. E. Froudakis, A. N. Andriotis, and M. Menon, Understanding the structure of metal encapsulated Si cages and nanotubes: Role of symmetry and d-band filling, J. Chem. Phys., 2003, 119(14): 7498-7502.
[23] G. Mpourmpakis, G. E. Froudakis, A. N. Andriotis, and M. Menon, Feencapsulation by silicon clusters: Ab initio electronic structure calculations, Phys. Rev. B, 2003, 68(12): 125407-1-5.
[24] L. Ma, J. J. Zhao, J. G. Wang, Q. L. Lu, L. Z. Zhu, and G. H. Wang, Structure and electronic properties of cobalt atoms encapsulated in Sin (n=1-13) clusters, Chem. Phys. Lett., 2005, 411: 279-284.
[25] L. Ma, J. J. Zhao, J. G. Wang, B. L. Wang, Q. L. Lu, and G. H. Wang, Growth behavior and magnetic properties of SinFe (n=2–14) clusters, Phys. Rev. B, 2006, 73(12): 125439-1-8.
[26] Z. U. Ren, F. Li, P. Guo, and J. G. Han, A computational investigation of the Ni-doped Sin (n=1-8) clusters by a density functional method, J. Mol. Struct.: THEOCHEM, 2005, 718: 165-173.
[27] E. N. Koukaras, C. S. Garoufalis, and A. D. Zdetsis, Structure and properties of the Ni@Si12 cluster from all-electron ab initio calculations, Phys. Rev. B, 2006, 73(23): 235417-1-10.
[28] A. K. Singh, T. M. Briere, V. Kumar, and Y. Kawazoe, Magnetism in transition-metal-doped silicon nanotubes, Phys. Rev. Lett., 2003, 91(44): 146802-1-4.
[29] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys., 1988, 88(4): 2547-2553; C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[30] T. A. Barckholtz and T. A. Miller, Quantitative insights about molecules exhibiting Jahn-Teller and related effects, Int. Rev. Phys. Chem., 1998, 17(4): 435-524.
[31] A. D. Zdetsis, Bonding and structural characteristics of Zn-, Cu-, and Ni-encapsulated Si clusters: Density-functional theory calculations, Phys. Rev. B, 2007, 75(8): 085409-1-10.
[32] R. S. Mulliken, Electron Population Analysis on LCAO-MO Molecular Wave Functions. II. Overlap Population, Bond Orders, and Covalent Bond Energies, J.Chem. Phys., 1955, 23(10): 1841-1846.
[33] B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules, J. Chem. Phys., 1990, 92(1): 508-517.
[34] B. Delley, From molecules to solids with the DMol3 approach, J. Chem. Phys., 2000, 113(18): 7756-7764.
[35] D. B. Zhang and J. Shen, Ground state, growth, and electronic properties of small lanthanum clusters, J. Chem. Phys., 2004, 120(11): 5104-5109.
[36] D. B. Zhang and J. Shen, First principles study of the stability and electronic structure of the icosahedral La13, La13-1, and La13+1 clusters, J. Chem. Phys., 2004, 120(11): 5081-5086.
[37] Z. Xie, Q. M. Ma, Y. Liu, and Y. C. Li, First-principles study of the stability and Jahn–Teller distortion of nickel clusters, Phys. Lett. A, 2005, 342: 459-467.
[38] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic properties of small Co clusters, Phys. Lett. A, 2006, 358: 289-296.
[39] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, binding energies and magnetic moments of small iron clusters: A study based on all-electron DFT, Solid State Commun., 2007, 142: 114-119.
[40] N. Liu, Q. M. Ma, Z. Xie, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic moments of small lanthanum-nickel clusters, Chem. Phys. Lett., 2007, 436: 184-188.
[41] K. Raghavachari, Theoretical study of small silicon clusters: Equilibrium geometries and electronic structures of Sin (n=2-7, 10), J. Chem. Phys., 1986, 84(10): 5672-5686.
[42] P. J. Bruna, S. D. Peyerimhoff, and R. J. Buenker, Theoretical prediction of the potential curves for the lowest-lying states of the isovalent diatomics CN+, Si2, SiC, CP+, and SiN+ using the ab initio MRD-CI method, J. Chem. Phys., 1980, 72(10): 5437-5445.
[43] A. D. Zdetsis, Bonding and structural characteristics of Zn-, Cu-, and Ni-encapsulated Si clusters: Density-functional theory calculations, Phys. Rev. A,2001, 64(8): 023202-1-10.
[44] P. Karamanis, D. Zhang-Negrerie, and C. Pouchan, A critical analysis of the performance of conventional ab initio and DFT methods in the computation of Si6 ground state, Chem. Phys., 2006, 331: 417-426.
[45] S. N. Khanna, B. K. Rao, and P. Jena, Magic Numbers in Metallo-Inorganic Clusters: Chromium Encapsulated in Silicon Cages, Phys. Rev. Lett., 2002, 89(1): 016803-1-4.
[46] J. Wang, Q. M. Ma, Z. Xie, Y. Liu, and Y. C. Li, From SinNi to Ni@Sin: An investigation of configurations and electronic structure, Phys. Rev. B, 2007, 76(3): 035406-1-8.
[1] K. M. Ho, A. A. Shvartsburg, B. Pan, Z. Y. Lu, C. Z. Wang, J. G. Wacker, J. Fye, and M. F. Jarrold, Structures of medium-sized silicon clusters, Nature (London), 1998, 392: 582-585.
[2] E. Kaxiras and K. Jackson, Shape of small silicon clusters, Phys. Rev. Lett., 1993, 71(5): 727-730.
[3] U. Rothlisberger, W. Andreoni, and M. Parrinello, Structure of nanoscale silicon clusters, Phys. Rev. Lett., 1994, 72: 665-668.
[4] I. Rata, A. A. Shvartsburg, M. Horoi, T. Frauenheim, K. W. Michael Siu, and K. A. Jackson, Single-parent evolution algorithm and the optimization of Si clusters, Phys. Rev. Lett., 2000, 85(3): 546-549.
[5] M. F. Jarrold, Nanosurface chemistry on size-selected silicon clusters, Science, 1991, 252(5009): 1085-1092.
[6] S. M. Beck, Studies of silicon cluster–metal atom compound formation in a supersonic molecular beam, J. Chem. Phys., 1987, 87: 4233-4234.
[7] S. M. Beck, Mixed metal–silicon clusters formed by chemical reaction in a supersonic molecular beam: Implications for reactions at the metal/silicon interface, J. Chem. Phys., 1989, 90: 6306-6312.
[8] H. Hiura, T. Miyazaki, and T. Kanayama, Formation of metal-encapsulating Si cage clusters, Phys. Rev. Lett., 2001, 86: 1733-1736.
[9] M. Ohara, K. Koyasu, A. Nakajima, and K. Kaya, Geometric and electronic structures of metal (M)-doped silicon clusters (M= Ti, Hf, Mo and W), Chem. Phys. Lett., 2003, 371: 490-497.
[10] K. Koyasu, M. Akutsu, M. Mitsui, and A. Nakajima, Selective Formation of MSi16 (M = Sc, Ti, and V), J. Am. Chem. Soc., 2005, 127(14): 4998-4999.
[11] V. Kumar and Y. Kawazoe, Metal-encapsulated fullerenelike and cubic caged clusters of silicon, Phys. Rev. Lett., 2001, 87: 045503-1-4.
[12] V. Kumar, T. M. Briere, and Y. Kawazoe, Ab initio calculations of electronic structures, polarizabilities, Raman and infrared spectra, optical gaps, and absorption spectra of M@Si16 (M=Ti and Zr) clusters, Phys. Rev. B, 2003, 68(15): 155412-1-9.
[13] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth behavior of metal-doped silicon clusters SinM(M= Ti, Zr, Hf; n= 8-16), Phys. Rev. B, 2005, 71: 075423-1-12.
[14] J. Lu and S. Nagase, Structural and electronic properties of metal-encapsulated silicon clusters in a large size range, Phys. Rev. Lett., 2003, 90(11): 115506-1-4.
[15] J. U. Reveles and S. N. Khanna, Electronic counting rules for the stability of metal-silicon clusters, Phys. Rev. B, 2006, 74: 035435-1-6.
[16] M. B. Torres, E. M. Fernández, L. C. Balbás, Structure and relative stability of Sin, Sin-, and doped SinM clusters (M =Sc-, Ti, V+) in the range n=14–18, Phys. Rev. B, 2007, 75: 205425-1-14.
[17] B. Hammer and J. K. Norskov, Why gold is the noblest of all the metals, Nature (London), 1995, 376: 238-240.
[18] R. F. Barrow, W. J. M. Gissane, and D. N. Travis, Electronic spectra of some gaseous diatomic compounds of gold, Nature (London), 1964, 201: 603-604.
[19] C. Majumder, A. K. Kandalam and P. Jena, Structure and bonding of Au5M (M=Na, Mg, Al, Si, P, and S) clusters, Phys. Rev. B, 2006, 74(20): 205437-1-6.
[20] Q. Sun, Q. Wang, G. Chen, and P. Jena, Structure of SiAu16: Can a silicon atom be stabilized in a gold cage? J. Chem. Phys., 2007, 127(21): 214706-1-4.
[21] B. Kiran, X. Li, H. J. Zhai, L. F. Cui, and L. S. Wang, Communication [SiAu4]: Aurosilane, Angew. Chem., Int. Ed. 2004, 43(16): 2125-2129.
[22] X. Li, B. Kiran, and L. S. Wang, Gold as Hydrogen. An experimental and theoretical study of the structures and bonding in disilicon gold clusters Si2Aun- and Si2Aun (n=2 and 4) and comparisons to Si2H2 and Si2H4, J. Phys. Chem. A, 2005, 109(19): 4373-4374.
[23] C. Xiao, J. Blundell, F. Hagelberg, and W. A. Lester, Jr., Silicon clusters doped with an yttrium metal atom impurity, Int. J. Quantum Chem., 2004, 96(4): 416-425.
[24] L. J. Guo, X. Liu, G. F. Zhao, and Y. H. Luo, Computational investigation ofTiSin (n=2–15) clusters by the density-functional theory, J. Chem. Phys., 2007, 126(23): 234704-1-7.
[25] J. Wang and J. G. Han, Geometries, stabilities, and electronic properties of different-sized ZrSin (n=1–16) clusters: A density-functional investigation, J. Chem. Phys., 2005, 123(6): 064306-1-16.
[26] P. Guo, Z. Y. Ren, F.Wang, J. Bian, J. G. Han, and G. H.Wang, Structural and electronic properties of TaSin (n=1–13) clusters: A relativistic density functional investigation, J. Chem. Phys., 2004, 121(24): 12265-75.
[27] J. G. Han and F. Hagelberg, A density functional theory investigation of CrSin (n= 1–6) clusters, Chem. Phys., 2001, 263: 255-262.
[28] J. G. Han and F. Hagelberg, A density functional investigation of MoSin (n= 1–6) clusters, J. Mol. Struct.: THEOCHEM, 2001, 549: 165-180.
[29] J. G. Han, C. Xiao, and F. Hagelberg, Geometric and electronic structure of WSiN (N= 1–6, 12) clusters, Struct. Chem., 2002, 13: 173-191.
[30] J. G. Han, Z. Y. Ren, and B. Z. Lu, Geometries and Stabilities of Re-Doped Sin (n= 1? 12) Clusters: A Density Functional Investigation, J. Phys. Chem. A, 2004, 108(23): 5100-5110.
[31] L. Ma, J. J. Zhao, J. G. Wang, B. L. Wang, Q. L. Lu, and G. H. Wang, Growth behavior and magnetic properties of SinFe (n=2–14) clusters, Phys. Rev. B, 2006, 73(12): 125439-1-8
[32] L. Ma, J. J. Zhao, J. G. Wang, Q. L. Lu, L. Z. Zhu, and G. H. Wang, Structure and electronic properties of cobalt atoms encapsulated in Sin (n=1–13) clusters, Chem. Phys. Lett., 2005, 411: 279-284.
[33] J. G. Han, A theoretical investigation on electronic properties and stability of IrSix (x= 1–6) clusters, Chem. Phys., 2003, 286: 181-192.
[34] J. Wang, Q. M. Ma, Y. Liu, and Y. C. Li, From SinNi to Ni@ Sin: An investigation of configurations and electronic structure, Phys. Rev. B, 2007, 76(3): 035406-1-8.
[35] C. Y. Xiao, F. Hagelberg, and W. A. Lester, Jr., Geometric, energetic, andbonding properties of neutral and charged copper-doped silicon clusters, Phys. Rev. B, 2002, 66(7): 075425-1-23.
[36] P. F. Zhang, J. G. Hana, and Q. R. Pu, A density functional investigation of AgSin (n= 1? 5) clusters, J. Mol. Struct.: THEOCHEM, 2003, 635: 25-35.
[37] F. C. Chuang, Y. Y. Hsieh, C. C. Hsu, and M. A. Albao, Geometries and stabilities of Ag-doped Sin (n= 1–13) clusters: A first-principles study, J. Chem. Phys., 2007, 127(14): 144313-1-6.
[38] T. T. Cao, X. J. Feng, L. X. Zhao, X. Liang, Y. M. Lei, and Y. H. Luo, Structure and magnetic properties of La-doped Sin(n=1-12, 24) clusters: a density functional theory investigation, Eur. Phys. J. D, 2008, 49: 343-351.
[39] M. Sankaran and B. Viswanathan, A DFT study of the electronic property of gold nanoclusters (Aux, x=1-12 atoms), Bulletin of the Catalysis Society of India, 2006, 5(1): 26-32.
[40] Q. Sun, Q. Wang, G. Chen, and P. Jena, Structure of SiAu16: Can a silicon atom be stabilized in a gold cage? J. Chem. Phys., 2007, 127(21): 214706-1-4.
[41] C. Majumder, Effect of Si adsorption on the atomic and electronic structure of Aun clusters (n=1–8) and the Au (111) surface: First-principles calculations, Phys. Rev. B, 2007, 75(23): 235409-1-8.
[42] P. J. Bruna, S. D. Peyerimhoff, and R. J. Buenker, Theoretical prediction of the potential curves for the lowest-lying states of the isovalent diatomics CN+, Si2, SiC, CP+, and SiN+ using the ab initio MRD-CI method, J. Chem. Phys., 1980, 72(10): 5437-5445.
[43] B. Douglas, D.H. McDaniel and J.J. Alexander, Concepts and models of inorganic chemistry (2nd ed.), Wiley, New York, 1983.
[44] J. J. Scherer, J. B. Paul, C. P. Collier, A. O’Keeffe, and R. J. Saykally, Cavity ringdown laser absorption spectroscopy and time-of-flight mass spectroscopy of jet-cooled gold silicides, J. Chem. Phys., 1995, 103(21): 9187-9192.
[45] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures and magnetic moments of Fe-C clusters, Phys. Rev. B, 2007, 76(3): 035412-1-7.
[46] N. Liu, Q. M. Ma, Z. Xie, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic moments of small lanthanum–nickel clusters, Chem. Phys. Lett., 2007, 436: 184-188.
[47] Z. Xie, Q. M. Ma, Y. Liu, Y. C. Li, First-principles study of the stability and Jahn-Teller distortion of nickel clusters, Phys. Lett. A, 2005, 342: 459-467.
[48] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic properties of small Co clusters, Phys. Lett. A, 2006, 358: 289-296.
[49] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, binding energies and magnetic moments of small iron clusters: A study based on all-electron DFT Solid State Comm., 2007, 142: 114-119.
[50] B. R. Wang, J. Wang, Q. M. Ma, and Y. Liu, Structures and magnetic ordering of MnnFe (n=1–12) clusters, Solid State Comm., 2008, 147: 53-56.
[51] J. Wang, H. Ning, Q. M. Ma, Y. Liu, and Y. C. Li, Au: A possible ground-state noble metallic nanotube, J. Chem. Phys., 2008, 129(13): 134705-1-4; http://www.natureasia.com/asiamaterials/highlight.php?id=337.
[52] W. R. Wadt and P. J. Hay, Ab initio effective core potentials for molecular calculations: Potential for main group elements Na to Bi, J. Chem. Phys., 1985, 82(1): 284-298.
[53] A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys., 1993, 98(7): 5648-5652.
[54] J. P. Perdew, K. Burke, and Y. Wang, Generalized gradient approximation for the exchange-correlation hole of a many-electron system, Phys. Rev. B, 1996, 54: 16533-16539.
[55] R. S. Mulliken, Electronic Population Analysis on LCAOMO Molecular Wave Functions. II. Overlap Populations, Bond Orders, and Covalent Bond Energies, J. Chem. Phys., 1955, 23(10): 1841-1846.
[56] M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., Gaussian 03, Revision D.01 (Gaussian, Inc., Wallingford CT, 2004).
[57] T. A. Barckholtz, T. A. Miller, Quantitative insights about molecules exhibitingJahn-Teller and related effects, Int. Rev. Phys. Chem., 1998, 17(4): 435-524.
[58] A. D. Zdetsis, Bonding and structural characteristics of Zn-, Cu-, and Ni-encapsulated Si clusters: Density-functional theory calculations, Phys. Rev. B, 2007, 75(8): 085409-1-10.
[59] A. D. Zdetsis, The real structure of the Si6 cluster, Phys. Rev. A, 2001, 64(2): 023202-1-4.
[60] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys., 1988, 88(4): 2547-2553; C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[61] K. Raghavachari, Theoretical study of small silicon clusters: Equilibrium geometries and electronic structures of Sin (n=2–7, 10), J. Chem. Phys., 1986, 84(10): 5672-5686.
[62] P. J. Bruna, S. D. Peyerimho, and R. J. Buenker, Theoretical prediction of the potential curves for the lowest-lying states of the isovalent diatomics CN+, Si2, SiC, CP+, and SiN+ using the ab initio MRD-CI method, J. Chem. Phys., 1980, 72(10): 5437-5445.
[63] B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules, J. Chem. Phys., 1990, 92(1): 508-517.
[64] B. Delley, From molecules to solids with the Dmol3 approach, J. Chem. Phys., 2000, 113(18): 7756-7764.
[65] P. Karamanis, D. Zhang-Negrerie, C. Pouchan, A critical analysis of the performance of conventional ab initio and DFT methods in the computation of Si6 ground state, Chem. Phys., 2006, 331: 417-426.
[66] S. N. Khanna, B. K. Rao, and P. Jena, Magic numbers in metallo-inorganic clusters: chromium encapsulated in silicon cages, Phys. Rev. Lett., 2002, 89(1): 016803-1-4.
[1] H. W. Kroto, J. R. Heath, S. C. OBrien, R. F. Curl, and R. E. Smalley, C60: buckminsterfullerene, Nature (London), 1985, 318: 162-163.
[2] J. Cioslowski, Endohedral chemistry: electronic structures of molecules trapped inside the C60 cage, J. Am. Chem. Soc., 1991, 113(11): 4139-4141.
[3] J. Cioslowski and A. Nanayakkara, Endohedral fullerites: A new class of ferroelectric materials, Phys. Rev. Lett., 1992, 69: 2871-2873.
[4] S. M. Beck, Studies of silicon cluster–metal atom compound formation in a supersonic molecular beam, J. Chem. Phys., 1987, 87: 4233-4234.
[5] S. M. Beck, Mixed metal–silicon clusters formed by chemical reaction in a supersonic molecular beam: Implications for reactions at the metal/silicon interface, J. Chem. Phys., 1989, 90: 6306-6312.
[6] H. Hiura, T. Miyazaki, and T. Kanayama, Formation of metal-encapsulating Si cage clusters, Phys. Rev. Lett., 2001, 86: 1733-1736.
[7] M. Ohara, K. Koyasu, A. Nakajima, and K. Kaya, Geometric and electronic strucutures of metal (M)-doped silicon clusters (M=Ti, Hf, Mo and W), Chem. Phys. Lett., 2003, 371: 490-497.
[8] K. Koyasu, M. Akutsu, M. Mitsui, and A. Nakajima, Selective formation of MSi16 (M=Sc, Ti, and V), J. Am. Chem. Soc., 2005, 127: 4998-4999.
[9] V. Kumar and Y. Kawazoe, Metal-encapsulated fullerenelike and cubic caged clusters of silicon, Phys. Rev. Lett., 2001, 87: 045503-1-4.
[10] V. Kumar and Y. Kawazoe, Magic behavior of Si15M and Si16M (M=Cr, Mo, and W) clusters, Phys. Rev. B, 2002, 65: 073404-1-4.
[11] V. Kumar, T. M. Briere, and Y. Kawazoe, Ab initio calculations of electronic structures, polarizabilities, Raman and infrared spectra, optical gaps, and absorption spectra of M@Si16 (M=Ti and Zr) clusters, Phys. Rev. B, 2003, 68: 155412-1-9.
[12] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth, magic behavior, andelectronic and vibrational properties of Cr-doped Si clusters, Phys. Rev. B, 2004, 70: 245433-1-10.
[13] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth behavior of metal-doped silicon clusters SinM (M=Ti, Zr, Hf; n=8–16), Phys. Rev. B, 2005, 71: 075423-1-12.
[14] J. Lu and S. Nagase, Structural and electronic properties of metal-encapsulated silicon clusters in a large size range, Phys. Rev. Lett., 2003, 90: 115506-1-4.
[15] J. U. Reveles and S. N. Khanna, Electronic counting rules for the stability of metal-silicon clusters, Phys. Rev. B, 2006, 74: 035435-1-6.
[16] M. B. Torres, E. M. Fernández, L. C. Balbás, Theoretical study of isoelectronic SinM clusters (M=Sc?, Ti, V+; n=14–18), Phys. Rev. B, 2007, 75: 205425-1-12.
[17] J. Wang, Q. M. Ma, Z. Xie, et al., From SinNi to Ni@Sin: An investigation of configurations and electronic structure, Phys. Rev. B, 2007, 76(3): 035406-1-8.
[18] H. Prinzbach, A. Weiler, P. Landenberger, F. Wahl, J. Wrth, L. T. Scott, M. Gelmont, D. Olevano, and B. Issendor, Gas-phase production and photoelectron spectroscopy of the smallest fullerene C20, Nature (London), 2000, 407: 60-63.
[19] Z. X. Wang, X. Z. Ke, Z. Y. Zhun, F. Y. Zhu, M. L. Ruan, H. Chen, R. B. Huang, L. S. Zheng, A new carbon solid made of the world’s smallest caged fullerene C20, Phys. Lett. A, 2001, 280: 351-356.
[20] M. F. Jarrold, The smallest fullerene (news and views article), Nature (London), 2000, 407: 26-27.
[21] K. M. Ho, A. A. Shvartsburg, B. Pan, Z. Y. Lu, C. Z. Wang, J. G. Wacker, J. L. Fye, and M. F. Jarrold, Structures of medium-sized silicon clusters, Nature (London), 1998, 392: 582-585.
[22] A. A. Shvartsburg, B. Liu, Z. Lu, C. Z. Wang, M. F. Jarrold, and K. M. Ho, Structures of Germanium Clusters: Where the growth patterns of silicon and germanium clusters diverge, Phys. Rev. Lett., 1999, 83: 2167-2170.
[23] L. Mitas, J. C. Grossman, I. Stich, et al., Silicon clusters of intermediate size: Energetics, dynamics, and thermal effects, Phys. Rev. Lett., 2000, 84: 1479-1482.
[24] B. X. Li and P. L. Cao, Stable structures for Si20 clusters, Phys. Rev. A, 2000, 62:023201-1-5.
[25] J.Wang, J. Zhao, F. Ding, W. Shen, H. Lee, and G. H.Wang, Thermal properties of medium-sized Ge clusters, Solid State Commun., 2001, 117: 593-598.
[26] Q. Sun, Q. Wang, T. M. Briere, V. Kumar, and Y. Kawazoe, First-principles calculations of metal stabilized Si20 cages, Phys. Rev. B, 2002, 65: 235417-1-5.
[27] A. K. Singh, V. Kumar, and Y. Kawazoe, Stabilizing the silicon fullerene Si20 by thorium encapsulation, Phys. Rev. B, 2005, 71: 115429-1-6.
[28] A. Grubisic, H. P. Wang, Y. J. Ko, and K. H. Bowena, Photoelectron spectroscopy of europium-silicon cluster anions, EuSin? ( 3≤n≤17), J. Chem. Phys., 2008, 129: 054302-1-5.
[29] J.Wang and J. H. Liu, Novel bi-transition metallic encapsulated naphthalene-like Si20 prismatic cage: A DFT investigation, J. Comput. Chem., 30(7): 1103-1110.
[30] B. Liu, Z. Y. Lu, B. Pan, C. Z. Wang, K. M. Ho, A. A. Shvartsburg, and M. F. Jarrold, Ionization of medium-sized silicon clusters and the geometries of the cations, J. Chem. Phys., 1998, 109: 9401-9409.
[31] X. L. Zhu, X. C. Zeng, Y. A. Lei, and B. Pan, Structures and stability of medium silicon clusters II. Ab initio molecular orbital calculations of Si12–Si20, J. Chem. Phys., 2004, 120: 8985-8995.
[32] S. Yoo, and X. C. Zeng, Structures and stability of medium-sized silicon clusters III. Reexamination of motif transition in growth pattern from Si15 to Si20, J. Chem. Phys., 2005, 123: 164303-1-6.
[33] S. Goedecker, W. Hellmann, and T. Lenosky, Global minimum determination of the born-oppenheimer surface within density functional theory, Phys. Rev. Lett., 2005, 95: 055501-1-4.
[34] A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys., 1993, 98(7): 5648-5652.
[35] J. P. Perdew, K. Burke, and Y. Wang, Generalized gradient approximation for the exchange-correlation hole of a many-electron system, Phys. Rev. B, 1996, 54: 16533-16539.
[36] C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[37] M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., Gaussian 03, Revision D.01 (Gaussian, Inc., Wallingford CT, 2004).
[38] A. D. Zdetsis, Bonding and structural characteristics of Zn-, Cu-, and Ni-encapsulated Si clusters: Density-functional theory calculations, Phys. Rev. B, 2007, 75(8): 085409-1-10.
[39] B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules, J. Chem. Phys., 1990, 92(1): 508-517.
[40] J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B, 1992, 45: 13244-13249.
[41] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys., 1988, 88(4): 2547-2553; C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[42] R. S. Mulliken, Electronic population analysis on LCAO-MO molecular wave functions. II. Overlap populations, bond orders, and covalent bond energies, J. Chem. Phys., 1955, 23(10): 1841-1846.
[43] B. Delley, From molecules to solids with the DMol3 approach, J. Chem. Phys., 2000, 113(18): 7756-7764.
[44] S. Yoo and X. C. Zeng, Structures and relative stability of medium-sized silicon clusters IV. Motif-based low-lying clusters Si21-Si30, J. Chem. Phys., 2006, 124: 054304-1-6.
[45] J. Wang, H. Ning, Q. M. Ma, Y. Liu, and Y. C. Li, Au42: A possible ground-state noble metallic nanotube, J. Chem. Phys., 2008, 129(13): 134705-1-4; http://www.natureasia.com/asiamaterials/highlight.php?id=337.
[1] H. Haberland, Clusters of Atoms and Molecules I and II, Berlin: Springer-Verlag, 1995.
[2] K. H. Meiwes-Broer, Clusters on Surfaces, Berlin: Springer-Verlag, 2000.
[3] V. Kumar, K. Esfarjani, and Y. Kawazoe, Cluster and Nanomaterials, Berlin: Spinger-Verlag, 2002.
[4] W. Eberhardt, Clusters as new materials, Surf. Sci., 2002, 500: 242-270.
[5] J. Bansmann, S. H. Baker, C. Binns, J. A. Blackman, J. P. Bucher, J. Dorantes-Dávila, V. Dupuis, L. Favre, D. Kechrakos, A. Kleibert, K. H. Meiwes-Broer, G. M. Pastor, A. Perez, O. Toulemonde, K. N. Trohidou, J. Tuaillon, and Y. Xie, Magnetic and structural properties of isolated and assembled clusters, Surf. Sci. Rep., 2005, 56: 189-275.
[6] I. M. L. Billas, A. Chatelain and W. A. de Heer, Magnetism from the atom to the bulk in nickel, cobalt and iron clusters, Science, 1994, 265(5179): 1682-1684.
[7] M. Sakurai, K. Watanabe, K. Sumiyama, and K. Suzuki, Magic numbers in transition metal (Fe, Ti, Zr, Nb, and Ta) clusters observed by time-of-flight mass spectrometry, J. Chem. Phys., 1999, 111(1), 235-238.
[8] J. L. Chen, C. S. Wang, K. A. Jackson, and M. R. Pederson, Theory of magnetic and structural ordering in iron clusters, Phys. Rev. B, 1991, 44: 6558-61.
[9] M. Castro and D. R. Salahub, Density-functional calculations for small iron clusters: Fen, Fen+, and Fen- for n≤5, Phys. Rev. B, 1994, 49: 11842-52.
[10] P. Ballone and R. O. Jones, Structure and spin in small iron clusters, Chem. Phys. Lett., 1995, 233: 632-638.
[11] O. Dieguez, M. M. G. Alemany, C. Rey, P. Ordejon, and L. J. Gallego, Density-functional calculations of the structures, binding energies, and magnetic moments of Fe clusters with 2 to 17 atoms, Phys. Rev. B, 2001, 63: 205407-1-6.
[12] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, binding energies andmagnetic moments of small iron clusters: A study based on all-electron DFT, Solid State Commun., 2007, 142: 114-119.
[13] H. Yoshida and A. Terasaki, Spin-polarized electronic structure of cobalt cluster anions studied by photoelectron spectroscopy, J. Chem. Phys., 1995, 102(15): 5960-5965.
[14] S. R. Liu, H. J. Zhai, and L. S. Wang, Electronic and structural evolution of Con clusters (n=1–108) by photoelectron spectroscopy, Phys. Rev. B, 2001, 64, 153402-1-4.
[15] X. S. Xu, S. Y. Yin, R. Moro, and W. A. de Heer, Magnetic Moments and Adiabatic Magnetization of Free Cobalt Clusters, Phys. Rev. Lett., 2005, 95: 237209-1-4.
[16] Z. Q. Li and B. L. Gu, Electronic-structure calculations of cobalt clusters, Phys. Rev. B, 1993, 47(20): 13611-14.
[17] H. J. Fan, C. W. Liu, and M. S. Liao, Geometry, electronic structure and magnetism of small Con (n=2?8) clusters, Chem. Phys. Lett., 1997, 273: 353-359.
[18] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic properties of small Co clusters, Phys. Lett. A, 2006, 358: 289-296.
[19] H. Basch, M. D. Newton, and J. W. Moskowitz, The electronic structure of small nickel atom clusters, J. Chem. Phys., 1980, 73(9): 4492-4510.
[20] F. A. Reuse and S. N. Khanna, Geometry, electronic structure, and magnetism of small Nin (n=2–6, 8, 13) clusters, Chem. Phys. Lett., 1995, 234: 77-81.
[21] S. E. Apsel, J. W. Emmert, J. Deng, and L. A. Bloomfield, Surface-Enhanced Magnetism in Nickel Clusters, Phys. Rev. Lett., 1996, 76: 1441-1444.
[22] X. G. Wan, L. Zhou, J. M. Dong, T. K. Lee, and D. S. Wang, Orbital polarization, surface enhancement and quantum confinement in nanocluster magnetism, Phys. Rev. B, 2004, 69: 174414-1-14.
[23] Z. Xie, Q. M. Ma, Y. Liu, and Y. C. Li, First-principles study of the stability and Jahn-Teller distortion of nickel clusters, Phys. Lett. A, 2005, 342: 459-467.
[24] W. Y. Ching, Y. N. Xu, B. N. Harmon, J. Ye, and T. C. Leung, Electronicstructures of FeB, Fe2B, and Fe3B compounds studied using first-principles spin-polarized calculations, Phys. Rev. B, 1990, 42: 4460-70.
[25] J. Hafner, M. Tegze, and Ch Becke, Amorphous magnetism in Fe-B alloys: First-principles spin-polarized electronic-structure calculations, Phys. Rev. B, 1994, 49: 285-298.
[26] M. L. Fdez-Gubieda, A. García-Arribas, J. M. Barandiarán, R. López Antón, I. Orue, P. Gorria, S. Pizzini, and A. Fontaine, Magnetic Compton scattering study of the ferromagnetic amorphous alloys Fe1-xBx, Phys. Rev. B, 2001, 63: 220404-1-4.
[27] Z. Y. Jiang, C. J. Yang, and S. T. Li, Structures and stability of B-doped Al clusters: AlnB and AlnB2 (n=1–7), J. Chem. Phys., 2005, 123(20): 204315-1-7.
[28] Q. Sun, X. G. Gong, Q. Q. Zheng, and G, H, Wang, The structures and magnetic properties of small Fe/sub n/B clusters, J. Phys.: Condens. Matter, 1996, 8(11): 1805-1810.
[29] G. S. Painter and F. W. Averill, Effects of segregation on grain-boundary cohesion: A density-functional cluster model of boron and sulfur in nickel, Phys. Rev. Lett., 1987, 58: 234-237.
[30] M. Deshpande, D. G. Kanhere, and R. Pandey, Structures, energetics, and magnetic properties of NinB clusters with n=1–8, 12, Phys. Rev. A, 2005, 71: 063202-1-7.
[31] D. B. Zhang and J. Shen, Ground state, growth, and electronic properties of small lanthanum clusters, J. Chem. Phys., 2004, 120(11): 5104-5109.
[32] D. B. Zhang and J. Shen, First principles study of the stability and electronic structure of the icosahedral La13, La13-1, and La13+1 clusters, J. Chem. Phys., 2004, 120(11): 5081-5086.
[33] N. Liu, Q. M. Ma, Z. Xie, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic moments of small lanthanum–nickel clusters, Chem. Phys. Lett., 2007, 436: 184-188.
[34] J. Wang, Q. M. Ma, Z. Xie, Y. Liu, and Y. C. Li, From SinNi to Ni@Sin: An investigation of configurations and electronic structure, Phys. Rev. B, 2007, 76:035406-1-8.
[35] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures and magnetic moments of Fe-C clusters, Phys. Rev. B, 2007, 76(3): 035412-1-7.
[36] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic properties of small Co clusters, Phys. Lett. A, 2006, 358: 289-296.
[37] B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules , J. Chem. Phys., 1990, 92(1): 508-517.
[38] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys., 1988, 88(4): 2547-2553.
[39] C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 1988, 37(2): 785-789.
[40] Electron Population Analysis on LCAO-MO Molecular wave functions. II. overlap population, bond orders, and covalent bond energies, J. Chem. Phys., 1955, 23(10): 1841-1846.
[41] B. Delley, From molecules to solids with the DMol3 approach, J. Chem. Phys., 2000, 113(18): 7756-7764.
[42] X. G. Wan, L. Zhou, J. M. Dong, T. K. Lee, and D. S. Wang, Orbital polarization, surface enhancement and quantum confinement in nanocluster magnetism, Phys. Rev. B, 2004, 69: 174414-1-14.
[43] N. Fujima and T. Yamaguchi, Magnetic moment in Ni clusters estimated by an electronic-shell model, Phys. Rev. B, 1996, 54: 26-28.
[1] H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, C60: buckminsterfullerene, Nature, 1995, 318: 162-163.
[2] S. Iijima, Helical microtubules of graphitic carbon, Nature, 1991, 354: 56-58.
[3] T. W. Ebbesen and P. M. Ajayan, Large-scale synthesis of carbon nanotubes, Nature, 1992, 358: 220-222.
[4] S. Iijima and T. Ichihashi, Single-shell carbon nanotubes of 1-nm diameter, Nature, 1993, 363: 603-605.
[5] D. S. Bethune and C. H. Kiang, Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer walls, Nature, 1993, 363: 605-607.
[6] Y. Kondo and K. Takayanag, Synthesis and Characterization of Helical multi-shell gold nanowires, Science, 2000, 289(5479): 606-608; E. Tosatti and S. Prestipino, Weird gold nanowire, Science, 2000, 289(5479): 561-563.
[7] Y. Oshima and A. Onga, Helical gold nanotube synthesized at 150 K, Phys. Rev. Lett., 2003, 91(20): 205503-1-4.
[8] M. D. Valle, C. Tejedor, and Gianaurelio Cuniberti, Scaling of the conductance in gold nanotubes, Phys. Rev. B, 2006, 74(4): 045408-1-5.
[9] F. Delogu, Numerical study of the melting behavior of Au nanotubes, Phys. Rev. B, 2007, 75(23): 235421-1-8.
[10] Y. Iguchi, T. Hoshi, and T. Fujiwara, Two-stage formation model and helicity of gold nanowires, Phys. Rev. Lett., 2007, 99(12): 125507-1-4.
[11] J. Li, X. Li, H. J. Zhai, and L. S. Wang, Au20: A tetrahedral cluster, Science, 2003, 299(5608): 864-867.
[12] X. Gu, M. Ji, S. H. Wei, and X. G. Gong, AuN clusters (N=32,33,34,35): Cagelike structures of pure metal atoms, Phys. Rev. B, 2004, 70(20): 205401-1-5.
[13] M. P.Johansson, D.Sundholm, and J. Vaara, Au32: A 24-carat golden fullerene, Angew. Chem. Int. Ed., 2004, 43: 2678-2681.
[14] J. L.Wang, G. H. Wang, and J. J. Zhao, Density-functional study of Aun(n=2–20) clusters: Lowest-energy structures and electronic properties, Phys. Rev. B, 2002, 66(3): 035418-1-6.
[15] L. Xiao and L. C. Wang, From planar to three-dimensional structural transition in gold clusters and the spin–orbit coupling effect, Chem. Phys. Lett., 2004, 392: 452-455.
[16] E. M. Fernandez, J. M.Soler, I. L.Garzon, and L. C.Balbas, Trends in the structure and bonding of noble metal clusters, Phys. Rev. B, 2004, 70(16): 165403-1-14.
[17] R. M. Olson, S. Varganov, M. S. Gordon, H. Metiu, S. Chretien, P. Piecuch, K.Kowalski, S. A.Kucharski, and M. Musial, Where does the planar-to-nonplanar turnover occur in small gold clusters? J. Am. Chem. Soc., 2005, 127(3): 1049-1052.
[18] P. Koskinen, H. H?kkinen, B. Huber, B. V. Issendorff, and M. Moseler, Liquid-liquid phase coexistence in gold clusters: 2D or not 2D? Phys. Rev. Lett., 2007, 98(1): 015701-1-4.
[19] W. Fa and J. M. Dong, Possible method to determine the two-dimensional to three-dimensional crossover of gold clusters by examining their vibrational modes, Appl. Phys. Lett., 2006, 89(1): 013117-1-3.
[20] F. Furche, R. Ahlrichs, P.Weis, C. Jacob, S.Gilb, T. Bierweiler, and M. M. Kappes, The structures of small gold cluster anions as determined by a combination of ion mobility measurements and density functional calculations, J. Chem. Phys., 2002, 117: 6982-6990.
[21] H. Hakkinen, B. Yoon, U. Landman, X. Li, H. J. Zhai, and L. S.Wang, On the electronic and atomic structures of small AuN- (N=4-14) clusters: A photoelectron spectroscopy and density-functional study, J. Phys. Chem. A, 2003, 107: 6168-6175.
[22] S. Gilb, P. Weis, F. Furche, R. Ahlrichs, and M. M. Kappes, Structures of small gold cluster cations (Aun+, n<14): Ion mobility measurements versus density functional calculations, J. Chem. Phys., 2002, 116: 4094-4101.
[23] M. Ji, X. Gu, X. Li, X. G. Gong, J. Li, and L. S.Wang, An experimental and theoretical investigation of the electronic and geometrical structures of the special Au32 cluster, Angew. Chem. Int. Ed., 2005, 44: 7119-7123.
[24] S. Bulusu, X. Li, L. S.Wang, and X. C. Zeng, Evidence of hollow golden cages, Proc. Natl. Acad. Sci., 2006, 103: 8326-8330.
[25] D. X. Tian, J. J. Zhao, B. L. Wang, and R. B. King, The dual relationship between large gold clusters (antifullerenes) and carbon fullerenes: a new lowest-energy cage structure for Au50, J. Phys. Chem. A, 2007, 111(3): 411-414.
[26] A. J. Karttunen, M. Linnolahti, T. A. Pakkanen, and P. Pyykk?, Icosahedral Au72: a predicted chiral and spherically aromatic golden fullerene, Chem. Commun., 2008, 4: 465-467.
[27] Y. Gao and X. C. Zeng, Au42: An alternative icosahedral golden fullerene cage, J. Am. Chem. Soc., 2005, 127(12): 3698-3699.
[28] R. T. Senger, S. Dag, and S. Ciraci, Chiral single-wall gold nanotubes, Phys. Rev. Lett., 2004, 93(19): 196807-1-4.
[29] X. P. Yang and J. M. Dong, Geometrical and electronic structures of the (5, 3) single-walled gold nanotube from first-principles calculations, Phys. Rev. B, 2005, 71(23): 233403-1-4.
[30] Y. Mokrousov, G. Bihlmayer, and S. Blügel, Full-potential linearized augmented plane-wave method for one-dimensional systems: Gold nanowire and iron monowires in a gold tube, Phys. Rev. B, 2005, 72(4): 045402-1-15.
[31] W. Fa and J. M. Dong, Possible ground-state structure of Au26: a highly symmetric tubelike cage, J. Chem. Phys., 2006, 124(11): 114310-1-4.
[32] W. Fa, C. F. Luo, and J. M. Dong, Bulk fragment and tubelike structures of AuN (N=2-26), Phys. Rev. B, 2005, 72(20): 205428-1-4.
[33] J. L. Wang, J. Jellinek, J. J. Zhao, Z. F. Chen, R. B. King, and P. R. Schleyer, Hollow cages versus space-filling structures for medium-sized gold clusters: The spherical aromaticity of the Au50 cage, J. Phys. Chem. A, 2005, 109(41): 9265-9269.
[34] B. Delley, Hardness conserving semilocal pseudopotentials, Phys. Rev. B, 2002,66(15): 155125-1-9.
[35] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1996, 77(18): 3865-3868.
[36] J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B, 1992, 45: 13244-49.
[37] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys., 1988, 88(4): 2547-2553.
[38] C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[39] B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules, J. Chem. Phys., 1990, 92(1): 508-517.
[40] See http://www-wales.ch.cam.ac.uk/CCD.html.
[41] J. Wang, H. Ning, Q. M. Ma, Y. Liu,and Y. C. Li, Au42: A possible ground-state noble metallic nanotube, J. Chem. Phys. 2008, 129(13): 134705-1-4.
[1] H. Kroto, J. Heath, S. OBrien, R. Curl, and R. Smalley, C60: buckminsterfullerene, Nature (London), 1985, 318: 162-163.
[2] S. Iijima, Helical microtubules of graphitic carbon, Nature (London), 1991, 354: 56-58.
[3] S. Iijima and T. Ichihashi, Single-shell carbon nanotubes of 1-nm dimeter, Nature, 1993, 363: 603-605.
[4] D. S. Bethune, C. H. Klang, M. S. Vries, et al., Cobalt-catalysed grownth of carbon nanotubes with single-atomic-layer walls, Nature, 1993, 363: 605-607.
[5] R. Saito, M. Fujita,M. S. Dresselaus,et al., Electronic structure of chiral graphene tubules, Appl. Phys. Lett., 1992, 60(18): 2204-06.
[6] W. Z. Li,S. X. Xie,B. H. Chang,et al., Large-Scale Synthesis of Aligned Carbon Nanotubes, Science, 1996, 274(5293): 1701-1703.
[7] M. Yudasaka,T. Ichihashi, T. Komatsu, et al.,Single-wall carbon nanotubes formed by a single larser-beampusle, Chem. Phys. Lett., 1999, 299: 9196.
[8] A. M. Cassell,N. R. Franklin, T. W. Tombler, et al., Direeted Growth of Free-Standing Single-Walled Carbon Nanotubes, Am. Chem. Soc. 1999, 121: 7975-7976.
[9]解思深,潘正伟,超长定向碳纳米竹列阵的制备,物理, 1999, 28(1): 1.
[10] L. Chico,V. H. Crespi, L. X. Benedict, et al., Pure carbon nanoscale devices: Nanotube heterojunctions, Phys. Rev. Lett., 1996, 76(6): 971-974.
[11] M. R. Falvo, G. J. Clary, R. M. Taylor,et al., Superfine, Bending and buckling of carbon nanotubes under large strain, Nature, 1997, 389: 582-584.
[12] A. Krishnan, E. Dujardin, T. W. Ebbesen, et al., Young's modulus of single-walled nanotubes, Phys. Rev. B, 1998, 58(20): 14013-19.
[13] S. S. Fan, M. G. Chapline,N. R. Franklin, et al., Self-oriented regular arrays of carbon nanotubes and their field emission properties, Science, 1999, 283(5401):512-514.
[14] R. H. Baughman, A. A. Zakhidov, and W. A. de Heer, Carbon Nanotubes--theRoute Toward Applications, Science, 2002, 297: 787-792.
[15] H. J. Zhai, B. Kiran, J. L. Li, and L. S. Wang, Hydrocarbon analogues of boronclusters--planarity, aromaticity and antiaromaticity, Nat. Mater., 2003, 2: 827-833.
[16] B. Kiran, S. Bulusu, H. J. Zhai, S. Yoo, X. C. Zeng, and L. S. Wang,Planar-to-tubular structural transition in boron clusters: B20 as the embryo ofsingle-walled boron nanotubes, Proc. Natl. Acad. Sci. U.S.A., 2005, 102: 961-964.
[17] S. Chacko, D. G. Kanhere, and I. Boustani, Ab initio density functionalinvestigation of B24 clusters: Rings, tubes, planes, and cages, Phys. Rev. B, 2003,68(3): 035414-1-11.
[18] I. Boustani, A. Rubio, and J. Alonso, Ab initio study of B32 clusters: competitionbetween spherical, quasiplanar and tubular isomers, Chem. Phys. Lett., 1999, 311:21-28.
[19] A. Quandt and I. Boustani, Boron Nanotubes, Chem. Phys. Chem., 2005, 6:2001-2008.
[20] I. Boustani and A. Quandt, Nanotubules of bare boron clusters: Ab initio anddensity functional study, Europhys. Lett., 1997, 39: 527-532.
[21] D. Ciuparu, R. F. Klie, Y. Zhu, and L. Pfefferle, Synthesis of Pure BoronSingle-Wall Nanotubes, J. Phys. Chem. B, 2004, 108: 3967-3969.
[22] K. C. Lau, R. Pati, R. Pandey, and A. C. Pineda, First-principles study of thestability and electronic properties of sheets and nanotubes of elemental boron, Chem.Phys. Lett., 2006, 418: 549-554.
[23] I. Cabria, M. J. Lopez, and J. A. Alonso, Density functional calculations ofhydrogen adsorption on boron nanotubes and boron sheets, Nanotechnology, 2006,17: 778-785.
[24] T. T. Xu, J. G. Zheng, N. Wu, A. W. Nicholls, J. R. Roth, D. A. Dikin, and R. S.Ruoff, Crystalline Boron Nanoribbons:Synthesis and Characterization, Nano Lett.,2004, 4: 963-968.
[25] J. Kunstmann and A. Quandt, Broad boron sheets and boron nanotubes: An ab initio study of structural, electronic, and mechanical properties, Phys. Rev. B, 2006, 74: 035413-1-14.
[26] R. N. Grimes, Boron clusters come of age, J. Chem. Educ., 2004, 81(5): 658-672.
[27] N. G. Szwacki, A. Sadrzadeh, and B. I. Yakobson, B80 Fullerene: An Ab Initio Prediction of Geometry, Stability, and Electronic Structure, Phys. Rev. Lett., 2007, 98: 166804-1-4.
[28] H. Tang and S. I. Beigi, Novel Precursors for Boron Nanotubes: The Competition of Two-Center and Three-Center Bonding in Boron Sheets, Phys. Rev. Lett., 2007, 99: 115501-1-4.
[29] X. Yang, Y. Ding, and J. Ni, Ab initio prediction of stable boron sheets and boron nanotubes: Structure, stability, and electronic properties, Phys. Rev. B, 2008, 77: 041402-1-4.
[30] A. K. Singh, A. Sadrzadeh, and B. I. Yakobson, Probing Properties of Boronα-Tubes by Ab Initio Calculations, Nano Lett., 2008, 8: 1314-17.
[31] G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B, 1993, 47: 558-561; Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium, Phys. Rev. B, 1994, 49: 14251-69.
[32] D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B, 1990, 41: 7892-95.
[33] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation, Phys. Rev. B, 1992, 46: 6671-87.
[34] H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B, 1976, 13: 5188-92.
[35] B. Delley, An all-electron numerical method for solving the local densityfunctional for polyatomic molecules, J. Chem. Phys., 1990, 92(1): 508-517.
[36] J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B, 1992, 45: 13244-49.
[37] B. Delley, From molecules to solids with the DMol3 approach, J. Chem. Phys., 2000, 113(18): 7756-7764.
[2] G. D. Stein, Atoms and molecules in small aggregates, Phys. Teach., 1997, 17: 503-512.
[3]王广厚,离子簇的奇异性质,物理学进展, 1987, 7: 1.
[4] E. W. Becker, Strahlen aus kondensierten Atomen und Molekeln im Hochvakuum, Z. Phys. 1956, 146(3): 333-338.
[5] W. D. Knight, K. Clemenger, W. A. de Heer, W. A. Saunders, M. Y. Chou, and M. L. Cohen, Electronic Shell Structure and Abundances of Sodium Clusters.Phys. Rev. Lett., 1984, 52(24): 2141-2143.
[6] H. W. Kroto, J. R. Heath, S. C. O'Brien, R. F. Curl,and R. E. Smaller, C60: Buckminsterfullerene, Nature, 1985, 318: 162-163.
[7] I .A. Harris, R. S. Kidwell,and J. A. Northby, Structure of Charged Argon Clusters Formed in a Free Jet Expansion, 1984, Phys. Rev. Lett., 53: 2390-2393.
[8] K. Rademann, B. Kaiser, U. Even, and F. Hensel,Size dependence of the gradual transition to metallic properties in isolated mercury clusters, Phys. Rev. Lett., 1987, 59: 2319-2321.
[9] O. Cheshnovsky, K. J. Taylor, J. Conceicao, and R. E. Smalley, Ultraviolet photoelectron spectra of mass-selected copper clusters: Evolution of the 3d band, Phys. Rev. Lett., 1990, 64: 1785-1788.
[10] J. Ho, K. M. Ervin, and W. C. Lineberger, Photoelectron spectroscopy of metal cluster anions: Cun-, Agn-, and Aun-, J. Chem. Phys., 1990, 93: 6987-7002.
[11] B. Kaiser and K. Rademann, Photoelectron spectroscopy of neutral mercury clusters Hgx (x≤109) in a molecular beam, Phys. Rev. Lett., 1992, 69: 3204-3207.
[12] J. Sinfelt, Structure of metal catalysts, Rev. Mod. Phys., 1979, 51: 569-589, and the references therein.
[13] S. N. Khanna and S. Linderoth, Magnetic behavior of clusters of ferromagnetic transition metals, Phys. Rev. Lett., 1991, 67: 742-745.
[14] D. M. Cox, D. J. Trevor, R. L. Whetten, E. A. Rohlfing, and A. Kaldor, Magnetic behavior of free-iron and iron oxide clusters, Phys. Rev. B, 1985, 32: 7290-7298.
[15] J. G. Louderback, A. J. Cox, L. J. Lising, D. C. Douglass, and L. A. Bloomfield, Magnetic properties of nickel clusters, Z. Phys. D, 1993, 26: 301-303.
[16] J. P. Bucher, D. C. Douglass, and L. A. Bloomfield, Magnetic properties of free cobalt clusters, Phys. Rev. Lett., 1991, 66: 3052-3055.
[17] D. C. Douglass, A. J. Cox, J. P. Bucher, and L. A. Bloomfield, Magnetic properties of free cobalt and gadolinium clusters, Phys. Rev. B, 1993, 47: 12874-12889.
[18] I. M. L. Billas,J. A. Becker, A. Chatelain, and W. A. de Heer, Magnetic moments of iron clusters with 25 to 700 atoms and their dependence on temperature, Phys. Rev. Lett., 1993, 71: 4067-4070.
[19] I. M. L. Billas, A. Chatelain, and W. A. de Heer, Magnetism in transition-metal clusters from the atom to the bulk, Surf. Rev. Lett., 1996, 3: 429-434.
[20] J. Zhao, M. Han, and G. Wang, Ionization potentials of transition-metal clusters, Phys. Rev. B, 1993, 48: 15297-15300, and the references therein.
[21] F. Liu, S. N. Khanna, and P. Jena, Magnetism in small vanadium clusters, Phys. Rev. B, 1991, 43: 8179-8182.
[22] K. Lee and J. Callaway, Electronic structure and magnetism of small V and Cr clusters, Phys. Rev. B, 1993, 48: 15358-15364.
[23] J. Dorantes-Dávila, and H. Dreysse, Magnetic behavior of small vanadium clusters, Phys. Rev. B, 1993, 47: 3857-3863.
[24] P. Alvarado, J. Dorantes-Dávila, and H. Dreysse, Structural effects on the magnetism of small vanadium clusters, Phys. Rev. B, 1994, 50: 1039-1045.
[25] G. M. Pastor, J. Dorantes-Dávila, and K. H. Bennemann, Size and structural dependence of the magnetic properties of small 3d-transition-metal clusters, Phys. Rev. B, 1989, 40: 7642-7654.
[26] H. Cheng and L. S. Wang, Dimer growth, structural transition, and antiferromagnetic ordering of small chromium clusters, Phys. Rev. Lett., 1996, 77: 51-54.
[27] D. C. Douglass, J. P. Bucher, and L. A. Bloomfield, Magnetic studies of free nonferromagnetic clusters, Phys. Rev. B, 1992, 45: 6341-6344.
[28] A. J. Cox, J. G. Louderback, and L. A. Bloomfield, Experimental observation of magnetism in rhodium clusters, Phys. Rev. Lett., 1993, 71: 923-926.
[29] A. J. Cox, J. G. Louderback, S. E. Aspel,and L. A. Bloomfield, Magnetism in 4d-transition metal clusters, Phys. Rev. B, 1994, 49: 12295-12298.
[30] Kreibig and M. Vollmer, Optical properties of metal c1usters, Springer-Verlag, Berlin Herdelberg, 1995.
[31] K. Selby, M. Vollmer, J. Masui,V. Kresin, W. A. de Heer, and W. D. Knight, Surface plasma resonances in free metal clusters, Phys. Rev. B, 1989, 40: 5417-5427.
[32] M. Brack, Multipole vibrations of small alkali-metal spheres in a semiclassical description, Phys. Rev. B, 1989, 39: 3533-3542.
[33] V. Kresin, Surface and volume collective modes in small clusters and their interaction with single-particle levels, Z. Phys. D, 1991, 19: 105-107.
[34] L. D. Landau and E. M. Lifshits, Quantum Mechanics, 3rd ed.,Pergamon, Oxford, 1977.
[35] L. Genzel,T. P. Martin, and U. Kreibig, Dielectric function and plasma resonances of small metal particles, Z. Phys. B, 1975, 21(4): 339-346.
[36] U. Kreibig and L. Genzel, Optical absorption of small metallic particles, Surf. Sci., 1985, 156: 678-700.
[37] X. Chen, J. Zhao, and G. Wang, Conductance resonance of metal-insulator-metal junction with embedded metal cluster, Appl. Phys. Lett., 1994, 65(19): 2419-21.
[38] J. X. Ma, M. Han, H. Q. Zhang, Y. C. Gong, and G. H. Wang, Dense randompacking formation of gold cluster-based film characterized by scanning tunneling microscope, Appl. Phys. Lett., 1994, 65: 1513-1515.
[39]王广厚,原子团簇科学,科技导报, 1994, 10: 9-11.
[40] S. Bjornholm, Clusters, condensed matter in embryonic form, Contemp. Phys., 1990, 31(5): 309-324.
[41]冯瑞,金国钧,凝聚态物理学的新进展Ⅲ,物理学进展, 1991, 11: 373.
[42]王金兰,半导体团体结构和性质及金纳米线热力学稳定性的理论研究,南京大学博士论文, 2001.
[43] K. Rademann, B. Kaiser, U. Even, and F. Hensel, Size dependence of the gradual transition to metallic properties in isolated mercury clusters, Phys. Rev. Lett., 1987, 59: 2319-2321.
[44] J. Ho, K. M. Ervin, and W. C. Lineberger, Photoelectron spectroscopy of metal cluster anions: Cun-, Agn-, and Aun-, J. Chem. Phys., 1990, 93: 6987-7002.
[45] K. Rademann, B. Kaiser, U. Even, and F. Hensel, Size dependence of the gradual transition to metallic properties in isolated mercury clusters, Phys. Rev. Lett., 1987, 59: 2319-22.
[46] J. L. Wang, G. H. Wang, and J. J. Zhao, Nonmetal-metal transition in Znn (n=2–20) clusters, Phys. Rev. A, 2003, 68: 013201-1-6.
[47] J. L. Wang, G. H. Wang, and J. J. Zhao, Density functional study of beryllium clusters, with gradient correction, J. Phys. Condens. Matter, 2001, 13: L753-L758.
[48] J. G. Louderback, A. J. Cox, L. J. Lising, D. C. Douglass, and L. A. Bloomfield, Magnetic properties of nickel clusters, Z. Phys. D, 1993, 26: 301-303.
[49] J. P. Bucher, D. C. Douglass, and L. A. Bloomfield, Magnetic properties of free cobalt clusters, Phys. Rev. Lett., 1991, 66: 3052-3055.
[50] J. Zhao, M. Han, and G. Wang, Ionization potentials of transition-metal clusters, Phys. Rev. B, 1993, 48: 15297-15300, and the references therein.
[51] S. N. Khanna and S. Linderoth, Magnetic behavior of clusters of ferromagnetic transition metals, Phys. Rev. Lett., 1991, 67: 742-745.
[52] D. M. Cox, D. J. Trevor, R. L. Whetten, E. A. Rohlfing, and A. Kaldor,Magnetic behavior of free-iron and iron oxide clusters, Phys. Rev. B, 1985, 32: 7290-7298.
[53] J. L. Wang, J. J. Zhao, F. Ding, W. F. Shen, H. Lee and G. H. Wang, Thermal properties of medium-sized Ge clusters, Solid State Commun., 2001, 117: 593-598.
[54] J. L. Wang, F. Ding, W. F. Shen, T. X. Li, G. H. Wang, and J. J. Zhao, Thermal behavior of Cu-Co bimetallic clusters, Solid State Commun., 2001, 119: 13-18.
[55] C. Binns, Nanoclusters deposited on surfaces, Surf. Sci. Rep., 2001, 44: 1-49.
[56]王远,徐东升,纳米尺度分子工程研究,新世纪的物理化/学科前沿与展望,科学出版社出版, 2004: 31.
[57] M. D. Ventra, S. T. Pantelides, and N. D. Lang, First-Principles calculation of transport properties of a molecular device, Phys. Rev. Lett., 2000, 84: 979-982.
[58] Y. Q. Xue, S. Datta, and M. A. Ratner, Charge transfer and "band lineup" in molecular electronic devices: A chemical and numerical interpretation, J. Chem. Phys., 2001, 115(9): 4292-4299.
[59] N. D. Lang, and P. Avouris, Electrical conductance of parallel atomic wires, Phys. Rev. B, 2000, 62: 7325-7392.
[60] R. N. Barnett, and U. Landman, Cluster-derived structures and fluctuations in nanowires, Nature, 1997, 387: 788-791.
[61] J. Lu, X. W. Zhang, and X. G. Zhao, Metal-cage hybridization in endohedral La@C60, Y@C60 and Sc@C60, Chem. Phys. Lett., 2000, 332: 51-57.
[62] C. Zybill, Structure and reactivity of silicon clusters in the gas phase, Angew. Chem. Int. Ed. Engl., 1992, 31: 173-174.
[63] Z. Slanina, S. L. Lee, K. Kobayashi, and S. Nagase, C61 clusters: AM1 computations, J. Mol. Struct.: THEOCHEM, 1994, 312: 173-179.
[64] K. M. Ho, A. A. Shvartsburg, B. Pan, Z. Y. Lu, C. Z. Wang, J. G. Wacker, J. L. Fye, and M. F. Jarrold, Structures of medium-sized silicon clusters, Nature, 1998, 392: 582-585.
[65] F. Hagelberg, J. Leszczynski, V. Murashov, Theoretical investigations on small closed-shell siliconN clusters, J. Mol. Struct.: THEOCHEM, 1998, 454: 209-216.
[66] I. Rata, A. A. Shvartsburg, M. Horoi, T. Frauenheim, K. W. M. Siu, and K. A. Jackson, Single-Parent Evolution Algorithm and the optimization of Si clusters, Phys. Rev. Lett., 2000, 85: 546-549.
[67] J. G. Han, Z. Y. Ren, L. S. Sheng, Y. W. Zhang, J. A. Morales, F. Hagelberg, The formation of new silicon cages: a semiempirical theoretical investigation, J. Mol. Struct.: THEOCHEM, 2003, 625: 47-58.
[68] K. Jackson, B. Nellemore, Zr@Si20: a strongly bound Si endohedral system, Chem. Phys. Lett., 1996, 254: 249-256.
[69] J. G. Han and F. Hagelberg, A density functional theory investigation on CrSin (n=1-6) Clusters, Chem. Phys., 2001, 263: 255-263.
[70] J. G. Han, A computational study on electronic structures of GenF? and GenF (n=3–6) clusters by density functional theory, Chem. Phys. Lett., 2000, 324: 143-148.
[71] J. G. Han, Density functional studies on the molecular geometries, vibrational frequencies, electron affinities of X2F? (X=C, Si, Ge) cluster, J. Mol. Struct.: THEOCHEM, 1999, 491: 41-47.
[72] J. G. Han and Y. Y. Shi, A computational study on geometries, electronic structures and ionization potentials of MSi15 (M=Cr, Mo, W) clusters by density functional method, Chem. Phys., 2001, 266(1): 33-40.
[73] J. J. Scherer, J. B. Paul,C. P. Collier, R. J. Saykally, Cavity ringdown laser absorption spectroscopy and time-of-flight mass spectroscopy of jet-cooled copper silicides, J. Chem. Phys., 1995, 102(13): 5190-5199.
[74] Y. M. Harrick, W. Jr. Weltner, Quenching of angular momentum in the ground states of VC, NbC, VSi, and NbSi molecules, J. Chem. Phys., 1991, 94(5): 3371-3380.
[75] H. Hiura, T. Miyazaki, and T. Kanayama, Formation of Metal-Encapsulating Si Cage Clusters, Phys. Rev. Lett., 2001, 86(9): 1733-1736.
[76] M. Ohara, K. Koyasu, A. Nakajima, and K. Kaya, Geometric and electronic structures of metal (M)-doped silicon clusters (M=Ti, Hf, Mo and W), Chem. Phys.Lett., 2003, 371: 490-497.
[77] K. Koyasu, M. Akutsu, M. Mitsui, and A. Nakajima, Selective Formation of MSi16 (M = Sc, Ti, and V), J. Am. Chem. Soc., 2005, 127(14): 4998-4999.
[78] V. Kumar and Y. Kawazoe, Metal-encapsulated fullerenelike and cubic caged clusters of silicon, Phys. Rev. Lett., 2001, 87: 045503-1-4.
[79] J. Lu and S. Nagase, Structural and electronic properties of metal-encapsulated silicon clusters in a large size range, Phys. Rev. Lett., 2003, 90: 115506-1-4.
[80] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth behavior of metal-doped silicon clusters SinM(M= Ti, Zr, Hf; n= 8-16), Phys. Rev. B, 2005, 71: 075423-1-12.
[81] J. U. Reveles and S. N. Khanna, Electronic counting rules for the stability of metal-silicon clusters, Phys. Rev. B, 2006, 74: 035435-1-6.
[82] M. B. Torres, E. M. Fernández, L. C. Balbás, Theoretical study of isoelectronic SinM clusters (M=Sc-, Ti, V+; n=14–18), Phys. Rev. B, 2007, 75: 205425-1-14.
[83] C. Xiao, J. Blundell, F. Hagelberg, and W. A. Lester, Silicon clusters doped with an yttrium metal atom impurity, Jr., Int. J. Quantum Chem., 2004, 96: 416-425.
[84] L. J. Guo, X. Liu, G. F. Zhao, and Y. H. Luo, Computational investigation of TiSin (n=2–15) clusters by the density-functional theory, J. Chem. Phys., 2007, 126(23): 234704-1-7.
[85] J. Wang and J. G. Han, Geometries, stabilities, and electronic properties of different-sized ZrSin (n=1–16) clusters: A density-functional investigation, J. Chem. Phys., 2005, 123(6): 064306-1-16.
[86] P. Guo, Z. Y. Ren, F.Wang, J. Bian, J. G. Han, and G. H.Wang, Structural and electronic properties of TaSin (n=1–13) clusters: A relativistic density functional investigation, J. Chem. Phys., 2004, 121(24): 12265-75.
[87] J. G. Han and F. Hagelberg, A density functional theory investigation of CrSin (n=1–6) clusters, Chem. Phys., 2001, 263: 255-262.
[88] J. G. Han and F. Hagelberg, A density functional investigation of MoSin (n=1–6) clusters, J. Mol. Struct.: THEOCHEM, 2001, 549: 165-180.
[89] J. G. Han, C. Xiao, and F. Hagelberg, Geometric and electronic structure ofWSin (n=1-6, 12) clusters, Struct. Chem., 2002, 13: 173-191.
[90] J. G. Han, Z. Y. Ren, and B. Z. Lu, Geometries and stabilities of re-doped Si-n (n=1-12) clusters: a density functional investigation, J. Phys. Chem. A, 2004, 108(23): 5100-5110.
[91] L. Ma, J. J. Zhao, J. G. Wang, B. L. Wang, Q. L. Lu, and G. H. Wang, Growth behavior and magnetic properties of SinFe (n=2–14) clusters, Phys. Rev. B, 2006, 73(12): 125439-1-8.
[92] L. Ma, J. J. Zhao, J. G. Wang, Q. L. Lu, L. Z. Zhu, and G. H. Wang, Structure and electronic properties of cobalt atoms encapsulated in Sin(n=1–13) clusters, Chem. Phys. Lett., 2005, 411: 279-284.
[93] J. G. Han, A theoretical investigation on electronic properties and stability of IrSix (x=1–6) clusters, Chem. Phys., 2003, 286: 181-192.
[94] J. Wang, Q. M. Ma, Y. Liu, and Y. C. Li, From SinNi to Ni@Sin: An investigation of configurations and electronic structure, Phys. Rev. B, 2007, 76(3): 035406-1-8.
[95] C. Y. Xiao, F. Hagelberg, and W. A. Lester, Jr., Geometric, energetic, and bonding properties of neutral and charged copper-doped silicon clusters, Phys. Rev. B, 2002, 66(7): 075425-1-23.
[96] P. F. Zhang, J. G. Hana, and Q. R. Pu, A density functional investigation of AgSin (n=1?5) clusters, J. Mol. Struct.: THEOCHE, 2003, 635: 25-35.
[97] F. C. Chuang, Y. Y. Hsieh, C. C. Hsu, and M. A. Albao, Geometries and stabilities of Ag-doped Sin (n=1–13) clusters: A first-principles study, J. Chem. Phys., 2007, 127(14): 144313-1-6.
[1] B. J. Alder and T. E. Wainwright, Phase Transition for a Hard Sphere System, J. Chem. Phys., 1957, 27(5): 1208.
[2] J. B. Gibson, A. N. Goland, M. Milgram, and G. H. Vmeyard, Dynamics of Radiation Damage, Phys. Rev., 1960, 120: 1229-1253.
[3] D. W. Heermann著,秦克诚译,理论物理中的计算机模拟方法,北京:北京大学出版社, 1996.
[4][德] K. Binder, D. W. Heermann,秦克诚译,统计物理学中的蒙特卡罗模拟方法,北京:北京大学出版社, 1994.
[5]张孝泽,蒙特卡罗方法在统计物理中的应用,河南:科学技术出社, 1991.
[6] Y. H. Luo, J. J. Zhao, S. T. Qiu, and G. H. Wang, Genetic-algorithm prediction of the magic-number structure of (C60)N clusters with a first-principles interaction potential, Phys. Rev. B, 1999, 59(23): 14903-14906.
[7]王广厚,遗传算法研究原子团簇,物理学进展, 2000, 20(3): 252-275.
[8]徐光宪,黎乐民,王德民,量子化学(中册),科学出版社,1999: 678.
[9] D. R. Hartree, Proc. Combidge, The wave mechanics of an atom with a non-coulomb central field. I. Theory and methods, Phil. Soc., 1928, 24: 89-110.
[10] V. Fock, N?herungsmethode zur L?sung des quantenmechanischen Mehrk?rperproblems, Z. Physik, 1930, 61: 126-148.
[11] W. J. Hehre, L. Radom, P. R. Schleyer, et al., Ab initio molecular orbital theory. New York: John Wiley&Sons, 1996.
[12] P. R. Schleyer, Encyclopaedia of computational chemistry. New York: John Wiley &Sons, 1998.
[13] R. G. Parr, W. Yang, Density-functional theory of atoms and molecules. Oxford: Oxford Science, 1989.
[14] H. Thomas, The calculation of atomic fields, Proc. Camb. Phil. Soc., 1927, 23: 542-548.
[15] E. Fermi, Un Metodo Statistico per la Determinazione di alcune Priorieta dell'Atome", Rend. Accad. Naz. Lincei, 1927, 6: 602-607.
[16] P. Hohnberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. B, 1964, 136: 864-871.
[17] W. Kohn and L. J. Sham, Self-consistent equations including exchange and correlation effects, Phys. Rev. A, 1965, 140: 1133-1138.
[18] A. S. Joseph and A. C. Thorsen, De Haas-van Alphen effect and fermi surface in rhenium, Phys. Rev. A, 1964, 133: 1546-1552.
[19] C. F. Weiszacker, Zur Theorie der Kernmassen, Z. Phys., 1935, 96: 431-458.
[20] F. Perrot, Hydrogen-hydrogen interaction in an electron gas, J. Phys. Condens. Matter, 1994, 6: 431-446.
[21] L. W. Wang and M. P. Teter, Kinetic-energy functional of the electron density, Phys. Rev. B, 1992, 45(23): 1319 -13220.
[22] E. Smargiassi and P. A. Madden, Orbital-free kinetic-energy functionals for first-principles molecular dynamics, Phys. Rev. B, 1994, 49(8): 5220-5226.
[23] J. Callaway and N. H. March, Density functional methods: theory and applications, Solid State Phys., 1984, 38: 135-221.
[24] J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy. Phys. Chem. B, 1992, 45: 13244-49.
[25] J. C. Slater, A simplification of the Hartree-Fock method, Phys. Rev., 1951, 81(3): 385-390.
[26] J. C. Slater, T. M. Wilson, and J. H. Wood, Comparison of several exchange potentials for electrons in the Cu+ Ion, Phys. Rev., 1969, 179(1): 28-38.
[27] E. Wigner, On the interaction of electrons in metals, Phys. Rev., 1934, 46(11): 1002-1011.
[28] D. M. Ceperley and B. J. Alder, Ground state of the electron gas by a stochastic method, Phys. Rev. Lett., 1980, 45(7): 566-569.
[29] S. H. Vosko, L. Wilk, and M. Nusair, Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis, Canadian J.Phys., 1980, 58(8): 1200-1211.
[30] J. P. Perdew and A. Zunger, Self-interaction correction to density-functional approximations for many-electron systems, Phys. Rev. B, 1981, 23: 5048-5079.
[31] L. A. Cole and J. P. Perdew, Calculated electron affinities of the elements, Phys. Rev. A, 1982, 25(3): 1265-1271.
[32] A. D. Becke, Density-functional exchange-energy approximation with correct asymptotic behavior, Phys. Chem. A, 1988, 38: 3098-3100.
[33] J. P. Perdew, J. A. Chevary, S. H. Vosko, et al., Atomic, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation, Phys. Chem. B, 1992, 46: 6671-6687.
[34] J. P. Perdew, K. Burke, and Y. Wang, Generalized gradient approximation for the exchange-correlation hole of a many-electron system, Phys. Chem. B, 1996, 54: 16533-16539.
[35] M. Filatov and W. Thiel, A new gradient-corrected exchange-correlation density functional, Mol. Phys. 1997, 91(5): 847-859.
[36] G. J. Laming, V. Termath, and N. C. Handy, A general purpose exchange-correlation energy functional, J. Chem. Phys., 1993, 99: 8765-8773.
[37] A. D. Becke, Density functional calculations of molecular-bond energies, J. Chem. Phys., 1986, 84: 4524-4529.
[38] J. P. Perdew and Y. Wang, Accurate and simple density functional for the electronic exchange energy: Generalized gradient approximation, Phys. Rev. B, 1986, 33: 8800-8802.
[39] D. J. Lacks and R. G. Gordon, Pair interactions of rare-gas atoms as a test of exchange-energy-density functionals in regions of large density gradients, Phys. Rev. A, 1993, 47: 4681-4690.
[40] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1986, 77: 3865-3868.
[41] J. P. Perdew, Denstity-functional approximation for the correlation energy of the inhomogeneous electron gas, Phys. Rev. B, 1986, 33: 8822-8824.
[42] C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[43] A. D. Becke, A new mixing of Hartree-Fock and local density-functional theories, J. Chem. Phys., 1993, 98: 1372-1377.
[44] A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys., 1993, 98(7): 5648-5652.
[45] P. J. Stevens, J. F. Devlin, C. F. Chabalowski, and M. J. Frisch, Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields, J. Chem. Phys., 1994, 98(45): 11623-11627.
[46] A. D. Becke, A new dynamical correlation functional and implications for exact-exchange mixing, J. Chem. Phys., 1995, 104: 1040-1046.
[47] A. D. Becke, Systematic optimization of exchange-correlation functionals, J. Chem. Phys., 1997, 107: 8554-8560.
[48] A. D. Becke, A new inhomogeneity parameter in density-functional theory, J. Chem. Phys., 1998, 109: 2092-2098.
[49] C. Adamo and V. Barone, Toward reliable density functional methods without adjustable parameters: The PBE0 model, J. Chem. Phys., 1999, 110: 6158-6170.
[50] G. Kresse and J. Hafner, Norm-conserving and ultrasoft pseudopotentials for first-row and transition elements, J. Phys.: Condens. Matter, 1994, 6(40): 9245-8257.
[51] G. Kresse and J. Furthmiiller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B, 1996, 54(16): 11169-86.
[52] G. Kresse and J. Furthmuller, VASP the GUIDE [EB/01]. http://flcms.mpi.univie.ac.atlvasp/vasp/vasp.html
[53] G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B, 1999, 59(3): 1758-1775.
[54] E. Polak, Computational Methods in Optimization, New York: Academic, 1971.
[55] E. R. Davidson, In G. H. F Diercksen, and S. Wilson, eds., Methods inComputational Molecular Physics, NATO Advanced Study Institute, Series C: Mathematical and Physical Sciences, Plenum, New York, 113: 95.
[56] P Pulay, Convergence acceleration of iterative sequences: the case of scf iteration, Chem. Phys. Lett., 1980, 73(2): 393-398.
[57] H. J. Monkhorst and D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B, 1976, 13(12): 5188-5192.
[58] O. Jepsen and O. K. Andersen, The electronic structure of h.c.p. Ytterbium, Solid State Commun., 1971, 9(20): 1763-1767.
[59] P. E. Bltichl, O. Jepsen and O. K. Andersen, Improved tetrahedron method for Brillouin-zone Integrations, Phys. Rev. B, 1994, 49(23): 16223-16233.
[60] C. L. Fu and K. M. Ho, First-principles calculation of the equilibrium ground-state properties of transition metals: Applications to Nb and Mo, Phys. Rev. B, 1983, 28(10): 5480-5486.
[61] M. Methfessel and A. T. Paxton, High-precision sampling for Brillouin-zone integration in metals, Phys. Rev. B, 1989, 40(6): 3616-3621.
[1] S. Li, R. J. Van Zee, W. Weltner, Jr., and K. Raghavachari, Si3-Si7: Experimental and theoretical infrared spectra, Chem. Phys. Lett., 1995, 243: 275-280.
[2] E. Kaxiras and K. Jackson, Shape of small silicon clusters, Phys. Rev. Lett., 1993, 71(5): 727-730.
[3] U. Rothlisberger, W. Andreoni, and M. Parrinello, Structure of nanoscale silicon clusters, Phys. Rev. Lett., 1994, 72: 665-668.
[4] K. M. Ho, A. A. Shvartsburg, B. Pan, Z. Y. Lu, C. Z. Wang, J. G. Wacker, J. Fye, and M. F. Jarrold, Structures of medium-sized silicon clusters, Nature (London), 1998, 392: 582-585.
[5] I. Rata, A. A. Shvartsburg, M. Horoi, T. Frauenheim, K. W. Michael Siu, and K. A. Jackson, Single-parent evolution algorithm and the optimization of Si clusters, Phys. Rev. Lett., 2000, 85(3): 546-549.
[6] M. F. Jarrold and J. E. Bower, Mobilities of silicon cluster ions: The reactivity of silicon sausages and spheres, J. Chem. Phys., 1992, 96(12): 9180-9190.
[7] S. M. Beck, Studies of silicon cluster-metal atom compound formation in a supersonic molecular beam, J. Chem. Phys., 1987, 87: 4233-4234.
[8] S. M. Beck, Mixed metal-silicon clusters formed by chemical reaction in a supersonic molecular beam: Implications for reactions at the metal/silicon interface, J. Chem. Phys., 1989, 90: 6306-6312.
[9] S. M. Beck, Photophysical studies of bare and metal-containing silicon clusters, Advances in Metal and Semiconductor Clusters, 1993, 1: 241-265.
[10] H. Hiura, T. Miyazaki,T. Kanayama, Formation of metal-encapsulating Si cage clusters, Phys. Rev. Lett., 2001, 86(9): 1733-1736.
[11] M. Ohara, K. Miyajima, A. Pramann, A. Nakajima, K. Kaya, Geometric and electronic structures of terbium?silicon mixed clusters (TbSin; 6≤n≤16), J. Phys. Chem. A, 2002, 106(15): 3702-3705.
[12] M. Ohara, K. Koyasu, A. Nakajima, K. Kaya, Geometric and electronic structures of metal (M)-doped silicon clusters (M=Ti, Hf, Mo, and W), Chem. Phys. Lett., 2003, 371: 490-497.
[13] K. Koyasu, M. Akutsu, M. Mitsui, and A. Nakajima, Selective formation of MSi16 (M = Sc, Ti, and V), J. Am. Chem. Soc., 2005, 127(14): 4998-4999.
[14] J. J. Scherer, J. B. Paul,C. P. Collier, R. J. Saykally, Cavity ringdown laser absorption spectroscopy and time-of-flight mass spectroscopy of jet-cooled copper silicides, J. Chem. Phys., 1995, 102(13): 5190-5199.
[15] Y. M. Harrick, W. Jr. Weltner, Quenching of angular momentum in the ground states of VC, NbC, VSP, and NbSi molecules, J. Chem. Phys., 1991, 94(5): 3371-3380.
[16] V. Kumar and Y. Kawazoe, Metal-encapsulated fullerenelike and cubic caged clusters of silicon, Phys. Rev. Lett., 2001, 87(4): 045503-1-4.
[17] V. Kumar and Y. Kawazoe, Magic behavior of Si15M and Si16M (M=Cr, Mo, and W) clusters, Phys. Rev. B, 2002, 65(7): 073404-1-4.
[18] V. Kumar and Y. Kawazoe, Metal-doped magic clusters of Si, Ge, and Sn: The finding of a magnetic superatom, Appl. Phys. Lett., 2003, 83(13): 2677-2679.
[19] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth, magic behavior, and electronic and vibrational properties of Cr-doped Si clusters, Phys. Rev. B, 2004, 70(24): 245433-1-10.
[20] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth behavior of metal-doped silicon clusters SinM (M=Ti, Zr, Hf; n=8–16), Phys. Rev. B, 2005, 71(7): 075423-1-12.
[21] J. Lu and S. Nagase, Structural and electronic properties of metal-encapsulated silicon clusters in a large size range, Phys. Rev. Lett., 2003, 90(11): 115506-1-4.
[22] G. Mpourmpakis, G. E. Froudakis, A. N. Andriotis, and M. Menon, Understanding the structure of metal encapsulated Si cages and nanotubes: Role of symmetry and d-band filling, J. Chem. Phys., 2003, 119(14): 7498-7502.
[23] G. Mpourmpakis, G. E. Froudakis, A. N. Andriotis, and M. Menon, Feencapsulation by silicon clusters: Ab initio electronic structure calculations, Phys. Rev. B, 2003, 68(12): 125407-1-5.
[24] L. Ma, J. J. Zhao, J. G. Wang, Q. L. Lu, L. Z. Zhu, and G. H. Wang, Structure and electronic properties of cobalt atoms encapsulated in Sin (n=1-13) clusters, Chem. Phys. Lett., 2005, 411: 279-284.
[25] L. Ma, J. J. Zhao, J. G. Wang, B. L. Wang, Q. L. Lu, and G. H. Wang, Growth behavior and magnetic properties of SinFe (n=2–14) clusters, Phys. Rev. B, 2006, 73(12): 125439-1-8.
[26] Z. U. Ren, F. Li, P. Guo, and J. G. Han, A computational investigation of the Ni-doped Sin (n=1-8) clusters by a density functional method, J. Mol. Struct.: THEOCHEM, 2005, 718: 165-173.
[27] E. N. Koukaras, C. S. Garoufalis, and A. D. Zdetsis, Structure and properties of the Ni@Si12 cluster from all-electron ab initio calculations, Phys. Rev. B, 2006, 73(23): 235417-1-10.
[28] A. K. Singh, T. M. Briere, V. Kumar, and Y. Kawazoe, Magnetism in transition-metal-doped silicon nanotubes, Phys. Rev. Lett., 2003, 91(44): 146802-1-4.
[29] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys., 1988, 88(4): 2547-2553; C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[30] T. A. Barckholtz and T. A. Miller, Quantitative insights about molecules exhibiting Jahn-Teller and related effects, Int. Rev. Phys. Chem., 1998, 17(4): 435-524.
[31] A. D. Zdetsis, Bonding and structural characteristics of Zn-, Cu-, and Ni-encapsulated Si clusters: Density-functional theory calculations, Phys. Rev. B, 2007, 75(8): 085409-1-10.
[32] R. S. Mulliken, Electron Population Analysis on LCAO-MO Molecular Wave Functions. II. Overlap Population, Bond Orders, and Covalent Bond Energies, J.Chem. Phys., 1955, 23(10): 1841-1846.
[33] B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules, J. Chem. Phys., 1990, 92(1): 508-517.
[34] B. Delley, From molecules to solids with the DMol3 approach, J. Chem. Phys., 2000, 113(18): 7756-7764.
[35] D. B. Zhang and J. Shen, Ground state, growth, and electronic properties of small lanthanum clusters, J. Chem. Phys., 2004, 120(11): 5104-5109.
[36] D. B. Zhang and J. Shen, First principles study of the stability and electronic structure of the icosahedral La13, La13-1, and La13+1 clusters, J. Chem. Phys., 2004, 120(11): 5081-5086.
[37] Z. Xie, Q. M. Ma, Y. Liu, and Y. C. Li, First-principles study of the stability and Jahn–Teller distortion of nickel clusters, Phys. Lett. A, 2005, 342: 459-467.
[38] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic properties of small Co clusters, Phys. Lett. A, 2006, 358: 289-296.
[39] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, binding energies and magnetic moments of small iron clusters: A study based on all-electron DFT, Solid State Commun., 2007, 142: 114-119.
[40] N. Liu, Q. M. Ma, Z. Xie, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic moments of small lanthanum-nickel clusters, Chem. Phys. Lett., 2007, 436: 184-188.
[41] K. Raghavachari, Theoretical study of small silicon clusters: Equilibrium geometries and electronic structures of Sin (n=2-7, 10), J. Chem. Phys., 1986, 84(10): 5672-5686.
[42] P. J. Bruna, S. D. Peyerimhoff, and R. J. Buenker, Theoretical prediction of the potential curves for the lowest-lying states of the isovalent diatomics CN+, Si2, SiC, CP+, and SiN+ using the ab initio MRD-CI method, J. Chem. Phys., 1980, 72(10): 5437-5445.
[43] A. D. Zdetsis, Bonding and structural characteristics of Zn-, Cu-, and Ni-encapsulated Si clusters: Density-functional theory calculations, Phys. Rev. A,2001, 64(8): 023202-1-10.
[44] P. Karamanis, D. Zhang-Negrerie, and C. Pouchan, A critical analysis of the performance of conventional ab initio and DFT methods in the computation of Si6 ground state, Chem. Phys., 2006, 331: 417-426.
[45] S. N. Khanna, B. K. Rao, and P. Jena, Magic Numbers in Metallo-Inorganic Clusters: Chromium Encapsulated in Silicon Cages, Phys. Rev. Lett., 2002, 89(1): 016803-1-4.
[46] J. Wang, Q. M. Ma, Z. Xie, Y. Liu, and Y. C. Li, From SinNi to Ni@Sin: An investigation of configurations and electronic structure, Phys. Rev. B, 2007, 76(3): 035406-1-8.
[1] K. M. Ho, A. A. Shvartsburg, B. Pan, Z. Y. Lu, C. Z. Wang, J. G. Wacker, J. Fye, and M. F. Jarrold, Structures of medium-sized silicon clusters, Nature (London), 1998, 392: 582-585.
[2] E. Kaxiras and K. Jackson, Shape of small silicon clusters, Phys. Rev. Lett., 1993, 71(5): 727-730.
[3] U. Rothlisberger, W. Andreoni, and M. Parrinello, Structure of nanoscale silicon clusters, Phys. Rev. Lett., 1994, 72: 665-668.
[4] I. Rata, A. A. Shvartsburg, M. Horoi, T. Frauenheim, K. W. Michael Siu, and K. A. Jackson, Single-parent evolution algorithm and the optimization of Si clusters, Phys. Rev. Lett., 2000, 85(3): 546-549.
[5] M. F. Jarrold, Nanosurface chemistry on size-selected silicon clusters, Science, 1991, 252(5009): 1085-1092.
[6] S. M. Beck, Studies of silicon cluster–metal atom compound formation in a supersonic molecular beam, J. Chem. Phys., 1987, 87: 4233-4234.
[7] S. M. Beck, Mixed metal–silicon clusters formed by chemical reaction in a supersonic molecular beam: Implications for reactions at the metal/silicon interface, J. Chem. Phys., 1989, 90: 6306-6312.
[8] H. Hiura, T. Miyazaki, and T. Kanayama, Formation of metal-encapsulating Si cage clusters, Phys. Rev. Lett., 2001, 86: 1733-1736.
[9] M. Ohara, K. Koyasu, A. Nakajima, and K. Kaya, Geometric and electronic structures of metal (M)-doped silicon clusters (M= Ti, Hf, Mo and W), Chem. Phys. Lett., 2003, 371: 490-497.
[10] K. Koyasu, M. Akutsu, M. Mitsui, and A. Nakajima, Selective Formation of MSi16 (M = Sc, Ti, and V), J. Am. Chem. Soc., 2005, 127(14): 4998-4999.
[11] V. Kumar and Y. Kawazoe, Metal-encapsulated fullerenelike and cubic caged clusters of silicon, Phys. Rev. Lett., 2001, 87: 045503-1-4.
[12] V. Kumar, T. M. Briere, and Y. Kawazoe, Ab initio calculations of electronic structures, polarizabilities, Raman and infrared spectra, optical gaps, and absorption spectra of M@Si16 (M=Ti and Zr) clusters, Phys. Rev. B, 2003, 68(15): 155412-1-9.
[13] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth behavior of metal-doped silicon clusters SinM(M= Ti, Zr, Hf; n= 8-16), Phys. Rev. B, 2005, 71: 075423-1-12.
[14] J. Lu and S. Nagase, Structural and electronic properties of metal-encapsulated silicon clusters in a large size range, Phys. Rev. Lett., 2003, 90(11): 115506-1-4.
[15] J. U. Reveles and S. N. Khanna, Electronic counting rules for the stability of metal-silicon clusters, Phys. Rev. B, 2006, 74: 035435-1-6.
[16] M. B. Torres, E. M. Fernández, L. C. Balbás, Structure and relative stability of Sin, Sin-, and doped SinM clusters (M =Sc-, Ti, V+) in the range n=14–18, Phys. Rev. B, 2007, 75: 205425-1-14.
[17] B. Hammer and J. K. Norskov, Why gold is the noblest of all the metals, Nature (London), 1995, 376: 238-240.
[18] R. F. Barrow, W. J. M. Gissane, and D. N. Travis, Electronic spectra of some gaseous diatomic compounds of gold, Nature (London), 1964, 201: 603-604.
[19] C. Majumder, A. K. Kandalam and P. Jena, Structure and bonding of Au5M (M=Na, Mg, Al, Si, P, and S) clusters, Phys. Rev. B, 2006, 74(20): 205437-1-6.
[20] Q. Sun, Q. Wang, G. Chen, and P. Jena, Structure of SiAu16: Can a silicon atom be stabilized in a gold cage? J. Chem. Phys., 2007, 127(21): 214706-1-4.
[21] B. Kiran, X. Li, H. J. Zhai, L. F. Cui, and L. S. Wang, Communication [SiAu4]: Aurosilane, Angew. Chem., Int. Ed. 2004, 43(16): 2125-2129.
[22] X. Li, B. Kiran, and L. S. Wang, Gold as Hydrogen. An experimental and theoretical study of the structures and bonding in disilicon gold clusters Si2Aun- and Si2Aun (n=2 and 4) and comparisons to Si2H2 and Si2H4, J. Phys. Chem. A, 2005, 109(19): 4373-4374.
[23] C. Xiao, J. Blundell, F. Hagelberg, and W. A. Lester, Jr., Silicon clusters doped with an yttrium metal atom impurity, Int. J. Quantum Chem., 2004, 96(4): 416-425.
[24] L. J. Guo, X. Liu, G. F. Zhao, and Y. H. Luo, Computational investigation ofTiSin (n=2–15) clusters by the density-functional theory, J. Chem. Phys., 2007, 126(23): 234704-1-7.
[25] J. Wang and J. G. Han, Geometries, stabilities, and electronic properties of different-sized ZrSin (n=1–16) clusters: A density-functional investigation, J. Chem. Phys., 2005, 123(6): 064306-1-16.
[26] P. Guo, Z. Y. Ren, F.Wang, J. Bian, J. G. Han, and G. H.Wang, Structural and electronic properties of TaSin (n=1–13) clusters: A relativistic density functional investigation, J. Chem. Phys., 2004, 121(24): 12265-75.
[27] J. G. Han and F. Hagelberg, A density functional theory investigation of CrSin (n= 1–6) clusters, Chem. Phys., 2001, 263: 255-262.
[28] J. G. Han and F. Hagelberg, A density functional investigation of MoSin (n= 1–6) clusters, J. Mol. Struct.: THEOCHEM, 2001, 549: 165-180.
[29] J. G. Han, C. Xiao, and F. Hagelberg, Geometric and electronic structure of WSiN (N= 1–6, 12) clusters, Struct. Chem., 2002, 13: 173-191.
[30] J. G. Han, Z. Y. Ren, and B. Z. Lu, Geometries and Stabilities of Re-Doped Sin (n= 1? 12) Clusters: A Density Functional Investigation, J. Phys. Chem. A, 2004, 108(23): 5100-5110.
[31] L. Ma, J. J. Zhao, J. G. Wang, B. L. Wang, Q. L. Lu, and G. H. Wang, Growth behavior and magnetic properties of SinFe (n=2–14) clusters, Phys. Rev. B, 2006, 73(12): 125439-1-8
[32] L. Ma, J. J. Zhao, J. G. Wang, Q. L. Lu, L. Z. Zhu, and G. H. Wang, Structure and electronic properties of cobalt atoms encapsulated in Sin (n=1–13) clusters, Chem. Phys. Lett., 2005, 411: 279-284.
[33] J. G. Han, A theoretical investigation on electronic properties and stability of IrSix (x= 1–6) clusters, Chem. Phys., 2003, 286: 181-192.
[34] J. Wang, Q. M. Ma, Y. Liu, and Y. C. Li, From SinNi to Ni@ Sin: An investigation of configurations and electronic structure, Phys. Rev. B, 2007, 76(3): 035406-1-8.
[35] C. Y. Xiao, F. Hagelberg, and W. A. Lester, Jr., Geometric, energetic, andbonding properties of neutral and charged copper-doped silicon clusters, Phys. Rev. B, 2002, 66(7): 075425-1-23.
[36] P. F. Zhang, J. G. Hana, and Q. R. Pu, A density functional investigation of AgSin (n= 1? 5) clusters, J. Mol. Struct.: THEOCHEM, 2003, 635: 25-35.
[37] F. C. Chuang, Y. Y. Hsieh, C. C. Hsu, and M. A. Albao, Geometries and stabilities of Ag-doped Sin (n= 1–13) clusters: A first-principles study, J. Chem. Phys., 2007, 127(14): 144313-1-6.
[38] T. T. Cao, X. J. Feng, L. X. Zhao, X. Liang, Y. M. Lei, and Y. H. Luo, Structure and magnetic properties of La-doped Sin(n=1-12, 24) clusters: a density functional theory investigation, Eur. Phys. J. D, 2008, 49: 343-351.
[39] M. Sankaran and B. Viswanathan, A DFT study of the electronic property of gold nanoclusters (Aux, x=1-12 atoms), Bulletin of the Catalysis Society of India, 2006, 5(1): 26-32.
[40] Q. Sun, Q. Wang, G. Chen, and P. Jena, Structure of SiAu16: Can a silicon atom be stabilized in a gold cage? J. Chem. Phys., 2007, 127(21): 214706-1-4.
[41] C. Majumder, Effect of Si adsorption on the atomic and electronic structure of Aun clusters (n=1–8) and the Au (111) surface: First-principles calculations, Phys. Rev. B, 2007, 75(23): 235409-1-8.
[42] P. J. Bruna, S. D. Peyerimhoff, and R. J. Buenker, Theoretical prediction of the potential curves for the lowest-lying states of the isovalent diatomics CN+, Si2, SiC, CP+, and SiN+ using the ab initio MRD-CI method, J. Chem. Phys., 1980, 72(10): 5437-5445.
[43] B. Douglas, D.H. McDaniel and J.J. Alexander, Concepts and models of inorganic chemistry (2nd ed.), Wiley, New York, 1983.
[44] J. J. Scherer, J. B. Paul, C. P. Collier, A. O’Keeffe, and R. J. Saykally, Cavity ringdown laser absorption spectroscopy and time-of-flight mass spectroscopy of jet-cooled gold silicides, J. Chem. Phys., 1995, 103(21): 9187-9192.
[45] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures and magnetic moments of Fe-C clusters, Phys. Rev. B, 2007, 76(3): 035412-1-7.
[46] N. Liu, Q. M. Ma, Z. Xie, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic moments of small lanthanum–nickel clusters, Chem. Phys. Lett., 2007, 436: 184-188.
[47] Z. Xie, Q. M. Ma, Y. Liu, Y. C. Li, First-principles study of the stability and Jahn-Teller distortion of nickel clusters, Phys. Lett. A, 2005, 342: 459-467.
[48] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic properties of small Co clusters, Phys. Lett. A, 2006, 358: 289-296.
[49] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, binding energies and magnetic moments of small iron clusters: A study based on all-electron DFT Solid State Comm., 2007, 142: 114-119.
[50] B. R. Wang, J. Wang, Q. M. Ma, and Y. Liu, Structures and magnetic ordering of MnnFe (n=1–12) clusters, Solid State Comm., 2008, 147: 53-56.
[51] J. Wang, H. Ning, Q. M. Ma, Y. Liu, and Y. C. Li, Au: A possible ground-state noble metallic nanotube, J. Chem. Phys., 2008, 129(13): 134705-1-4; http://www.natureasia.com/asiamaterials/highlight.php?id=337.
[52] W. R. Wadt and P. J. Hay, Ab initio effective core potentials for molecular calculations: Potential for main group elements Na to Bi, J. Chem. Phys., 1985, 82(1): 284-298.
[53] A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys., 1993, 98(7): 5648-5652.
[54] J. P. Perdew, K. Burke, and Y. Wang, Generalized gradient approximation for the exchange-correlation hole of a many-electron system, Phys. Rev. B, 1996, 54: 16533-16539.
[55] R. S. Mulliken, Electronic Population Analysis on LCAOMO Molecular Wave Functions. II. Overlap Populations, Bond Orders, and Covalent Bond Energies, J. Chem. Phys., 1955, 23(10): 1841-1846.
[56] M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., Gaussian 03, Revision D.01 (Gaussian, Inc., Wallingford CT, 2004).
[57] T. A. Barckholtz, T. A. Miller, Quantitative insights about molecules exhibitingJahn-Teller and related effects, Int. Rev. Phys. Chem., 1998, 17(4): 435-524.
[58] A. D. Zdetsis, Bonding and structural characteristics of Zn-, Cu-, and Ni-encapsulated Si clusters: Density-functional theory calculations, Phys. Rev. B, 2007, 75(8): 085409-1-10.
[59] A. D. Zdetsis, The real structure of the Si6 cluster, Phys. Rev. A, 2001, 64(2): 023202-1-4.
[60] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys., 1988, 88(4): 2547-2553; C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[61] K. Raghavachari, Theoretical study of small silicon clusters: Equilibrium geometries and electronic structures of Sin (n=2–7, 10), J. Chem. Phys., 1986, 84(10): 5672-5686.
[62] P. J. Bruna, S. D. Peyerimho, and R. J. Buenker, Theoretical prediction of the potential curves for the lowest-lying states of the isovalent diatomics CN+, Si2, SiC, CP+, and SiN+ using the ab initio MRD-CI method, J. Chem. Phys., 1980, 72(10): 5437-5445.
[63] B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules, J. Chem. Phys., 1990, 92(1): 508-517.
[64] B. Delley, From molecules to solids with the Dmol3 approach, J. Chem. Phys., 2000, 113(18): 7756-7764.
[65] P. Karamanis, D. Zhang-Negrerie, C. Pouchan, A critical analysis of the performance of conventional ab initio and DFT methods in the computation of Si6 ground state, Chem. Phys., 2006, 331: 417-426.
[66] S. N. Khanna, B. K. Rao, and P. Jena, Magic numbers in metallo-inorganic clusters: chromium encapsulated in silicon cages, Phys. Rev. Lett., 2002, 89(1): 016803-1-4.
[1] H. W. Kroto, J. R. Heath, S. C. OBrien, R. F. Curl, and R. E. Smalley, C60: buckminsterfullerene, Nature (London), 1985, 318: 162-163.
[2] J. Cioslowski, Endohedral chemistry: electronic structures of molecules trapped inside the C60 cage, J. Am. Chem. Soc., 1991, 113(11): 4139-4141.
[3] J. Cioslowski and A. Nanayakkara, Endohedral fullerites: A new class of ferroelectric materials, Phys. Rev. Lett., 1992, 69: 2871-2873.
[4] S. M. Beck, Studies of silicon cluster–metal atom compound formation in a supersonic molecular beam, J. Chem. Phys., 1987, 87: 4233-4234.
[5] S. M. Beck, Mixed metal–silicon clusters formed by chemical reaction in a supersonic molecular beam: Implications for reactions at the metal/silicon interface, J. Chem. Phys., 1989, 90: 6306-6312.
[6] H. Hiura, T. Miyazaki, and T. Kanayama, Formation of metal-encapsulating Si cage clusters, Phys. Rev. Lett., 2001, 86: 1733-1736.
[7] M. Ohara, K. Koyasu, A. Nakajima, and K. Kaya, Geometric and electronic strucutures of metal (M)-doped silicon clusters (M=Ti, Hf, Mo and W), Chem. Phys. Lett., 2003, 371: 490-497.
[8] K. Koyasu, M. Akutsu, M. Mitsui, and A. Nakajima, Selective formation of MSi16 (M=Sc, Ti, and V), J. Am. Chem. Soc., 2005, 127: 4998-4999.
[9] V. Kumar and Y. Kawazoe, Metal-encapsulated fullerenelike and cubic caged clusters of silicon, Phys. Rev. Lett., 2001, 87: 045503-1-4.
[10] V. Kumar and Y. Kawazoe, Magic behavior of Si15M and Si16M (M=Cr, Mo, and W) clusters, Phys. Rev. B, 2002, 65: 073404-1-4.
[11] V. Kumar, T. M. Briere, and Y. Kawazoe, Ab initio calculations of electronic structures, polarizabilities, Raman and infrared spectra, optical gaps, and absorption spectra of M@Si16 (M=Ti and Zr) clusters, Phys. Rev. B, 2003, 68: 155412-1-9.
[12] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth, magic behavior, andelectronic and vibrational properties of Cr-doped Si clusters, Phys. Rev. B, 2004, 70: 245433-1-10.
[13] H. Kawamura, V. Kumar, and Y. Kawazoe, Growth behavior of metal-doped silicon clusters SinM (M=Ti, Zr, Hf; n=8–16), Phys. Rev. B, 2005, 71: 075423-1-12.
[14] J. Lu and S. Nagase, Structural and electronic properties of metal-encapsulated silicon clusters in a large size range, Phys. Rev. Lett., 2003, 90: 115506-1-4.
[15] J. U. Reveles and S. N. Khanna, Electronic counting rules for the stability of metal-silicon clusters, Phys. Rev. B, 2006, 74: 035435-1-6.
[16] M. B. Torres, E. M. Fernández, L. C. Balbás, Theoretical study of isoelectronic SinM clusters (M=Sc?, Ti, V+; n=14–18), Phys. Rev. B, 2007, 75: 205425-1-12.
[17] J. Wang, Q. M. Ma, Z. Xie, et al., From SinNi to Ni@Sin: An investigation of configurations and electronic structure, Phys. Rev. B, 2007, 76(3): 035406-1-8.
[18] H. Prinzbach, A. Weiler, P. Landenberger, F. Wahl, J. Wrth, L. T. Scott, M. Gelmont, D. Olevano, and B. Issendor, Gas-phase production and photoelectron spectroscopy of the smallest fullerene C20, Nature (London), 2000, 407: 60-63.
[19] Z. X. Wang, X. Z. Ke, Z. Y. Zhun, F. Y. Zhu, M. L. Ruan, H. Chen, R. B. Huang, L. S. Zheng, A new carbon solid made of the world’s smallest caged fullerene C20, Phys. Lett. A, 2001, 280: 351-356.
[20] M. F. Jarrold, The smallest fullerene (news and views article), Nature (London), 2000, 407: 26-27.
[21] K. M. Ho, A. A. Shvartsburg, B. Pan, Z. Y. Lu, C. Z. Wang, J. G. Wacker, J. L. Fye, and M. F. Jarrold, Structures of medium-sized silicon clusters, Nature (London), 1998, 392: 582-585.
[22] A. A. Shvartsburg, B. Liu, Z. Lu, C. Z. Wang, M. F. Jarrold, and K. M. Ho, Structures of Germanium Clusters: Where the growth patterns of silicon and germanium clusters diverge, Phys. Rev. Lett., 1999, 83: 2167-2170.
[23] L. Mitas, J. C. Grossman, I. Stich, et al., Silicon clusters of intermediate size: Energetics, dynamics, and thermal effects, Phys. Rev. Lett., 2000, 84: 1479-1482.
[24] B. X. Li and P. L. Cao, Stable structures for Si20 clusters, Phys. Rev. A, 2000, 62:023201-1-5.
[25] J.Wang, J. Zhao, F. Ding, W. Shen, H. Lee, and G. H.Wang, Thermal properties of medium-sized Ge clusters, Solid State Commun., 2001, 117: 593-598.
[26] Q. Sun, Q. Wang, T. M. Briere, V. Kumar, and Y. Kawazoe, First-principles calculations of metal stabilized Si20 cages, Phys. Rev. B, 2002, 65: 235417-1-5.
[27] A. K. Singh, V. Kumar, and Y. Kawazoe, Stabilizing the silicon fullerene Si20 by thorium encapsulation, Phys. Rev. B, 2005, 71: 115429-1-6.
[28] A. Grubisic, H. P. Wang, Y. J. Ko, and K. H. Bowena, Photoelectron spectroscopy of europium-silicon cluster anions, EuSin? ( 3≤n≤17), J. Chem. Phys., 2008, 129: 054302-1-5.
[29] J.Wang and J. H. Liu, Novel bi-transition metallic encapsulated naphthalene-like Si20 prismatic cage: A DFT investigation, J. Comput. Chem., 30(7): 1103-1110.
[30] B. Liu, Z. Y. Lu, B. Pan, C. Z. Wang, K. M. Ho, A. A. Shvartsburg, and M. F. Jarrold, Ionization of medium-sized silicon clusters and the geometries of the cations, J. Chem. Phys., 1998, 109: 9401-9409.
[31] X. L. Zhu, X. C. Zeng, Y. A. Lei, and B. Pan, Structures and stability of medium silicon clusters II. Ab initio molecular orbital calculations of Si12–Si20, J. Chem. Phys., 2004, 120: 8985-8995.
[32] S. Yoo, and X. C. Zeng, Structures and stability of medium-sized silicon clusters III. Reexamination of motif transition in growth pattern from Si15 to Si20, J. Chem. Phys., 2005, 123: 164303-1-6.
[33] S. Goedecker, W. Hellmann, and T. Lenosky, Global minimum determination of the born-oppenheimer surface within density functional theory, Phys. Rev. Lett., 2005, 95: 055501-1-4.
[34] A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys., 1993, 98(7): 5648-5652.
[35] J. P. Perdew, K. Burke, and Y. Wang, Generalized gradient approximation for the exchange-correlation hole of a many-electron system, Phys. Rev. B, 1996, 54: 16533-16539.
[36] C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[37] M. J. Frisch, G. W. Trucks, H. B. Schlegel, et al., Gaussian 03, Revision D.01 (Gaussian, Inc., Wallingford CT, 2004).
[38] A. D. Zdetsis, Bonding and structural characteristics of Zn-, Cu-, and Ni-encapsulated Si clusters: Density-functional theory calculations, Phys. Rev. B, 2007, 75(8): 085409-1-10.
[39] B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules, J. Chem. Phys., 1990, 92(1): 508-517.
[40] J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B, 1992, 45: 13244-13249.
[41] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys., 1988, 88(4): 2547-2553; C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[42] R. S. Mulliken, Electronic population analysis on LCAO-MO molecular wave functions. II. Overlap populations, bond orders, and covalent bond energies, J. Chem. Phys., 1955, 23(10): 1841-1846.
[43] B. Delley, From molecules to solids with the DMol3 approach, J. Chem. Phys., 2000, 113(18): 7756-7764.
[44] S. Yoo and X. C. Zeng, Structures and relative stability of medium-sized silicon clusters IV. Motif-based low-lying clusters Si21-Si30, J. Chem. Phys., 2006, 124: 054304-1-6.
[45] J. Wang, H. Ning, Q. M. Ma, Y. Liu, and Y. C. Li, Au42: A possible ground-state noble metallic nanotube, J. Chem. Phys., 2008, 129(13): 134705-1-4; http://www.natureasia.com/asiamaterials/highlight.php?id=337.
[1] H. Haberland, Clusters of Atoms and Molecules I and II, Berlin: Springer-Verlag, 1995.
[2] K. H. Meiwes-Broer, Clusters on Surfaces, Berlin: Springer-Verlag, 2000.
[3] V. Kumar, K. Esfarjani, and Y. Kawazoe, Cluster and Nanomaterials, Berlin: Spinger-Verlag, 2002.
[4] W. Eberhardt, Clusters as new materials, Surf. Sci., 2002, 500: 242-270.
[5] J. Bansmann, S. H. Baker, C. Binns, J. A. Blackman, J. P. Bucher, J. Dorantes-Dávila, V. Dupuis, L. Favre, D. Kechrakos, A. Kleibert, K. H. Meiwes-Broer, G. M. Pastor, A. Perez, O. Toulemonde, K. N. Trohidou, J. Tuaillon, and Y. Xie, Magnetic and structural properties of isolated and assembled clusters, Surf. Sci. Rep., 2005, 56: 189-275.
[6] I. M. L. Billas, A. Chatelain and W. A. de Heer, Magnetism from the atom to the bulk in nickel, cobalt and iron clusters, Science, 1994, 265(5179): 1682-1684.
[7] M. Sakurai, K. Watanabe, K. Sumiyama, and K. Suzuki, Magic numbers in transition metal (Fe, Ti, Zr, Nb, and Ta) clusters observed by time-of-flight mass spectrometry, J. Chem. Phys., 1999, 111(1), 235-238.
[8] J. L. Chen, C. S. Wang, K. A. Jackson, and M. R. Pederson, Theory of magnetic and structural ordering in iron clusters, Phys. Rev. B, 1991, 44: 6558-61.
[9] M. Castro and D. R. Salahub, Density-functional calculations for small iron clusters: Fen, Fen+, and Fen- for n≤5, Phys. Rev. B, 1994, 49: 11842-52.
[10] P. Ballone and R. O. Jones, Structure and spin in small iron clusters, Chem. Phys. Lett., 1995, 233: 632-638.
[11] O. Dieguez, M. M. G. Alemany, C. Rey, P. Ordejon, and L. J. Gallego, Density-functional calculations of the structures, binding energies, and magnetic moments of Fe clusters with 2 to 17 atoms, Phys. Rev. B, 2001, 63: 205407-1-6.
[12] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, binding energies andmagnetic moments of small iron clusters: A study based on all-electron DFT, Solid State Commun., 2007, 142: 114-119.
[13] H. Yoshida and A. Terasaki, Spin-polarized electronic structure of cobalt cluster anions studied by photoelectron spectroscopy, J. Chem. Phys., 1995, 102(15): 5960-5965.
[14] S. R. Liu, H. J. Zhai, and L. S. Wang, Electronic and structural evolution of Con clusters (n=1–108) by photoelectron spectroscopy, Phys. Rev. B, 2001, 64, 153402-1-4.
[15] X. S. Xu, S. Y. Yin, R. Moro, and W. A. de Heer, Magnetic Moments and Adiabatic Magnetization of Free Cobalt Clusters, Phys. Rev. Lett., 2005, 95: 237209-1-4.
[16] Z. Q. Li and B. L. Gu, Electronic-structure calculations of cobalt clusters, Phys. Rev. B, 1993, 47(20): 13611-14.
[17] H. J. Fan, C. W. Liu, and M. S. Liao, Geometry, electronic structure and magnetism of small Con (n=2?8) clusters, Chem. Phys. Lett., 1997, 273: 353-359.
[18] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic properties of small Co clusters, Phys. Lett. A, 2006, 358: 289-296.
[19] H. Basch, M. D. Newton, and J. W. Moskowitz, The electronic structure of small nickel atom clusters, J. Chem. Phys., 1980, 73(9): 4492-4510.
[20] F. A. Reuse and S. N. Khanna, Geometry, electronic structure, and magnetism of small Nin (n=2–6, 8, 13) clusters, Chem. Phys. Lett., 1995, 234: 77-81.
[21] S. E. Apsel, J. W. Emmert, J. Deng, and L. A. Bloomfield, Surface-Enhanced Magnetism in Nickel Clusters, Phys. Rev. Lett., 1996, 76: 1441-1444.
[22] X. G. Wan, L. Zhou, J. M. Dong, T. K. Lee, and D. S. Wang, Orbital polarization, surface enhancement and quantum confinement in nanocluster magnetism, Phys. Rev. B, 2004, 69: 174414-1-14.
[23] Z. Xie, Q. M. Ma, Y. Liu, and Y. C. Li, First-principles study of the stability and Jahn-Teller distortion of nickel clusters, Phys. Lett. A, 2005, 342: 459-467.
[24] W. Y. Ching, Y. N. Xu, B. N. Harmon, J. Ye, and T. C. Leung, Electronicstructures of FeB, Fe2B, and Fe3B compounds studied using first-principles spin-polarized calculations, Phys. Rev. B, 1990, 42: 4460-70.
[25] J. Hafner, M. Tegze, and Ch Becke, Amorphous magnetism in Fe-B alloys: First-principles spin-polarized electronic-structure calculations, Phys. Rev. B, 1994, 49: 285-298.
[26] M. L. Fdez-Gubieda, A. García-Arribas, J. M. Barandiarán, R. López Antón, I. Orue, P. Gorria, S. Pizzini, and A. Fontaine, Magnetic Compton scattering study of the ferromagnetic amorphous alloys Fe1-xBx, Phys. Rev. B, 2001, 63: 220404-1-4.
[27] Z. Y. Jiang, C. J. Yang, and S. T. Li, Structures and stability of B-doped Al clusters: AlnB and AlnB2 (n=1–7), J. Chem. Phys., 2005, 123(20): 204315-1-7.
[28] Q. Sun, X. G. Gong, Q. Q. Zheng, and G, H, Wang, The structures and magnetic properties of small Fe/sub n/B clusters, J. Phys.: Condens. Matter, 1996, 8(11): 1805-1810.
[29] G. S. Painter and F. W. Averill, Effects of segregation on grain-boundary cohesion: A density-functional cluster model of boron and sulfur in nickel, Phys. Rev. Lett., 1987, 58: 234-237.
[30] M. Deshpande, D. G. Kanhere, and R. Pandey, Structures, energetics, and magnetic properties of NinB clusters with n=1–8, 12, Phys. Rev. A, 2005, 71: 063202-1-7.
[31] D. B. Zhang and J. Shen, Ground state, growth, and electronic properties of small lanthanum clusters, J. Chem. Phys., 2004, 120(11): 5104-5109.
[32] D. B. Zhang and J. Shen, First principles study of the stability and electronic structure of the icosahedral La13, La13-1, and La13+1 clusters, J. Chem. Phys., 2004, 120(11): 5081-5086.
[33] N. Liu, Q. M. Ma, Z. Xie, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic moments of small lanthanum–nickel clusters, Chem. Phys. Lett., 2007, 436: 184-188.
[34] J. Wang, Q. M. Ma, Z. Xie, Y. Liu, and Y. C. Li, From SinNi to Ni@Sin: An investigation of configurations and electronic structure, Phys. Rev. B, 2007, 76:035406-1-8.
[35] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures and magnetic moments of Fe-C clusters, Phys. Rev. B, 2007, 76(3): 035412-1-7.
[36] Q. M. Ma, Z. Xie, J. Wang, Y. Liu, and Y. C. Li, Structures, stabilities and magnetic properties of small Co clusters, Phys. Lett. A, 2006, 358: 289-296.
[37] B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules , J. Chem. Phys., 1990, 92(1): 508-517.
[38] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys., 1988, 88(4): 2547-2553.
[39] C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 1988, 37(2): 785-789.
[40] Electron Population Analysis on LCAO-MO Molecular wave functions. II. overlap population, bond orders, and covalent bond energies, J. Chem. Phys., 1955, 23(10): 1841-1846.
[41] B. Delley, From molecules to solids with the DMol3 approach, J. Chem. Phys., 2000, 113(18): 7756-7764.
[42] X. G. Wan, L. Zhou, J. M. Dong, T. K. Lee, and D. S. Wang, Orbital polarization, surface enhancement and quantum confinement in nanocluster magnetism, Phys. Rev. B, 2004, 69: 174414-1-14.
[43] N. Fujima and T. Yamaguchi, Magnetic moment in Ni clusters estimated by an electronic-shell model, Phys. Rev. B, 1996, 54: 26-28.
[1] H. W. Kroto, J. R. Heath, S. C. O’Brien, R. F. Curl, and R. E. Smalley, C60: buckminsterfullerene, Nature, 1995, 318: 162-163.
[2] S. Iijima, Helical microtubules of graphitic carbon, Nature, 1991, 354: 56-58.
[3] T. W. Ebbesen and P. M. Ajayan, Large-scale synthesis of carbon nanotubes, Nature, 1992, 358: 220-222.
[4] S. Iijima and T. Ichihashi, Single-shell carbon nanotubes of 1-nm diameter, Nature, 1993, 363: 603-605.
[5] D. S. Bethune and C. H. Kiang, Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer walls, Nature, 1993, 363: 605-607.
[6] Y. Kondo and K. Takayanag, Synthesis and Characterization of Helical multi-shell gold nanowires, Science, 2000, 289(5479): 606-608; E. Tosatti and S. Prestipino, Weird gold nanowire, Science, 2000, 289(5479): 561-563.
[7] Y. Oshima and A. Onga, Helical gold nanotube synthesized at 150 K, Phys. Rev. Lett., 2003, 91(20): 205503-1-4.
[8] M. D. Valle, C. Tejedor, and Gianaurelio Cuniberti, Scaling of the conductance in gold nanotubes, Phys. Rev. B, 2006, 74(4): 045408-1-5.
[9] F. Delogu, Numerical study of the melting behavior of Au nanotubes, Phys. Rev. B, 2007, 75(23): 235421-1-8.
[10] Y. Iguchi, T. Hoshi, and T. Fujiwara, Two-stage formation model and helicity of gold nanowires, Phys. Rev. Lett., 2007, 99(12): 125507-1-4.
[11] J. Li, X. Li, H. J. Zhai, and L. S. Wang, Au20: A tetrahedral cluster, Science, 2003, 299(5608): 864-867.
[12] X. Gu, M. Ji, S. H. Wei, and X. G. Gong, AuN clusters (N=32,33,34,35): Cagelike structures of pure metal atoms, Phys. Rev. B, 2004, 70(20): 205401-1-5.
[13] M. P.Johansson, D.Sundholm, and J. Vaara, Au32: A 24-carat golden fullerene, Angew. Chem. Int. Ed., 2004, 43: 2678-2681.
[14] J. L.Wang, G. H. Wang, and J. J. Zhao, Density-functional study of Aun(n=2–20) clusters: Lowest-energy structures and electronic properties, Phys. Rev. B, 2002, 66(3): 035418-1-6.
[15] L. Xiao and L. C. Wang, From planar to three-dimensional structural transition in gold clusters and the spin–orbit coupling effect, Chem. Phys. Lett., 2004, 392: 452-455.
[16] E. M. Fernandez, J. M.Soler, I. L.Garzon, and L. C.Balbas, Trends in the structure and bonding of noble metal clusters, Phys. Rev. B, 2004, 70(16): 165403-1-14.
[17] R. M. Olson, S. Varganov, M. S. Gordon, H. Metiu, S. Chretien, P. Piecuch, K.Kowalski, S. A.Kucharski, and M. Musial, Where does the planar-to-nonplanar turnover occur in small gold clusters? J. Am. Chem. Soc., 2005, 127(3): 1049-1052.
[18] P. Koskinen, H. H?kkinen, B. Huber, B. V. Issendorff, and M. Moseler, Liquid-liquid phase coexistence in gold clusters: 2D or not 2D? Phys. Rev. Lett., 2007, 98(1): 015701-1-4.
[19] W. Fa and J. M. Dong, Possible method to determine the two-dimensional to three-dimensional crossover of gold clusters by examining their vibrational modes, Appl. Phys. Lett., 2006, 89(1): 013117-1-3.
[20] F. Furche, R. Ahlrichs, P.Weis, C. Jacob, S.Gilb, T. Bierweiler, and M. M. Kappes, The structures of small gold cluster anions as determined by a combination of ion mobility measurements and density functional calculations, J. Chem. Phys., 2002, 117: 6982-6990.
[21] H. Hakkinen, B. Yoon, U. Landman, X. Li, H. J. Zhai, and L. S.Wang, On the electronic and atomic structures of small AuN- (N=4-14) clusters: A photoelectron spectroscopy and density-functional study, J. Phys. Chem. A, 2003, 107: 6168-6175.
[22] S. Gilb, P. Weis, F. Furche, R. Ahlrichs, and M. M. Kappes, Structures of small gold cluster cations (Aun+, n<14): Ion mobility measurements versus density functional calculations, J. Chem. Phys., 2002, 116: 4094-4101.
[23] M. Ji, X. Gu, X. Li, X. G. Gong, J. Li, and L. S.Wang, An experimental and theoretical investigation of the electronic and geometrical structures of the special Au32 cluster, Angew. Chem. Int. Ed., 2005, 44: 7119-7123.
[24] S. Bulusu, X. Li, L. S.Wang, and X. C. Zeng, Evidence of hollow golden cages, Proc. Natl. Acad. Sci., 2006, 103: 8326-8330.
[25] D. X. Tian, J. J. Zhao, B. L. Wang, and R. B. King, The dual relationship between large gold clusters (antifullerenes) and carbon fullerenes: a new lowest-energy cage structure for Au50, J. Phys. Chem. A, 2007, 111(3): 411-414.
[26] A. J. Karttunen, M. Linnolahti, T. A. Pakkanen, and P. Pyykk?, Icosahedral Au72: a predicted chiral and spherically aromatic golden fullerene, Chem. Commun., 2008, 4: 465-467.
[27] Y. Gao and X. C. Zeng, Au42: An alternative icosahedral golden fullerene cage, J. Am. Chem. Soc., 2005, 127(12): 3698-3699.
[28] R. T. Senger, S. Dag, and S. Ciraci, Chiral single-wall gold nanotubes, Phys. Rev. Lett., 2004, 93(19): 196807-1-4.
[29] X. P. Yang and J. M. Dong, Geometrical and electronic structures of the (5, 3) single-walled gold nanotube from first-principles calculations, Phys. Rev. B, 2005, 71(23): 233403-1-4.
[30] Y. Mokrousov, G. Bihlmayer, and S. Blügel, Full-potential linearized augmented plane-wave method for one-dimensional systems: Gold nanowire and iron monowires in a gold tube, Phys. Rev. B, 2005, 72(4): 045402-1-15.
[31] W. Fa and J. M. Dong, Possible ground-state structure of Au26: a highly symmetric tubelike cage, J. Chem. Phys., 2006, 124(11): 114310-1-4.
[32] W. Fa, C. F. Luo, and J. M. Dong, Bulk fragment and tubelike structures of AuN (N=2-26), Phys. Rev. B, 2005, 72(20): 205428-1-4.
[33] J. L. Wang, J. Jellinek, J. J. Zhao, Z. F. Chen, R. B. King, and P. R. Schleyer, Hollow cages versus space-filling structures for medium-sized gold clusters: The spherical aromaticity of the Au50 cage, J. Phys. Chem. A, 2005, 109(41): 9265-9269.
[34] B. Delley, Hardness conserving semilocal pseudopotentials, Phys. Rev. B, 2002,66(15): 155125-1-9.
[35] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1996, 77(18): 3865-3868.
[36] J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B, 1992, 45: 13244-49.
[37] A. D. Becke, A multicenter numerical integration scheme for polyatomic molecules, J. Chem. Phys., 1988, 88(4): 2547-2553.
[38] C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B, 1988, 37(2): 785-789.
[39] B. Delley, An all-electron numerical method for solving the local density functional for polyatomic molecules, J. Chem. Phys., 1990, 92(1): 508-517.
[40] See http://www-wales.ch.cam.ac.uk/CCD.html.
[41] J. Wang, H. Ning, Q. M. Ma, Y. Liu,and Y. C. Li, Au42: A possible ground-state noble metallic nanotube, J. Chem. Phys. 2008, 129(13): 134705-1-4.
[1] H. Kroto, J. Heath, S. OBrien, R. Curl, and R. Smalley, C60: buckminsterfullerene, Nature (London), 1985, 318: 162-163.
[2] S. Iijima, Helical microtubules of graphitic carbon, Nature (London), 1991, 354: 56-58.
[3] S. Iijima and T. Ichihashi, Single-shell carbon nanotubes of 1-nm dimeter, Nature, 1993, 363: 603-605.
[4] D. S. Bethune, C. H. Klang, M. S. Vries, et al., Cobalt-catalysed grownth of carbon nanotubes with single-atomic-layer walls, Nature, 1993, 363: 605-607.
[5] R. Saito, M. Fujita,M. S. Dresselaus,et al., Electronic structure of chiral graphene tubules, Appl. Phys. Lett., 1992, 60(18): 2204-06.
[6] W. Z. Li,S. X. Xie,B. H. Chang,et al., Large-Scale Synthesis of Aligned Carbon Nanotubes, Science, 1996, 274(5293): 1701-1703.
[7] M. Yudasaka,T. Ichihashi, T. Komatsu, et al.,Single-wall carbon nanotubes formed by a single larser-beampusle, Chem. Phys. Lett., 1999, 299: 9196.
[8] A. M. Cassell,N. R. Franklin, T. W. Tombler, et al., Direeted Growth of Free-Standing Single-Walled Carbon Nanotubes, Am. Chem. Soc. 1999, 121: 7975-7976.
[9]解思深,潘正伟,超长定向碳纳米竹列阵的制备,物理, 1999, 28(1): 1.
[10] L. Chico,V. H. Crespi, L. X. Benedict, et al., Pure carbon nanoscale devices: Nanotube heterojunctions, Phys. Rev. Lett., 1996, 76(6): 971-974.
[11] M. R. Falvo, G. J. Clary, R. M. Taylor,et al., Superfine, Bending and buckling of carbon nanotubes under large strain, Nature, 1997, 389: 582-584.
[12] A. Krishnan, E. Dujardin, T. W. Ebbesen, et al., Young's modulus of single-walled nanotubes, Phys. Rev. B, 1998, 58(20): 14013-19.
[13] S. S. Fan, M. G. Chapline,N. R. Franklin, et al., Self-oriented regular arrays of carbon nanotubes and their field emission properties, Science, 1999, 283(5401):512-514.
[14] R. H. Baughman, A. A. Zakhidov, and W. A. de Heer, Carbon Nanotubes--theRoute Toward Applications, Science, 2002, 297: 787-792.
[15] H. J. Zhai, B. Kiran, J. L. Li, and L. S. Wang, Hydrocarbon analogues of boronclusters--planarity, aromaticity and antiaromaticity, Nat. Mater., 2003, 2: 827-833.
[16] B. Kiran, S. Bulusu, H. J. Zhai, S. Yoo, X. C. Zeng, and L. S. Wang,Planar-to-tubular structural transition in boron clusters: B20 as the embryo ofsingle-walled boron nanotubes, Proc. Natl. Acad. Sci. U.S.A., 2005, 102: 961-964.
[17] S. Chacko, D. G. Kanhere, and I. Boustani, Ab initio density functionalinvestigation of B24 clusters: Rings, tubes, planes, and cages, Phys. Rev. B, 2003,68(3): 035414-1-11.
[18] I. Boustani, A. Rubio, and J. Alonso, Ab initio study of B32 clusters: competitionbetween spherical, quasiplanar and tubular isomers, Chem. Phys. Lett., 1999, 311:21-28.
[19] A. Quandt and I. Boustani, Boron Nanotubes, Chem. Phys. Chem., 2005, 6:2001-2008.
[20] I. Boustani and A. Quandt, Nanotubules of bare boron clusters: Ab initio anddensity functional study, Europhys. Lett., 1997, 39: 527-532.
[21] D. Ciuparu, R. F. Klie, Y. Zhu, and L. Pfefferle, Synthesis of Pure BoronSingle-Wall Nanotubes, J. Phys. Chem. B, 2004, 108: 3967-3969.
[22] K. C. Lau, R. Pati, R. Pandey, and A. C. Pineda, First-principles study of thestability and electronic properties of sheets and nanotubes of elemental boron, Chem.Phys. Lett., 2006, 418: 549-554.
[23] I. Cabria, M. J. Lopez, and J. A. Alonso, Density functional calculations ofhydrogen adsorption on boron nanotubes and boron sheets, Nanotechnology, 2006,17: 778-785.
[24] T. T. Xu, J. G. Zheng, N. Wu, A. W. Nicholls, J. R. Roth, D. A. Dikin, and R. S.Ruoff, Crystalline Boron Nanoribbons:Synthesis and Characterization, Nano Lett.,2004, 4: 963-968.
[25] J. Kunstmann and A. Quandt, Broad boron sheets and boron nanotubes: An ab initio study of structural, electronic, and mechanical properties, Phys. Rev. B, 2006, 74: 035413-1-14.
[26] R. N. Grimes, Boron clusters come of age, J. Chem. Educ., 2004, 81(5): 658-672.
[27] N. G. Szwacki, A. Sadrzadeh, and B. I. Yakobson, B80 Fullerene: An Ab Initio Prediction of Geometry, Stability, and Electronic Structure, Phys. Rev. Lett., 2007, 98: 166804-1-4.
[28] H. Tang and S. I. Beigi, Novel Precursors for Boron Nanotubes: The Competition of Two-Center and Three-Center Bonding in Boron Sheets, Phys. Rev. Lett., 2007, 99: 115501-1-4.
[29] X. Yang, Y. Ding, and J. Ni, Ab initio prediction of stable boron sheets and boron nanotubes: Structure, stability, and electronic properties, Phys. Rev. B, 2008, 77: 041402-1-4.
[30] A. K. Singh, A. Sadrzadeh, and B. I. Yakobson, Probing Properties of Boronα-Tubes by Ab Initio Calculations, Nano Lett., 2008, 8: 1314-17.
[31] G. Kresse and J. Hafner, Ab initio molecular dynamics for liquid metals, Phys. Rev. B, 1993, 47: 558-561; Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium, Phys. Rev. B, 1994, 49: 14251-69.
[32] D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B, 1990, 41: 7892-95.
[33] J. P. Perdew, J. A. Chevary, S. H. Vosko, K. A. Jackson, M. R. Pederson, D. J. Singh, and C. Fiolhais, Atoms, molecules, solids, and surfaces: Applications of the generalized gradient approximation for exchange and correlation, Phys. Rev. B, 1992, 46: 6671-87.
[34] H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B, 1976, 13: 5188-92.
[35] B. Delley, An all-electron numerical method for solving the local densityfunctional for polyatomic molecules, J. Chem. Phys., 1990, 92(1): 508-517.
[36] J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B, 1992, 45: 13244-49.
[37] B. Delley, From molecules to solids with the DMol3 approach, J. Chem. Phys., 2000, 113(18): 7756-7764.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |