两种混合原子团簇及原子吸附氮化镓单层的结构与性质研究
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摘要
纳米材料由于其尺寸接近电子的相干长度而呈现出明显的表面效应、量子尺寸效应和量子隧道效应等,在热力学、磁性、光学和导电性等方面表现出迥异于块体和原子态的性质,因此给医学、制造业、信息通信、材料学和环境保护等领域带来了革命性的变革。近年来,以分子、团簇、纳米线、纳米管和石墨烯等低维结构为基元构建纳米材料的研究蓬勃发展,成为纳米科学技术中最为耀眼的领域之一。这些纳米材料不仅拥有广阔的应用前景,而且有助于从介观的尺度和角度探索微观系统和宏观系统之间的内在联系。
团簇作为介于微观原子、分子和宏观凝聚态物质之间的桥梁,是用来构建纳米材料的理想基元。在使用团簇组装各种新型纳米材料之前,首先要弄清楚其性质如何随尺寸和形貌演化,然后弄清楚如何调制其性质以满足特定的需求。混合原子团簇,尤其是二元半导体团簇和合金团簇,由于其性质可以通过改变组分来简单地调制,因而受到人们的广泛关注。此外,随着电子元器件和磁存储器件的飞速发展,元器件和电路的尺寸越来越小,表面和界面的作用变得愈来愈重要。吸附是一种常见的表面现象,它可以对表面吸附物的活性、材料的磁性和能带结构等物理化学性质产生重大影响。在本论文中,我们采用各种经验的和第一性原理的方法对中等尺寸的GanAsm团簇(n+m=17-24,n-m=0,±1)、Mn原子替代掺杂的Pd。团簇(n=3-19)和吸附F、O与N原子的GaN类石墨烯单层的结构和性质进行了研究,具体内容如下：
通过使用遗传算法(GA)、Basin-hopping Monte Carlo方法(BHMC)结合Stillinger-Weber经验势和密度泛函理论(DFT)系统地研究了化学计量的和非化学计量的GanAsm团簇(n+m=17-24,n-m=0,±1)的结构、电子性质和极化性质,并重点讨论了决定团簇极化率的因素。我们发现研究范围内的所有最低能量结构都是笼形结构,总的键的数目大约是2n+m。团簇的总极化率对团簇体积表现出近乎与组分无关的线性依赖关系。此外,离化势和组分对极化率也有着重要影响。与化学计量的GanAsm团簇相比,非化学计量的团簇倾向于拥有更大的极化率,但是由于异构体效应这种奇偶震荡行为很难在实验中观察到。由于拥有特殊的构型和特殊的HOMO-LUMO电子分布,Ga10As11表现出反常的电子性质,其HOMO-LUMO能隙和离化势与化学计量的团簇十分相似。
通过使用自旋极化的密度泛函方法(DFT)结合遗传算法(GA)和嵌入原子势(EAM)系统地研究了Pdn团簇和双金属Pdn-1Mn团簇(n=3-19)的结构和磁性质,并重点讨论了掺杂锰的钯团簇的磁性随尺寸和结构的演化以及锰元素影响钯团簇磁性的机制。首先我们将所得到的Pdn团簇与前人的结果进行了比较,发现了新的最低能量结构,包括Pd11,Pd12,Pd14,Pd17。通过结构和杂化解释了Pdn团簇的总磁矩的跳跃行为。当n=3-9时,Mn原子替代掺杂几乎不改变Pdn团簇的结构,但是随着团簇尺寸增大,掺杂Mn原子倾向于替代一个内部原子,使团簇发生结构重构,并倾向于形成二十面体基的结构。Mn原子掺杂不仅能增强钯团簇的稳定性,而且可以将绝大多数钯团簇的磁性增强3-5μB。此外,Pdn-1Mn团簇的总磁矩表现出台阶行为基础上的震荡行为,这种行为与Pd-Mn键长密切相关,并且可归因于Pd原子和Mn原子之间的d-d互作用。
使用自旋极化的密度泛函理论研究了具有强烈非金属性的F、O和N原子以不同覆盖率(1/8和1/2)吸附在GaN类石墨烯单层上对其磁性和能带结构的影响。通过吸附F原子可以将间接带隙半导体的GaN单层转变为磁性半金属,当F的覆盖率增长到很高时,体系又变回非磁性的半导体。我们使用Ising模型和Monte Carlo模拟估算低覆盖率(1/8)吸附F的GaN单层的的居里温度为260K。不论是高覆盖率(1/2)吸附还是低覆盖率(1/8)吸附N原子,GaN单层都能转变为磁性半金属,相应的居里温度分别估算为220K和50K。上述的吸附诱导磁性主要来自N2p(尤其是N2pz)轨道的自旋劈裂。吸附O原子不会诱导出磁性,但可以减小体系的带隙,且覆盖率越高带隙越小。
The size of nanomaterials is comparable to the electron coherent length, which leads to obvious surface effect, quantum size effect, quantum tunnel effect, and so on. Accordingly, they exhibit many unusual properties in the fields of thermodynamics, magnetism, optics and conductivity, etc, which are much different from those of corresponding bulk and atomic state. In the past few decades, nanomaterials based on molecules, clusters, nanowires, nanotubes or graphene developed rapidly, which bring about a revolutionary change in medical science, manufacturing industry, information communication, material science, and so on. The nanomaterials have not only wide application prospect but also a great fundamental importance of exploring the internal relations between macroscopic and microscopic systems.
Clusters, as the bridge between microscopic atoms or molecules and macroscopic condensed matter, are ideal building blocks to design new nanomaterials. Before assembling new materials from clusters, we need to make it clear how the properties of clusters vary with their shapes and sizes, and how to modulate their properties for different purpose as well. Mixed atomic clusters, especially binary semiconductor clusters and alloy clusters, have drawn much attention, due to that their properties can be modulated easily by changing the composition. In addition, with the rapid development of electronic components and magnetic storage devices, the size of the components and electric circuit becomes smaller and smaller, and as a result the surface and interface get more and more important. The adsorption is a common surface phenomenon, which can exert a great influence on the activity of adsorbate, the magnetism and band structure of the materials, and so on. In this thesis, we use various methods from empirical to first-principles to study the structures and properties of medium-sized GanAsm clusters (n+m=17-24, n-m=0,±1), Pdn clusters (n=3-19) doped by Mn atoms and graphene-like GaN monolayer adsorbing F, O and N adatoms.
By using genetic algorithm(GA), basin-hopping Monte Carlo method (BHMC) combined with Stillinger-Weber empirical potential and density functional theory (DFT) calculations, the geometries, electronic properties and polarizabilities of stoichiometric and nonstoichiometric GanAsm clusters (n+m=17-24, n-m=0,±) are investigated systematically, with emphasis on what determines the polarizabilities. All the lowest energy structures are hollow cages with a total number of bonds of about2n+m. The total polarizabilities of GanAsm clusters exhibit a linear dependence on their volumes despite of different composition. The polarizabilities are also strongly correlated to ionization potentials and composition. The nonstoichiometric GanAsm clusters tend to possess higher polarizabilities than stoichiometric ones, but this behavior is hard to be observed from experiment due to isomerization. Ga10As11, seen as a fragment of Ga12As12, has special HOMO-LUMO electron density distribution which accounts for its unusual electronic properties like stoichiometric clusters.
The geometries and magnetic properties of both Pdn and Pdn-1Mn (n=3-19) clusters are calculated by using spin-polarized density functional theory approach combined with genetic algorithm and embedded atom method (EAM).We emphatically discussed the magnetism evolution of the Mn-doped palladium clusters with their structures and size, and how the Mn element influences the magnetic behavior of palladium clusters as well. By comparing our geometries with early results, several new lowest energy structures of Pdn clusters (n=11,12,14,17) are found. The jump of the total magnetic moments of Pdn clusters is explained in terms of structures and hybridization. For large cluster size (n>9), when a Mn atom is doped into the Pdn cluster, it tends to occupy an interior site of the cluster and the geometry reconstruction generally occurs, and the cluster is apt to form an icosahedron based structure for n>13. The doping of Mn atoms not only enhances the stability of Pdn clusters, but also increases their total magnetic moments by a magnitude of3-5μB. Moreover, the doping of Mn atoms causes the Pdn_1Mn clusters to give rise to an evident oscillation of step-like magnetic behavior, which is closely related to the Pd-Mn bond length and can be attributed to the d-d interaction between Pd and Mn atoms.
The effect of adatoms (F, N and O) on the magnetism and band structure of graphenelike GaN monolayer (ML) at different coverages (1/2and1/8) is studied by spin-polarized density functional theory calculations. Adsorbing F adatoms at low coverage causes the GaN monolayer to be transformed from a nonmagnetic indirect-band-gap semiconductor into a magnetic half metal, whereas the monolayer turns back to a nonmagnetic semiconductor at high coverage. Using the Ising model and Monte Carlo simulation, we get an estimation of the Curie temperature of low coverage F-adsorbed GaN monolayer of260K. The GaN monolayer becomes a magnetic half metal after adsorbing N adatoms, no matter whether the coverage is high (1/2) or low (1/8), and their Curie temperatures are estimated to be220K and50K. The magnetism mentioned above mainly comes from the spin splitting of N2p (especially N2pz) orbits. On the other hand, the adsorption of O does not induce magnetism but reduces the band gap of the GaN monolayer and the higher the coverage is the smaller the gap is.
团簇作为介于微观原子、分子和宏观凝聚态物质之间的桥梁,是用来构建纳米材料的理想基元。在使用团簇组装各种新型纳米材料之前,首先要弄清楚其性质如何随尺寸和形貌演化,然后弄清楚如何调制其性质以满足特定的需求。混合原子团簇,尤其是二元半导体团簇和合金团簇,由于其性质可以通过改变组分来简单地调制,因而受到人们的广泛关注。此外,随着电子元器件和磁存储器件的飞速发展,元器件和电路的尺寸越来越小,表面和界面的作用变得愈来愈重要。吸附是一种常见的表面现象,它可以对表面吸附物的活性、材料的磁性和能带结构等物理化学性质产生重大影响。在本论文中,我们采用各种经验的和第一性原理的方法对中等尺寸的GanAsm团簇(n+m=17-24,n-m=0,±1)、Mn原子替代掺杂的Pd。团簇(n=3-19)和吸附F、O与N原子的GaN类石墨烯单层的结构和性质进行了研究,具体内容如下：
通过使用遗传算法(GA)、Basin-hopping Monte Carlo方法(BHMC)结合Stillinger-Weber经验势和密度泛函理论(DFT)系统地研究了化学计量的和非化学计量的GanAsm团簇(n+m=17-24,n-m=0,±1)的结构、电子性质和极化性质,并重点讨论了决定团簇极化率的因素。我们发现研究范围内的所有最低能量结构都是笼形结构,总的键的数目大约是2n+m。团簇的总极化率对团簇体积表现出近乎与组分无关的线性依赖关系。此外,离化势和组分对极化率也有着重要影响。与化学计量的GanAsm团簇相比,非化学计量的团簇倾向于拥有更大的极化率,但是由于异构体效应这种奇偶震荡行为很难在实验中观察到。由于拥有特殊的构型和特殊的HOMO-LUMO电子分布,Ga10As11表现出反常的电子性质,其HOMO-LUMO能隙和离化势与化学计量的团簇十分相似。
通过使用自旋极化的密度泛函方法(DFT)结合遗传算法(GA)和嵌入原子势(EAM)系统地研究了Pdn团簇和双金属Pdn-1Mn团簇(n=3-19)的结构和磁性质,并重点讨论了掺杂锰的钯团簇的磁性随尺寸和结构的演化以及锰元素影响钯团簇磁性的机制。首先我们将所得到的Pdn团簇与前人的结果进行了比较,发现了新的最低能量结构,包括Pd11,Pd12,Pd14,Pd17。通过结构和杂化解释了Pdn团簇的总磁矩的跳跃行为。当n=3-9时,Mn原子替代掺杂几乎不改变Pdn团簇的结构,但是随着团簇尺寸增大,掺杂Mn原子倾向于替代一个内部原子,使团簇发生结构重构,并倾向于形成二十面体基的结构。Mn原子掺杂不仅能增强钯团簇的稳定性,而且可以将绝大多数钯团簇的磁性增强3-5μB。此外,Pdn-1Mn团簇的总磁矩表现出台阶行为基础上的震荡行为,这种行为与Pd-Mn键长密切相关,并且可归因于Pd原子和Mn原子之间的d-d互作用。
使用自旋极化的密度泛函理论研究了具有强烈非金属性的F、O和N原子以不同覆盖率(1/8和1/2)吸附在GaN类石墨烯单层上对其磁性和能带结构的影响。通过吸附F原子可以将间接带隙半导体的GaN单层转变为磁性半金属,当F的覆盖率增长到很高时,体系又变回非磁性的半导体。我们使用Ising模型和Monte Carlo模拟估算低覆盖率(1/8)吸附F的GaN单层的的居里温度为260K。不论是高覆盖率(1/2)吸附还是低覆盖率(1/8)吸附N原子,GaN单层都能转变为磁性半金属,相应的居里温度分别估算为220K和50K。上述的吸附诱导磁性主要来自N2p(尤其是N2pz)轨道的自旋劈裂。吸附O原子不会诱导出磁性,但可以减小体系的带隙,且覆盖率越高带隙越小。
The size of nanomaterials is comparable to the electron coherent length, which leads to obvious surface effect, quantum size effect, quantum tunnel effect, and so on. Accordingly, they exhibit many unusual properties in the fields of thermodynamics, magnetism, optics and conductivity, etc, which are much different from those of corresponding bulk and atomic state. In the past few decades, nanomaterials based on molecules, clusters, nanowires, nanotubes or graphene developed rapidly, which bring about a revolutionary change in medical science, manufacturing industry, information communication, material science, and so on. The nanomaterials have not only wide application prospect but also a great fundamental importance of exploring the internal relations between macroscopic and microscopic systems.
Clusters, as the bridge between microscopic atoms or molecules and macroscopic condensed matter, are ideal building blocks to design new nanomaterials. Before assembling new materials from clusters, we need to make it clear how the properties of clusters vary with their shapes and sizes, and how to modulate their properties for different purpose as well. Mixed atomic clusters, especially binary semiconductor clusters and alloy clusters, have drawn much attention, due to that their properties can be modulated easily by changing the composition. In addition, with the rapid development of electronic components and magnetic storage devices, the size of the components and electric circuit becomes smaller and smaller, and as a result the surface and interface get more and more important. The adsorption is a common surface phenomenon, which can exert a great influence on the activity of adsorbate, the magnetism and band structure of the materials, and so on. In this thesis, we use various methods from empirical to first-principles to study the structures and properties of medium-sized GanAsm clusters (n+m=17-24, n-m=0,±1), Pdn clusters (n=3-19) doped by Mn atoms and graphene-like GaN monolayer adsorbing F, O and N adatoms.
By using genetic algorithm(GA), basin-hopping Monte Carlo method (BHMC) combined with Stillinger-Weber empirical potential and density functional theory (DFT) calculations, the geometries, electronic properties and polarizabilities of stoichiometric and nonstoichiometric GanAsm clusters (n+m=17-24, n-m=0,±) are investigated systematically, with emphasis on what determines the polarizabilities. All the lowest energy structures are hollow cages with a total number of bonds of about2n+m. The total polarizabilities of GanAsm clusters exhibit a linear dependence on their volumes despite of different composition. The polarizabilities are also strongly correlated to ionization potentials and composition. The nonstoichiometric GanAsm clusters tend to possess higher polarizabilities than stoichiometric ones, but this behavior is hard to be observed from experiment due to isomerization. Ga10As11, seen as a fragment of Ga12As12, has special HOMO-LUMO electron density distribution which accounts for its unusual electronic properties like stoichiometric clusters.
The geometries and magnetic properties of both Pdn and Pdn-1Mn (n=3-19) clusters are calculated by using spin-polarized density functional theory approach combined with genetic algorithm and embedded atom method (EAM).We emphatically discussed the magnetism evolution of the Mn-doped palladium clusters with their structures and size, and how the Mn element influences the magnetic behavior of palladium clusters as well. By comparing our geometries with early results, several new lowest energy structures of Pdn clusters (n=11,12,14,17) are found. The jump of the total magnetic moments of Pdn clusters is explained in terms of structures and hybridization. For large cluster size (n>9), when a Mn atom is doped into the Pdn cluster, it tends to occupy an interior site of the cluster and the geometry reconstruction generally occurs, and the cluster is apt to form an icosahedron based structure for n>13. The doping of Mn atoms not only enhances the stability of Pdn clusters, but also increases their total magnetic moments by a magnitude of3-5μB. Moreover, the doping of Mn atoms causes the Pdn_1Mn clusters to give rise to an evident oscillation of step-like magnetic behavior, which is closely related to the Pd-Mn bond length and can be attributed to the d-d interaction between Pd and Mn atoms.
The effect of adatoms (F, N and O) on the magnetism and band structure of graphenelike GaN monolayer (ML) at different coverages (1/2and1/8) is studied by spin-polarized density functional theory calculations. Adsorbing F adatoms at low coverage causes the GaN monolayer to be transformed from a nonmagnetic indirect-band-gap semiconductor into a magnetic half metal, whereas the monolayer turns back to a nonmagnetic semiconductor at high coverage. Using the Ising model and Monte Carlo simulation, we get an estimation of the Curie temperature of low coverage F-adsorbed GaN monolayer of260K. The GaN monolayer becomes a magnetic half metal after adsorbing N adatoms, no matter whether the coverage is high (1/2) or low (1/8), and their Curie temperatures are estimated to be220K and50K. The magnetism mentioned above mainly comes from the spin splitting of N2p (especially N2pz) orbits. On the other hand, the adsorption of O does not induce magnetism but reduces the band gap of the GaN monolayer and the higher the coverage is the smaller the gap is.
引文
[1]王广厚,《团簇物理学》,上海科学技术出版社,2003.
[2]B. Kaiser and K. Rademann, "Photoelectron spectroscopy of neutral mercury clusters Hg_{x} (x≤109) in a molecular beam", Phys. Rev. Lett.69,3204 (1992).
[3]C. Brechignac, Ph Cahuzac, J. Leygnier, and A. Sarfati, "Optical response of large lithium clusters:Evolution toward the bulk", Phys. Rev. Lett.70,2036 (1993).
[4]Yang Jinlong, F. Toigo, and Wang Kelin, "Structural, electronic, and magnetic properties of small rhodium clusters", Phys. Rev. B 50,7915 (1994).
[5]K. Rademann, O. Dimopoulou-Rademann, M. Schlauf, U. Even, and F. Hensel, "Evolution of surface plasmon resonance absorption in large gas phase clusters of mercury:Approaching the bulk", Phys. Rev. Lett.69,3208 (1992).
[6]M. G. Bawendi, M. L. Steigerwald, and L. E. Brus, "The Quantum-Mechanics of Larger Semiconductor Clusters (Quantum Dots)", Annu. Rev. Phys. Chem.41, 477 (1990).
[7]E. W. Becker, K. Bier, and W. Henkes, "STRAHLEN AUS KONDENSIERTEN ATOMEN UND MOLEKELN IM HOCHVAKUUM", Z. Phys. D 146,333 (1956).
[8]W. D. Knight, Keith Clemenger, Walt A. de Heer, Winston A. Saunders, M. Y. Chou, and Marvin L. Cohen, "Electronic Shell Structure and Abundances of Sodium Clusters", Phys. Rev. Lett.52,2141 (1984).
[9]H. W. Kroto, J. R. Heath, S. C. Obrien, R. F. Curl, and R. E. Smalley, "C-60-Buckminsterfullerene", Nature 318,162 (1985).
[10]T. Bergmann, H. Limberger, and T. P. Martin, "Evidence of electronic shell structure in Cs-O clusters", Phys. Rev. Lett.60,1767 (1988).
[11]Kenneth E. Schriver, John L. Persson, Eric C. Honea, and Robert L. Whetten, "Electronic shell structure of group-ⅢA metal atomic clusters", Phys. Rev. Lett. 64,2539(1990).
[12]S.N. Khanna and S. Linderoth, "Magnetic behavior of clusters of ferromagnetic transition metals", Phys. Rev. Lett.67,742 (1991).
[13]A. J. Cox, J. G. Louderback, S. E. Apsel, and L. A. Bloomfield, "MAGNETISM IN 4D-TRANSITION METAL-CLUSTERS", Phys. Rev. B 49,12295 (1994).
[14]M. Moseler, H. Hakkinen, R. N. Barnett, and U. Landman, "Structure and magnetism of neutral and anionic palladium clusters", Phys. Rev. Lett.86,2545 (2001).
[15]Walt A. de Heer, Kathy Selby, Vitaly Kresin, Jun Masui, Michael Vollmer, A. Chatelain, and W. D. Knight, "Collective dipole oscillations in small sodium clusters", Phys. Rev. Lett.59,1805 (1987).
[16]L. N. Lewis, "CHEMICAL CATALYSIS BY COLLOIDS AND CLUSTERS", Chem. Rev.93,2693 (1993).
[17]Keeyung Lee, Joseph Callaway, and S. Dhar, "Electronic structure of small iron clusters", Phys. Rev. B 30,1724 (1984).
[18]Jose Luis Martins, Jean Buttet, and Roberto Car, "Equilibrium Geometries and Electronic Structures of Small Sodium Clusters", Phys. Rev. Lett.53,655 (1984).
[19]Krishnan Raghavachari and Veronika Logovinsky, "Structure and bonding in small silicon clusters", Phys. Rev. Lett.55,2853 (1985).
[20]Pietro Ballone, Wanda Andreoni, Roberto Car, and Michele Parrinello, "Equilibrium Structures and Finite Temperature Properties of Silicon Microclusters from ab initio Molecular-Dynamics Calculations", Phys. Rev. Lett. 60,271 (1988).
[21]S. N. Khanna, F. Reuse, and J. Buttet, "Stability and Observability of Charged Beryllium Clusters", Phys. Rev. Lett.61,535 (1988).
[22]P. Moriarty, "Nanostructured materials", Rep. Prog. Phys.64,297 (2001).
[23]J. Friedel, "PHYSICS OF CLEAN METAL-SURFACES", Ann. Phys-paris.1, 257(1976).
[24]J. J. Zhao and R. H. Xie, "Genetic Algorithms for the Geometry Optimization of Atomic and Molecular Clusters", J. Comput. Theor. Nanosci.1,117 (2004).
[25]D. M. Deaven and K. M. Ho, "Molecular-Geometry Optimization with a Genetic Algorithm", Phys. Rev. Lett.75,288 (1995).
[26]D. J. Wales and H. A. Scheraga, "Review:Chemistry-Global optimization of clusters, crystals, and biomolecules", Science 285,1368 (1999).
[27]S. Yoo, J. J. Zhao, J. L. Wang, and X. C. Zeng, "Endohedral silicon fullerenes Si-N (27<= N<= 39)", J. Am. Chem. Soc.126,13845 (2004).
[28]J. L. Wang, J. L. Bai, J. Jellinek, and X. C. Zeng, "Gold-coated transition-metal anion Mn-13@Au-20 (-) with ultrahigh magnetic moment", J. Am. Chem. Soc. 129,4110(2007).
[29]F. Ding, A. Rosen, and K. Bolton, "Size dependence of the coalescence and melting of iron clusters:A molecular-dynamics study", Phys. Rev. B 70,075416 (2004).
[30]J. L. Wang, M. L. Yang, J. Jellinek, and G. H. Wang, "Dipole polarizabilities of medium-sized gold clusters", Phys. Rev. A 74,023202 (2006).
[31]G. L. Gutsev, R. H. O'Neal, B. C. Saha, M. D. Mochena, E. Johnson, and C. W. Bauschlicher, "Optical Properties of (GaAs)(n) Clusters (n=2-16)", J. Phys. Chem. A 112,10728(2008).
[32]W. E. Kaden, T. P. Wu, W. A. Kunkel, and S. L. Anderson, "Electronic Structure Controls Reactivity of Size-Selected Pd Clusters Adsorbed on TiO2 Surfaces", Science 326,826 (2009).
[33]T. Mitsui, M. K. Rose, E. Fomin, D. F. Ogletree, and M. Salmeron, "Water diffusion and clustering on Pd(111)", Science 297,1850 (2002).
[34]Y. Lei, F. Mehmood, S. Lee, J. Greeley, B. Lee, S. Seifert, R. E. Winans, J. W. Elam, R. J. Meyer, P. C. Redfern, D. Teschner, R. Schlogl, M. J. Pellin, L. A. Curtiss, and S. Vajda, "Increased Silver Activity for Direct Propylene Epoxidation via Subnanometer Size Effects", Science 328,224 (2010).
[35]B. Yoon, H. Hakkinen, U. Landman, A. S. Worz, J. M. Antonietti, S. Abbet, K. Judai, and U. Heiz, "Charging effects on bonding and catalyzed oxidation of CO on Au-8 clusters on MgO", Science 307,403 (2005).
[36]W. D. Luedtke and U. Landman, "Slip diffusion and Levy flights of an adsorbed gold nanocluster", Phys. Rev. Lett.82,3835 (1999).
[37]X. Q. Dai, Y. N. Tang, J. H. Zhao, and Y. W. Dai, "Absorption of Pt clusters and the induced magnetic properties of graphene", J. Phys-condens. Mat.22,316005 (2010).
[38]R. Schafer, S. Schlecht, J. Woenckhaus, and J. A. Becker, "Polarizabilities of isolated semiconductor clusters", Phys. Rev. Lett.76,471 (1996).
[39]I. Vasiliev, S. Ogut, and J. R. Chelikowsky, "Ab initio calculations for the polarizabilities of small semiconductor clusters", Phys. Rev. Lett.78,4805 (1997).
[40]Y. P. Feng, T. B. Boo, H. H. Kwong, C. K. Ong, A. Kumar, and S. Kabana, "Composition dependence of structural and electronic properties of GamAsn clusters from first principles", Phys. Rev. B 76,045336 (2007).
[41]S. Y. Yin, R. Moro, X. S. Xu, and W. A. de Heer, "Magnetic enhancement in cobalt-manganese alloy clusters", Phys. Rev. Lett.98,113401 (2007).
[42]F. Tao, M. E. Grass, Y. W. Zhang, D. R. Butcher, J. R. Renzas, Z. Liu, J. Y. Chung, B. S. Mun, M. Salmeron, and G. A. Somorjai, "Reaction-Driven Restructuring of Rh-Pd and Pt-Pd Core-Shell Nanoparticles", Science 322,932 (2008).
[43]Lucas Fernandez-Seivane and Jaime Ferrer, "Magnetic Anisotropies of Late Transition Metal Atomic Clusters", Phys. Rev. Lett.99,183401 (2007).
[44]G. Pastor, J. Dorantes-Davila, S. Pick, and H. Dreysse, "Magnetic Anisotropy of 3d Transition-Metal Clusters", Phys. Rev. Lett.75,326 (1995).
[45]B. Yoon and U. Landman, "Electric field control of structure, dimensionality, and reactivity of gold nanoclusters on metal-supported MgO films", Phys. Rev. Lett. 100,056102 (2008).
[46]X. Li, A. E. Kuznetsov, H. F. Zhang, A. I. Boldyrev, and L. S. Wang, "Observation of all-metal aromatic molecules", Science 291,859 (2001).
[47]D. K. Seo and J. D. Corbett, "Perspectives:Chemistry-Aromatic metal clusters", Science 291,841 (2001).
[48]Victor M. Medel, Jose Ulises Reveles, Shiv N. Khanna, Vikas Chauhan, Prasenjit Sen, and A. Welford Castleman, "Hund's rule in superatoms with transition metal impurities", Proc. Natl. Acad. Sci. U. S. A.108,10062 (2011).
[49]D. E. Bergeron, P. J. Roach, A. W. Castleman, N. Jones, and S. N. Khanna, "Al cluster superatoms as halogens in polyhalides and as alkaline earths in iodide salts", Science 307,231 (2005).
[50]A. W. Castleman and S. N. Khanna, "Clusters, Superatoms, and Building Blocks of New Materials", J. Phys. Chem. C 113,2664 (2009).
[51]R. P. Andres, R. S. Averback, W. L. Brown, L. E. Brus, W. A. Goddard, A. Kaldor, S. G. Louie, M. Moscovits, P. S. Peercy, S. J. Riley, R. W. Siegel, F. Spaepen, and Y. Wang, "RESEARCH OPPORTUNITIES ON CLUSTERS AND CLUSTER-ASSEMBLED MATERIALS-A DEPARTMENT OF ENERGY, COUNCIL ON MATERIALS SCIENCE PANEL REPORT", J. Mater. Res.4, 704(1989).
[52]M. Brust, D. Bethell, C. J. Kiely, and D. J. Schiffrin, "Self-assembled gold nanoparticle thin films with nonmetallic optical and electronic properties", Langmuir.14,5425(1998).
[53]P. Melinon, V. Paillard, V. Dupuis, A. Perez, P. Jensen, A. Hoareau, M. Broyer, J. L. Vialle, M. Pellarin, B. Baguenard, and J. Lerme, "FROM FREE CLUSTERS TO CLUSTER-ASSEMBLED MATERIALS", Int. J. Mod. Phys. B 9,339 (1995).
[54]J. Bansmann, S. H. Baker, C. Binns, J. A. Blackman, J. P. Bucher, J. Dorantes-Davila, 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.56,189 (2005).
[55]W. A. Deheer, "THE PHYSICS OF SIMPLE METAL-CLUSTERS EXPERIMENTAL ASPECTS AND SIMPLE-MODELS", Rev. Mod. Phys.65, 611(1993).
[56]王广厚,”原子团簇的稳定结构和幻数”,物理学进展20,52(2000).
[57]黄昆,韩汝琦,《固体物理学》,高等教育出版社,1983.
[58]冯端,金国钧,《凝聚态物理系》,高等教育出版社,2006.
[59]A. Vega, J. Dorantes-Davila, L. C. Balbas, and G. M. Pastor, "Calculated sp-electron and spd-hybridization effects on the magnetic properties of small Fe_{N} clusters", Phys. Rev. B 47,4742 (1993).
[60]Isabelle M. L. Billas, J. A. Becker, A. Chatelain, and Walt A. de Heer, "Magnetic moments of iron clusters with 25 to 700 atoms and their dependence on temperature", Phys. Rev. Lett.71,4067 (1993).
[61]Isabelle M.L. Billas, A. Chatelain, and Walt A. de Heer, "Magnetism from the Atom to the Bulk in Iron, Cobalt, and Nickel Clusters", Science 265,1682 (1994).
[62]Y. H. Luo, H. Q. Sun, J. J. Zhao, and G. H. Wang, "Structural dependence of electronic and magnetic properties of the Cr-13 cluster", Commun. Theor. Phys. 34,43 (2000).
[63]J. A. Alonso, "Electronic and atomic structure, and magnetism of transition-metal clusters", Chem. Rev.100,637 (2000).
[64]Brett I. Dunlap, "Symmetry and cluster magnetism", Phys. Rev. A 41,5691 (1990).
[65]Zhi-qiang Li and Bing-lin Gu, "Electronic-structure calculations of cobalt clusters", Phys. Rev. B 47,13611 (1993).
[66]H. L. Zhang, D. X. Tian, and J. J. Zhao, "Structural evolution of medium-sized Pd-n (n= 15-25) clusters from density functional theory", J. Chem. Phys.129, 114302(2008).
[67]K. D. Gross, D. Riegel, and R. Zeller, "Magnetic-moment formation and spin dynamics of isolated 4d ions in palladium", Phys. Rev. Lett.65,3044 (1990).
[68]D. Riegel, L. Buermann, K. D. Gross, M. Luszik-Bhadra, and S. N. Mishra, "Existence and Stability of Magnetic 3d Moments in Noble-and Transition-Metal Hosts", Phys. Rev. Lett.62,316 (1989).
[69]Martin Schmidt, Robert Kusche, Bernd von Issendorff, and Hellmut Haberland, "Irregular variations in the melting point of size-selected atomic clusters", Nature 393,238(1998).
[70]S. Chacko, Kavita Joshi, D. G. Kanhere, and S. A. Blundell, "Why Do Gallium Clusters Have a Higher Melting Point than the Bulk?", Phys. Rev. Lett.92, 135506(2004).
[71]Gary A. Breaux, Robert C. Benirschke, Toshiki Sugai, Brian S. Kinnear, and Martin F. Jarrold, "Hot and Solid Gallium Clusters:Too Small to Melt", Phys. Rev. Lett.91,215508(2003).
[72]B. Kalita and R. C. Deka, "Reaction Intermediates of CO Oxidation on Gas Phase Pd-4 Clusters:A Density Functional Study", J. Am. Chem. Soc.131, 13252(2009).
[73]C. Zhang, B. Yoon, and U. Landman, "Predicted oxidation of CO catalyzed by Au nanoclusters on a thin defect-free MgO film supported on a Mo(100) surface", J. Am. Chem. Soc.129,2228 (2007).
[74]B. Huber, P. Koskinen, H. Hakkinen, and M. Moseler, "Oxidation of magnesia-supported Pd-clusters leads to the ultimate limit of epitaxy with a catalytic function", Nat. Mater.5,44 (2006).
[75]K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, "Electric field effect in atomically thin carbon films", Science 306,666 (2004).
[76]A. K. Geim and K. S. Novoselov, "The rise of graphene", Nat. Mater.6,183 (2007).
[77]Changgu Lee, Xiaoding Wei, Jeffrey W. Kysar, and James Hone, "Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene", Science 321,385 (2008).
[78]R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, "Fine Structure Constant Defines Visual Transparency of Graphene", Science 320,1308 (2008).
[79]J. R. Williams, L. DiCarlo, and C. M. Marcus, "Quantum Hall Effect in a Gate-Controlled p-n Junction of Graphene", Science 317,638 (2007).
[80]D. A. Abanin and L. S. Levitov, "Quantized Transport in Graphene p-n Junctions in a Magnetic Field", Science 317,641 (2007).
[81]S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, "Giant intrinsic carrier mobilities in graphene and its bilayer", Phys. Rev. Lett.100,016602 (2008).
[82]H. Sahin and R. T. Senger, "First-principles calculations of spin-dependent conductance of graphene flakes", Phys. Rev. B 78,205423 (2008).
[83]Xiaolin Li, Xinran Wang, Li Zhang, Sangwon Lee, and Hongjie Dai, "Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors", Science 319,1229(2008).
[84]H. Sevincli, M. Topsakal, E. Durgun, and S. Ciraci, "Electronic and magnetic properties of 3d transition-metal atom adsorbed graphene and graphene nanoribbons", Phys. Rev. B 77,195434 (2008).
[85]Y. F. Li, Z. Zhou, P. W. Shen, and Z. F. Chen, "Spin Gapless Semiconductor-Metal-Half-Metal Properties in Nitrogen-Doped Zigzag Graphene Nanoribbons", Acs Nano 3,1952 (2009).
[86]N. Gorjizadeh, A. A. Farajian, K. Esfarjani, and Y. Kawazoe, "Spin and band-gap engineering in doped graphene nanoribbons", Phys. Rev. B 78,155427 (2008).
[87]S. Dutta, A. K. Manna, and S. K. Pati, "Intrinsic Half-Metallicity in Modified Graphene Nanoribbons", Phys. Rev. Lett.102,096601 (2009).
[88]D. W. Boukhvalov and M. I. Katsnelson, "Chemical Functionalization of Graphene with Defects", Nano Lett.8,4373 (2008).
[89]D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V. Morozov, P. Blake, M. P. Halsall, A. C. Ferrari, D. W. Boukhvalov, M. I. Katsnelson, A. K. Geim, and K. S. Novoselov, "Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane", Science 323,610 (2009).
[90]J. Zhou, Q. Wang, Q. Sun, X. S. Chen, Y. Kawazoe, and P. Jena, "Ferromagnetism in Semihydrogenated Graphene Sheet", Nano Lett.9,3867 (2009).
[91]M. H. Wu, Y. Pei, and X. C. Zeng, "Planar Tetracoordinate Carbon Strips in Edge Decorated Graphene Nanoribbon", J. Am. Chem. Soc.132,5554 (2010).
[92]E. J. Kan, Z. Y. Li, J. L. Yang, and J. G. Hou, "Half-metallicity in edge-modified zigzag graphene nanoribbons", J. Am. Chem. Soc.130,4224 (2008).
[93]Chuanhong Jin, Fang Lin, Kazu Suenaga, and Sumio Iijima, "Fabrication of a Freestanding Boron Nitride Single Layer and Its Defect Assignments", Phys. Rev. Lett.102,195505 (2009).
[94]B. Lalmi, H. Oughaddou, H. Enriquez, A. Kara, S. Vizzini, B. Ealet, and B. Aufray, "Epitaxial growth of a silicene sheet", Appl. Phys. Lett.97,223109 (2010).
[95]C. Tusche, H. L. Meyerheim, and J. Kirschner, "Observation of depolarized ZnO(0001) monolayers:Formation of unreconstructed planar sheets", Phys. Rev. Lett.99,026102(2007).
[96]H. Sahin, S. Cahangirov, M. Topsakal, E. Bekaroglu, E. Akturk, R. T. Senger, and S. Ciraci, "Monolayer honeycomb structures of group-IV elements and Ⅲ-Ⅴ binary compounds:First-principles calculations", Phys. Rev. B 80,155453 (2009).
[97]A. R. Botello-Mendez, F. Lopez-Urias, M. Terrones, and H. Terrones, "Magnetic behavior in zinc oxide zigzag nanoribbons", Nano Lett.8,1562 (2008).
[98]E. Kan, H. J. Xiang, F. Wu, C. Lee, J. L. Yang, and M. H. Whangbo, "Ferrimagnetism in zigzag graphene nanoribbons induced by main-group adatoms", Appl. Phys. Lett.96,102503 (2010).
[99]Q. Chen, J. L. Wang, L. Y. Zhu, S. D. Wang, and F. Ding, "Fluorination induced half metallicity in two-dimensional few zinc oxide layers", J. Chem. Phys.132, 204703 (2010).
[100]B. Xu, J. Yin, Y. D. Xia, X. G. Wan, and Z. G. Liu, "Ferromagnetic and antiferromagnetic properties of the semihydrogenated SiC sheet", Appl. Phys. Lett.96,143111 (2010).
[101]E. Bekaroglu, M. Topsakal, S. Cahangirov, and S. Ciraci, "First-principles study of defects and adatoms in silicon carbide honeycomb structures", Phys. Rev. B 81,075433 (2010).
[102]C. Ataca and S. Ciraci, "Functionalization of BN honeycomb structure by adsorption and substitution of foreign atoms", Phys. Rev. B 82,165402 (2010).
[103]Arun K Manna and Swapan K Pati, "Tunable Electronic and Magnetic Properties in B x N y C z Nanohybrids:Effect of Domain Segregation", The Journal of Physical Chemistry C 115,10842 (2011).
[104]Natalia Berseneva, Arkady Krasheninnikov, and Risto Nieminen, "Mechanisms of Postsynthesis Doping of Boron Nitride Nanostructures with Carbon from First-Principles Simulations", Phys. Rev. Lett.107,035501 (2011).
[105]Somnath Bhowmick, Abhishek K Singh, and Boris I Yakobson, "Quantum Dots and Nanoroads of Graphene Embedded in Hexagonal Boron Nitride", The Journal of Physical Chemistry C 115,9889 (2011).
[106]F. Diederich and M. Kivala, "All-Carbon Scaffolds by Rational Design", Adv. Mater.22,803(2010).
[107]Jian Zhou, Kun Lv, Qian Wang, X. S. Chen, Qiang Sun, and Puru Jena, "Electronic structures and bonding of graphyne sheet and its BN analog", The Journal of Chemical Physics 134,174701 (2011).
[1]E. Wimmer,《Prediction of Materials Properties》,1998.
[2]N. Metropolis and S. Ulam, "THE MONTE CARLO METHOD", J. Am. Stat. Assoc.44,335(1949).
[3]N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, "EQUATION OF STATE CALCULATIONS BY FAST COMPUTING MACHINES", J. Chem. Phys.21,1087 (1953).
[4]张跃,谷景华,尚家香,马岳,《计算材料学基础》,北京航空航天大学出版社,2007.
[5]D. Frenkel and B. Smit,《Understanding Molecular Simulations:From Algorithms to Applications》, (Academic Press,1996).
[6]R. D. Mountain and D. Thirumalai, "QUANTITATIVE MEASURE OF EFFICIENCY OF MONTE-CARLO SIMULATIONS", Physica A 210,453 (1994).
[7]D. J. Wales and J. P. K. Doye, "Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms", J. Phys. Chem. A 101,5111 (1997).
[8]D. J. Wales and M. P. Hodges, "Global minima of water clusters (H2O)(n), n<= 21, described by an empirical potential", Chem. Phys. Lett.286,65 (1998).
[9]D. J. Wales and H. A. Scheraga, "Review:Chemistry- Global optimization of clusters, crystals, and biomolecules", Science 285,1368 (1999).
[10]GMIN, http://www-wales.ch.cam.ac.uk/GMIN/
[11]B. J. Alder and T. E. Wainwright, "PHASE TRANSITION FOR A HARD SPHERE SYSTEM", J. Chem. Phys.27,1208 (1957).
[12]B. J. Alder and T. E. Wainwright, "STUDIES IN MOLECULAR DYNAMICS.1. GENERAL METHOD", J. Chem. Phys.31,459 (1959).
[13]唐景昌,徐伦彪,《固体理论导论》,浙江大学出报社,1997.
[14]L. Verlet, "COMPUTER EXPERIMENTS ON CLASSICAL FLUIDS.1. THERMODYNAMICAL PROPERTIES OF LENNARD-JONES MOLECULES", Phys. Rev.159,98 (1967).
[15]R. W. Hockney, "The potential calculation and some applications", Methods in Computational Physics 9,135 (1970).
[16]W. C. Swope, H. C. Andersen, P. H. Berens, and K. R. Wilson, "A COMPUTER-SIMULATION METHOD FOR THE CALCULATION OF EQUILIBRIUM-CONSTANTS FOR THE FORMATION OF PHYSICAL CLUSTERS OF MOLECULES-APPLICATION TO SMALL WATER CLUSTERS", J. Chem. Phys.76,637 (1982).
[17]D. Beeman, "SOME MULTISTEP METHODS FOR USE IN MOLECULAR-DYNAMICS CALCULATIONS", J. Comput. Phys.20,130 (1976).
[18]S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "OPTIMIZATION BY SIMULATED ANNEALING", Science 220,671 (1983).
[19]S. Geman and D. Geman, "STOCHASTIC RELAXATION, GIBBS DISTRIBUTIONS, AND THE BAYESIAN RESTORATION OF IMAGES", IEEE. T. Pattern. Anal.6,721 (1984).
[20]H. C. Andersen, "MOLECULAR-DYNAMICS SIMULATIONS AT CONSTANT PRESSURE AND-OR TEMPERATURE", J. Chem. Phys.72,2384 (1980).
[21]William G. Hoover, "Canonical dynamics:Equilibrium phase-space distributions", Phys. Rev. A 31,1695(1985).
[22]陈正隆,《分子模拟》,2002.
[23]D. M. Deaven and K. M. Ho, "Molecular-Geometry Optimization with a Genetic Algorithm", Phys. Rev. Lett.75,288 (1995).
[24]J. Maddox, "GENETICS HELPING MOLECULAR-DYNAMICS", Nature 376, 209(1995).
[25]J. J. Zhao and R. H. Xie, "Genetic Algorithms for the Geometry Optimization of Atomic and Molecular Clusters", J. Comput. Theor. Nanosci.1,117 (2004).
[26]J. A. Niesse and H. R. Mayne, "Global geometry optimization of atomic clusters using a modified genetic algorithm in space-fixed coordinates", J. Chem. Phys. 105,4700(1996).
[27]Sougata Pal, Rahul Sharma, Biplab Goswami, Pranab Sarkar, and S. P. Bhattacharyya, "A search for lowest energy structures of ZnS quantum dots: Genetic algorithm tight-binding study", The Journal of Chemical Physics 130, 214703 (2009).
[28]Jijun Zhao, Li Ma, and Bin Wen, "Lowest-energy endohedral fullerene structure of Si 60 from a genetic algorithm and density-functional theory", J. Phys.: Condens. Matter 19,226208 (2007).
[29]J. L. Wang, G. H. Wang, and J. J. Zhao, "Structure and electronic properties of Ge-n (n=2-25) clusters from density-functional theory", Phys. Rev. B 64,205411 (2001).
[30]J. L. Wang, G. H. Wang, and J. J. Zhao, "Density-functional study of Au-n (n= 2-20) clusters:Lowest-energy structures and electronic properties", Phys. Rev. B 66,035418(2002).
[31]B. L. Wang, S. Y. Yin, G. H. Wang, A. Buldum, and J. J. Zhao, "Novel structures and properties of gold nanowires", Phys. Rev. Lett.86,2046 (2001).
[32]B. L. Wang, S. Y. Yin, G. H. Wang, and J. J. Zhao, "Structures and electronic properties of ultrathin titanium nanowires", J. Phys.:Condens. Matter 13, L403 (2001).
[33]R. L. Johnston, "Evolving better nanoparticles:Genetic algorithms for optimising cluster geometries", Dalton Trans.,4193 (2003).
[34]Frank H. Stillinger and Thomas A. Weber, "Computer simulation of local order in condensed phases of silicon", Phys. Rev. B 31,5262 (1985).
[35]J. Tersoff, "Modeling solid-state chemistry:Interatomic potentials for multicomponent systems", Phys. Rev. B 39,5566 (1989).
[36]Donald W. Brenner, "Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films", Phys. Rev. B 42,9458 (1990).
[37]Fabrizio Cleri and Vittorio Rosato, "Tight-binding potentials for transition metals and alloys", Phys. Rev. B 48,22 (1993).
[38]Murray S. Daw and M. I. Baskes, "Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals", Phys. Rev. Lett.50,1285 (1983).
[39]M. S. Daw and M. I. Baskes, "EMBEDDED-ATOM METHOD-DERIVATION AND APPLICATION TO IMPURITIES, SURFACES, AND OTHER DEFECTS IN METALS", Phys. Rev. B 29,6443 (1984).
[40]F. Ercolessi, E. Tosatti, and M. Parrinello, "Au (100) Surface Reconstruction", Phys. Rev. Lett.57,719 (1986).
[41]Z. Q. Wang, D. Stroud, and A. J. Markworth, "Monte Carlo study of the liquid CdTe surface", Phys. Rev. B 40,3129 (1989).
[42]V. Rosato, M. Guillope, and B. Legrand, "THERMODYNAMICAL AND STRUCTURAL-PROPERTIES OF FCC TRANSITION-METALS USING A SIMPLE TIGHT-BINDING MODEL", Philos. Mag. A 59,321 (1989).
[43]I. L. Garzon and J. Jellinek, "MELTING OF GOLD MICROCLUSTERS", Zeitschrift Fur Physik D 20,235 (1991).
[44]L. Hui, F. Pederiva, B. L. Wang, J. L. Wang, and G. H. Wang, "How does the nickel nanowire melt?", Appl. Phys. Lett.86,011913 (2005).
[45]P. Hohenberg and W. Kohn, "INHOMOGENEOUS ELECTRON GAS", Phys. Rev.136, B864 (1964).
[46]R. A. Johnson, "Analytic nearest-neighbor model for fcc metals", Phys. Rev. B 37,3924 (1988).
[47]S. M. Foiles, M. I. Baskes, and M. S. Daw, "Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys", Phys. Rev. B 33, 7983 (1986).
[48]M. W. Finnis and J. E. Sinclair, "A SIMPLE EMPIRICAL N-BODY POTENTIAL FOR TRANSITION-METALS", Philos. Mag. A 50,45 (1984).
[49]R. A. Johnson and D. J. Oh, "ANALYTIC EMBEDDED ATOM METHOD MODEL FOR BCC METALS", J. Mater. Res.4,1195 (1989).
[50]S. L. Chen, J. C. Xu, and H. S. Zhang, "A new scheme of many-body potentials for hep metals", Comp. Mater. Sci.29,428 (2004).
[51]D. J. Oh and R. A. Johnson, "SIMPLE EMBEDDED ATOM METHOD MODEL FOR FCC AND HCP METALS", J. Mater. Res.3,471 (1988).
[52]M. I. Baskes, "Modified embedded-atom potentials for cubic materials and impurities", Phys. Rev. B 46,2727 (1992).
[53]欧阳义芳,钟夏平,”凝聚态物质计算和模拟中使用的相互作用势”,力学进展36,321(2006).
[54]D. R. Hartree, "The wave mechanics of an atom with a non-Coulomb central field Part I theory and methods", Proc. Cambridge Philos. Soc 24,89 (1928).
[55]J. C. Slater and G. F. Koster, "Simplified LCAO Method for the Periodic Potential Problem", Phys. Rev.94,1498 (1954).
[56]L. H. Thomas, "The calculation of atomic fields", Proc. Cambridge Philos. Soc 23,542 (1927).
[57]E. Fermi, "Un Metodo Statistico per la Determinazione di alcune Prioprieta dell'Atomo", Rend. Acad. Maz. Lancei 6,602 (1927).
[58]W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects", Phys. Rev.140, A1133 (1965).
[59]冯端,金国钧,《凝聚态物理系》,高等教育出版社,2006.
[60]W. Kohn, "Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms", Phys. Rev. Lett.76,3168 (1996).
[61]D. M. Ceperley and B. J. Alder, "GROUND-STATE OF THE ELECTRON-GAS BY A STOCHASTIC METHOD", Phys. Rev. Lett.45,566 (1980).
[62]J. P. Perdew and A. Zunger, "SELF-INTERACTION CORRECTION TO DENSITY-FUNCTIONAL APPROXIMATIONS FOR MANY-ELECTRON SYSTEMS", Phys. Rev. B 23,5048 (1981).
[63]John P. Perdew and Yue Wang, "Accurate and simple analytic representation of the electron-gas correlation energy", Phys. Rev. B 45,13244 (1992).
[64]John P. Perdew, J. A. Chevary, S. H. Vosko, Koblar A. Jackson, Mark R. Pederson, D. J. Singh, and Carlos Fiolhais, "Atoms, molecules, solids, and surfaces:Applications of the generalized gradient approximation for exchange and correlation", Phys. Rev. B 46,6671 (1992).
[65]A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, "Density-functional theory and strong interactions:Orbital ordering in Mott-Hubbard insulators", Phys. Rev. B 52, R5467 (1995).
[66]E. Wimmer, 《All electron methods》,2001.
[1]X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S. Weiss, "Quantum dots for live cells, in vivo imaging, and diagnostics", Science 307,538 (2005).
[2]T. Calarco, A. Datta, P. Fedichev, E. Pazy, and P. Zoller, "Spin-based all-optical quantum computation with quantum dots:Understanding and suppressing decoherence", Phys. Rev. A 68,012310 (2003).
[3]Y. Z. Lan, W. D. Cheng, D. S. Wu, J. Shen, S. P. Huang, H. Zhang, Y. J. Gong, and F. F. Li, "A theoretical investigation of hyperpolarizability for small GanAsm (n+m=4-10) clusters", J. Chem. Phys.124,094302 (2006).
[4]P. Karamanis, D. Begue, and C. Pouchan, "Ab initio finite field (hyper)polarizability computations on stoichiometric gallium arsenide clusters GanAsn (n=2-9)", J. Chem. Phys.127,094706 (2007).
[5]S. C. O'brien, Y Liu, Q. Zhang, J. R. Heath, F. K. Tittel, R. F. Curl, and R. E. Smalley, "Supersonic Cluster Beams of Iii-V Semiconductors-Gaxasy", J. Chem. Phys.84,4074 (1986).
[6]R. Schafer, S. Schlecht, J. Woenckhaus, and J. A. Becker, "Polarizabilities of isolated semiconductor clusters", Phys. Rev. Lett.76,471 (1996).
[7]R. Schafer and J. A. Becker, "Photoabsorption spectroscopy on isolated GaNAsM clusters", Phys. Rev. B 54,10296 (1996).
[8]J. J. BelBruno, "Bonding and energetics in small clusters of gallium and arsenic", Heteroatom Chem.14,189 (2003).
[9]L. Lou, L. Wang, L. P. F. Chibante, R. T. Laaksonen, P. Nordlander, and R. E. Smalley, "Electronic-Structure of Small Gaas Clusters", J. Chem. Phys.94,8015 (1991).
[10]I. Vasiliev, S. Ogut, and J. R. Chelikowsky, "Ab initio calculations for the polarizabilities of small semiconductor clusters", Phys. Rev. Lett.78,4805 (1997).
[11]Y. P. Feng, T. B. Boo, H. H. Kwong, C. K. Ong, A. Kumar, and S. Kabana, "Composition dependence of structural and electronic properties of GamAsn clusters from first principles", Phys. Rev. B 76,045336 (2007).
[12]G. L. Gutsev, E. Johnson, M. D. Mochena, and C. W. Bauschlicher, "The structure and energetics of (GaAS)(n), (GaAs)(n)(-), and (GaAs)(n)(+) (n=2-15)", J. Chem. Phys.128,144707 (2008).
[13]G. L. Gutsev, R. H. O'Neal, B. C. Saha, M. D. Mochena, E. Johnson, and C. W. Bauschlicher, "Optical Properties of (GaAs)(n) Clusters (n=2-16)", J. Phys. Chem. A112,10728(2008).
[14]J. J. Zhao, R. H. Xie, X. L. Zhou, X. S. Chen, and W. Lu, "Formation of stable fullerenelike GanAsn clusters (6<= n<= 9):Gradient-corrected density-functional theory and a genetic global optimization approach", Phys. Rev. B 74,035319 (2006).
[15]Z. Q. Wang and D. Stroud, "MONTE-CARLO STUDY OF LIQUID GAAS-BULK AND SURFACE-PROPERTIES", Phys. Rev. B 42,5353 (1990).
[16]D. M. Deaven and K. M. Ho, "Molecular-Geometry Optimization with a Genetic Algorithm", Phys. Rev. Lett.75,288 (1995).
[17]J. J. Zhao and R. H. Xie, "Genetic Algorithms for the Geometry Optimization of Atomic and Molecular Clusters", J. Comput. Theor. Nanosci.1,117 (2004).
[18]D. J. Wales and J. P. K. Doye, "Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms", J. Phys.Chem.A 101,5111 (1997).
[19]Frank H. Stillinger and Thomas A. Weber, "Computer simulation of local order in condensed phases of silicon", Phys. Rev. B 31,5262 (1985).
[20]B. Delley, "AN ALL-ELECTRON NUMERICAL-METHOD FOR SOLVING THE LOCAL DENSITY FUNCTIONAL FOR POLYATOMIC-MOLECULES", J. Chem. Phys.92,508 (1990).
[21]John P. Perdew and Yue Wang, "Accurate and simple analytic representation of the electron-gas correlation energy", Phys. Rev. B 45,13244 (1992).
[22]John P. Perdew, J. A. Chevary, S. H. Vosko, Koblar A. Jackson, Mark R. Pederson, D. J. Singh, and Carlos Fiolhais, "Atoms, molecules, solids, and surfaces:Applications of the generalized gradient approximation for exchange and correlation", Phys. Rev. B 46,6671 (1992).
[23]J. P. Perdew, K. Burke, and M. Ernzerhof, "Generalized gradient approximation made simple", Phys. Rev. Lett.77,3865 (1996).
[24]G.W. Trucks M.J. Frisch, H.B. Schlegel, G.E. Scuseria,M.A. Robb, J.R. Cheeseman,, J.A. Montgomery V.G. Zakrzewski, Jr., R.E. Stratmann, J.C. Burant, S. Dapprich,, A.D. Daniels J.M. Millam, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V., M. Cossi Barone, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J., G.A. Petersson Ochterski, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D., K. Raghavachari Rabuck, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul,, G. Liu B.B. Stefanov, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M., P.M.W. Gill Challacombe, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C., M. Head-Gordon Gonzalez, E.S. Replogle, J.A. Pople, GAUSSIAN 03, Gaussian,, and Pittsburgh Inc., PA,2003., "GAUSSIAN 03, Gaussian, Inc., Pittsburgh, PA,2003.".
[25]A. D. Becke, "DENSITY-FUNCTIONAL EXCHANGE-ENERGY APPROXIMATION WITH CORRECT ASYMPTOTIC-BEHAVIOR", Phys. Rev. A 38,3098 (1988).
[26]J. P. Perdew, K. Burke, and Y. Wang, "Generalized gradient approximation for the exchange-correlation hole of a many-electron system", Phys. Rev. B 54,16533 (1996).
[27]L. A. Curtiss, M. P. Mcgrath, J. P. Blaudeau, N. E. Davis, R. C. Binning, and L. Radom, "Extension of Gaussian-2 Theory to Molecules Containing 3rd-Row Atoms Ga-Kr", J. Chem. Phys.103,6104 (1995).
[28]B. L. Wang, S. Y. Yin, G. H. Wang, A. Buldum, and J. J. Zhao, "Novel structures and properties of gold nanowires", Phys. Rev. Lett.86,2046 (2001).
[29]A. D. McLean and Yoshimin.M, "THEORY OF MOLECULAR POLARIZABILITIES", J. Chem. Phys.47,1927 (1967).
[30]S. Schlecht, R. Schafer, J. Woenckhaus, and J. A. Becker, "ELECTRIC-DIPOLE POLARIZABILITIES OF ISOLATED GALLIUM-ARSENIDE CLUSTERS", Chem. Phys. Lett.246,315 (1995).
[31]K. E. Laidig and R. F. W. Bader, "PROPERTIES OF ATOMS IN MOLECULES-ATOMIC POLARIZABILITIES", J. Chem. Phys.93,7213 (1990).
[32]K. R. S. Chandrakumar, T. K. Ghanty, and S. K. Ghosh, "Relationship between ionization potential, polarizability, and softness:A case study of lithium and sodium metal clusters", J. Phys. Chem. A 108,6661 (2004).
[33]J. L. Wang, M. L. Yang, J. Jellinek, and G. H. Wang, "Dipole polarizabilities of medium-sized gold clusters", Phys. Rev. A 74,023202 (2006).
[34]R. F. W. Bader, M. T. Carroll, J. R. Cheeseman, and C. Chang, "PROPERTIES OF ATOMS IN MOLECULES-ATOMIC VOLUMES", J. Am. Chem. Soc.109, 7968 (1987).
[35]B. J. Orr and J. F. Ward, "Perturbation Theory of Non-Linear Optical Polarization of an Isolated System", Mol. Phys.20,513(1971).
[1]O. M. Wilson, M. R. Knecht, J. C. Garcia-Martinez, and R. M. Crooks, "Effect of Pd nanoparticle size on the catalytic hydrogenation of allyl alcohol", J. Am. Chem. Soc.128,4510 (2006).
[2]B. Kalita and R. C. Deka, "Reaction Intermediates of CO Oxidation on Gas Phase Pd-4 Clusters:A Density Functional Study", J. Am. Chem. Soc.131,13252 (2009).
[3]A. S. Worz, K. Judai, S. Abbet, and U. Heiz, "Cluster size-dependent mechanisms of the CO+NO reaction on small Pd-n (n<= 30) clusters on oxide surfaces", J. Am. Chem. Soc.125,7964 (2003).
[4]G. Gantefor and W. Eberhardt, "Localization of 3d and 4d electrons in small clusters:The "roots" of magnetism", Phys. Rev. Lett.76,4975 (1996).
[5]T. Taniyama, E. Ohta, and T. Sato, "Observation of 4d ferromagnetism in free-standing Pd fine particles", Europhys. Lett.38,195 (1997).
[6]T. Shinohara, T. Sato, and T. Taniyama, "Surface ferromagnetism of Pd fine particles", Phys. Rev. Lett.91,197201 (2003).
[7]V. Kumar and Y. Kawazoe, "Icosahedral growth, magnetic behavior, and adsorbate-induced metal-nonmetal transition in palladium clusters", Phys. Rev. B 66,144413 (2002).
[8]M. Moseler, H. Hakkinen, R. N. Barnett, and U. Landman, "Structure and magnetism of neutral and anionic palladium clusters", Phys. Rev. Lett.86,2545 (2001).
[9]H. L. Zhang, D. X. Tian, and J. J. Zhao, "Structural evolution of medium-sized Pd-n (n=15-25) clusters from density functional theory", J. Chem. Phys.129, 114302(2008).
[10]A. J. Cox, J. G. Louderback, S. E. Apsel, and L. A. Bloomfield, "MAGNETISM IN 4D-TRANSITION METAL-CLUSTERS", Phys. Rev. B 49,12295 (1994).
[11]D. C. Douglass, J. P. Bucher, and L. A. Bloomfield, "MAGNETIC STUDIES OF FREE NONFERROMAGNETIC CLUSTERS", Phys. Rev. B 45,6341 (1992).
[12]T. Futschek, M. Marsman, and J. Hafner, "Structural and magnetic isomers of small Pd and Rh clusters:an ab initio density functional study", J. Phys.: Condens. Matter 17,5927 (2005).
[13]J. Rogan, G. Garcia, M. Ramirez, V. Munoz, J. A. Valdivia, X. Andrade, R. Ramirez, and M. Kiwi, "The structure and properties of small Pd clusters", Nanotechnology 19,205701 (2008).
[14]C. M. Chang and M. Y. Chou, "Alternative low-symmetry structure for 13-atom metal clusters", Phys. Rev. Lett.93,133401 (2004).
[15]Andreas M Koster, Patrizia Calaminici, Emilio Orgaz, Debesh R Roy, Jose Ulises Reveles, and Shiv N Khanna, "On the Ground State of Pd(13).", J. Am. Chem. Soc.133,12192(2011).
[16]M. J. Piotrowski, P. Piquini, and J. L. F. Da Silva, "Density functional theory investigation of 3d,4d, and 5d 13-atom metal clusters", Phys. Rev. B 81,155446 (2010).
[17]C. Jing, Y. Yang, S. X. Cao, and J. C. Zhang, "Electronic structure and magnetism of Mnl-xPdx alloys", Mod. Phys. Lett. B 20,305 (2006).
[18]S. Nigam, C. Majumder, and S. K. Kulshreshtha, "Geometry and electronic and magnetic properties of MPdl2 clusters (M=Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, and Pd) from first principles", Phys. Rev. B 76,195430 (2007).
[19]D. M. Deaven and K. M. Ho, "Molecular-Geometry Optimization with a Genetic Algorithm", Phys. Rev. Lett.75,288 (1995).
[20]Bin Shan, Ligen Wang, Sang Yang, Jangsuk Hyun, Neeti Kapur, Yujun Zhao, John Nicholas, and Kyeongjae Cho, "First-principles-based embedded atom method for PdAu nanoparticles", Phys. Rev. B 80,1 (2009).
[21]W. Q. Zhang, Q. F. Ge, and L. C. Wang, "Structure effects on the energetic, electronic, and magnetic properties of palladium nanoparticles", J. Chem. Phys. 118,5793 (2003).
[22]J. Rogan, G. Garcia, J. A. Valdivia, W. Orellana, A. H. Romero, R. Ramirez, and M. Kiwi, "Small Pd clusters:A comparison of phenomenological and ab initio approaches", Phys. Rev. B 72,115421 (2005).
[23]N. F. Shen, J. L. Wang, and L. Y. Zhu, "Ab initio study of magnetic properties of bimetallic Con-1Mn and Con-1V clusters", Chem. Phys. Lett.467,114 (2008).
[24]K. Huber and G. Herzberg,{Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules》, (Van Nostrand Reinhold,1979).
[25]M. D. Morse, "CLUSTERS OF TRANSITION-METAL ATOMS", Chem. Rev. 86,1049(1986).
[26]K. D. Bier, T. L. Haslett, A. D. Kirkwood, and M. Moskovits, "THE RESONANCE RAMAN AND VISIBLE ABSORBANCE SPECTRA OF MATRIX-ISOLATED MN-2 AND MN-3", J. Chem. Phys.89,6 (1988).
[27]G. Kresse and J. Furthmuller, "Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set", Phys. Rev. B 54,11169 (1996).
[28]G. Kresse and J. Hafner, "NORM-CONSERVING AND ULTRASOFT PSEUDOPOTENTIALS FOR FIRST-ROW AND TRANSITION-ELEMENTS", J. Phys.:Condens. Matter 6,8245 (1994).
[29]P. E. Blochl, "PROJECTOR AUGMENTED-WAVE METHOD", Phys. Rev. B 50, 17953 (1994).
[30]G. Kresse and D. Joubert, "From ultrasoft pseudopotentials to the projector augmented-wave method", Phys. Rev. B 59,1758 (1999).
[31]J. P. Perdew, K. Burke, and M. Ernzerhof, "Generalized gradient approximation made simple", Phys. Rev. Lett.77,3865 (1996).
[32]F. Aguilera-Granja, A. Vega, J. Rogan, W. Orellana, and G. Garcia, "Magnetic properties of Pd atomic clusters from different theoretical approaches", Eur. Phys. J. D 44,125(2007).
[33]P. Blonski and J. Hafner, "Magneto-structural properties and magnetic anisotropy of small transition-metal clusters:a first-principles study", J. Phys.:Condens. Matter 23,136001 (2011).
[34]V. Kumar and Y. Kawazoe, "Magnetism in clusters of non-magnetic elements:Pd, Rh, and Ru-Magnetism in clusters of non-magnetic elements", Eur. Phys. J. D 24,81 (2003).
[35]H. Chen, N. E. Brener, and J. Callaway, "Electronic-Structure, Optical and Magnetic-Properties of Fcc Palladium", Phys. Rev. B 40,1443 (1989).
[36]M. Brack, "THE PHYSICS OF SIMPLE METAL-CLUSTERS SELF-CONSISTENT JELLIUM MODEL AND SEMICLASSICAL APPROACHES", Rev. Mod. Phys.65,677 (1993).
[37]Mark B. Knickelbein, "Experimental Observation of Superparamagnetism in Manganese Clusters", Phys. Rev. Lett.86,5255 (2001).
[38]Mark B. Knickelbein, "Magnetic ordering in manganese clusters", Phys. Rev. B 70,014424 (2004).
[39]L. Vitos, B. Johansson, and J. Kollar, "Size-dependent paramagnetic-ferromagnetic phase transition in palladium clusters", Phys. Rev. B 62, R11957 (2000).
[40]P. Bobadova-Parvanova, K. A. Jackson, S. Srinivas, and M. Horoi, "Density-functional investigations of the spin ordering in Fel3 clusters", Phys. Rev. B 66,195402(2002).
[1]F. A. Ponce and D. P. Bour, "Nltride-based semiconductors for blue and green light-emitting devices", Nature 386,351 (1997).
[2]S. Nakamura, "The roles of structural imperfections in InGaN-Based blue light-emitting diodes and laser diodes", Science 281,956 (1998).
[3]H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, and M. Burns, "LARGE-BAND-GAP SIC,Ⅳ-Ⅴ NITRIDE, AND Ⅱ-Ⅵ ZNSE-BASED SEMICONDUCTOR-DEVICE TECHNOLOGIES", J. Appl. Phys.76,1363 (1994).
[4]J. M. de Almeida, T. Kar, and P. Piquini, "AlN, GaN, AlxGal-xN nanotubes and GaN/AlxGal-xN nanotube heterojunctions", Phys. Lett. A 374,877 (2010).
[5]J. Goldberger, R. R. He, Y. F. Zhang, S. W. Lee, H. Q. Yan, H. J. Choi, and P. D. Yang, "Single-crystal gallium nitride nanotubes", Nature 422,599 (2003).
[6]L. Yang, X. Zhang, R. Huang, G. Y. Zhang, and X. An, "Synthesis of single crystalline GaN nanoribbons on sapphire(0001) substrates", Solid State Commun. 130,769 (2004).
[7]X. Xiang, C. B. Cao, F. L. Huang, R. T. Lv, and H. S. Zhu, "Synthesis and characterization of crystalline gallium nitride nanoribbon rings", J. Cryst. Growth 263,25 (2004).
[8]S. Y. Bae, H. W. Seo, J. Park, H. Yang, and S. A. Song, "Synthesis and structure of gallium nitride nanobelts", Chem. Phys. Lett.365,525 (2002).
[9]Jian Yu Huang, He Zheng, S X Mao, Qiming Li, and George T Wang, "In Situ Nanomechanics of GaN Nanowires.", Nano Lett.11,1618 (2011).
[10]H.Sahin, S. Cahangirov, M. Topsakal, E. Bekaroglu, E. Akturk, R. T. Senger, and S. Ciraci, "Monolayer honeycomb structures of group-Ⅳ elements and Ⅲ-Ⅴ binary compounds:First-principles calculations", Phys. Rev. B 80,155453 (2009).
[11]H. M. Li, J. Dai, J. Li, S. Zhang, J. Zhou, L. J. Zhang, W. S. Chu, D. L. Chen, H. R. Zhao, J. L. Yang, and Z. Y. Wu, "Electronic Structures and Magnetic Properties of GaN Sheets and Nanoribbons", J. Phys. Chem. C 114,11390 (2010).
[12]E. Kan, H. J. Xiang, F. Wu, C. Lee, J. L. Yang, and M. H. Whangbo, "Ferrimagnetism in zigzag graphene nanoribbons induced by main-group adatoms", Appl. Phys. Lett.96,102503 (2010).
[13]Q. Chen, J. L. Wang, L. Y. Zhu, S. D. Wang, and F. Ding, "Fluorination induced half metallicity in two-dimensional few zinc oxide layers", J. Chem. Phys.132, 204703 (2010).
[14]C. Ataca and S. Ciraci, "Functionalization of BN honeycomb structure by adsorption and substitution of foreign atoms", Phys. Rev. B 82,165402 (2010).
[15]A. R. Botello-Mendez, F. Lopez-Urias, M. Terrones, and H. Terrones, "Magnetic behavior in zinc oxide zigzag nanoribbons", Nano Lett.8,1562 (2008).
[16]G. Kresse and J. Furthmuller, "Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set", Phys. Rev. B 54,11169 (1996).
[17]G. Kresse and J. Hafner, "NORM-CONSERVING AND ULTRASOFT PSEUDOPOTENTIALS FOR FIRST-ROW AND TRANSITION-ELEMENTS", J. Phys.:Condens. Matter 6,8245 (1994).
[18]P. E. Blochl, "PROJECTOR AUGMENTED-WAVE METHOD", Phys. Rev. B 50, 17953(1994).
[19]G. Kresse and D. Joubert, "From ultrasoft pseudopotentials to the projector augmented-wave method", Phys. Rev. B 59,1758 (1999).
[20]J. P. Perdew, K. Burke, and M. Ernzerhof, "Generalized gradient approximation made simple", Phys. Rev. Lett.77,3865 (1996).
[21]Hendrik J. Monkhorst and James D. Pack, "Special points for Brillouin-zone integrations", Phys. Rev. B 13,5188 (1976).
[22]Quantum ESPRESSO, http://www.quantum-espresso.org/.
[23]F. D. Murnaghan, "Finite Deformations of an Elastic Solid", Am. J. Math.59, 235(1937).
[24]Roy Papiya Bose and Roy Sushil Bose, "Applicability of isothermal three-parameter equations of state of solids-a reappraisal", J. Phys.:Condens. Matter 17,6193(2005).
[25]J. Zhou, Q. Wang, Q. Sun, X. S. Chen, Y. Kawazoe, and P. Jena, "Ferromagnetism in Semihydrogenated Graphene Sheet", Nano Lett.9,3867 (2009).
[26]G. Bouzerar, J. Kudrnovsky, L. Bergqvist, and P. Bruno, "Ferromagnetism in diluted magnetic semiconductors:A comparison between ab initio mean-field, RPA, and Monte Carlo treatments", Phys. Rev. B 68 (2003).
[27]Jian Zhou and Qiang Sun, "Magnetism of phthalocyanine-based organometallic single porous sheet.", J. Am. Chem. Soc.133,15113 (2011).
[28]N. F. Shen, J. L. Wang, and L. Y. Zhu, "Ab initio study of magnetic properties of bimetallic Con-IMn and Con-1V clusters", Chem. Phys. Lett.467,114 (2008).
[2]B. Kaiser and K. Rademann, "Photoelectron spectroscopy of neutral mercury clusters Hg_{x} (x≤109) in a molecular beam", Phys. Rev. Lett.69,3204 (1992).
[3]C. Brechignac, Ph Cahuzac, J. Leygnier, and A. Sarfati, "Optical response of large lithium clusters:Evolution toward the bulk", Phys. Rev. Lett.70,2036 (1993).
[4]Yang Jinlong, F. Toigo, and Wang Kelin, "Structural, electronic, and magnetic properties of small rhodium clusters", Phys. Rev. B 50,7915 (1994).
[5]K. Rademann, O. Dimopoulou-Rademann, M. Schlauf, U. Even, and F. Hensel, "Evolution of surface plasmon resonance absorption in large gas phase clusters of mercury:Approaching the bulk", Phys. Rev. Lett.69,3208 (1992).
[6]M. G. Bawendi, M. L. Steigerwald, and L. E. Brus, "The Quantum-Mechanics of Larger Semiconductor Clusters (Quantum Dots)", Annu. Rev. Phys. Chem.41, 477 (1990).
[7]E. W. Becker, K. Bier, and W. Henkes, "STRAHLEN AUS KONDENSIERTEN ATOMEN UND MOLEKELN IM HOCHVAKUUM", Z. Phys. D 146,333 (1956).
[8]W. D. Knight, Keith Clemenger, Walt A. de Heer, Winston A. Saunders, M. Y. Chou, and Marvin L. Cohen, "Electronic Shell Structure and Abundances of Sodium Clusters", Phys. Rev. Lett.52,2141 (1984).
[9]H. W. Kroto, J. R. Heath, S. C. Obrien, R. F. Curl, and R. E. Smalley, "C-60-Buckminsterfullerene", Nature 318,162 (1985).
[10]T. Bergmann, H. Limberger, and T. P. Martin, "Evidence of electronic shell structure in Cs-O clusters", Phys. Rev. Lett.60,1767 (1988).
[11]Kenneth E. Schriver, John L. Persson, Eric C. Honea, and Robert L. Whetten, "Electronic shell structure of group-ⅢA metal atomic clusters", Phys. Rev. Lett. 64,2539(1990).
[12]S.N. Khanna and S. Linderoth, "Magnetic behavior of clusters of ferromagnetic transition metals", Phys. Rev. Lett.67,742 (1991).
[13]A. J. Cox, J. G. Louderback, S. E. Apsel, and L. A. Bloomfield, "MAGNETISM IN 4D-TRANSITION METAL-CLUSTERS", Phys. Rev. B 49,12295 (1994).
[14]M. Moseler, H. Hakkinen, R. N. Barnett, and U. Landman, "Structure and magnetism of neutral and anionic palladium clusters", Phys. Rev. Lett.86,2545 (2001).
[15]Walt A. de Heer, Kathy Selby, Vitaly Kresin, Jun Masui, Michael Vollmer, A. Chatelain, and W. D. Knight, "Collective dipole oscillations in small sodium clusters", Phys. Rev. Lett.59,1805 (1987).
[16]L. N. Lewis, "CHEMICAL CATALYSIS BY COLLOIDS AND CLUSTERS", Chem. Rev.93,2693 (1993).
[17]Keeyung Lee, Joseph Callaway, and S. Dhar, "Electronic structure of small iron clusters", Phys. Rev. B 30,1724 (1984).
[18]Jose Luis Martins, Jean Buttet, and Roberto Car, "Equilibrium Geometries and Electronic Structures of Small Sodium Clusters", Phys. Rev. Lett.53,655 (1984).
[19]Krishnan Raghavachari and Veronika Logovinsky, "Structure and bonding in small silicon clusters", Phys. Rev. Lett.55,2853 (1985).
[20]Pietro Ballone, Wanda Andreoni, Roberto Car, and Michele Parrinello, "Equilibrium Structures and Finite Temperature Properties of Silicon Microclusters from ab initio Molecular-Dynamics Calculations", Phys. Rev. Lett. 60,271 (1988).
[21]S. N. Khanna, F. Reuse, and J. Buttet, "Stability and Observability of Charged Beryllium Clusters", Phys. Rev. Lett.61,535 (1988).
[22]P. Moriarty, "Nanostructured materials", Rep. Prog. Phys.64,297 (2001).
[23]J. Friedel, "PHYSICS OF CLEAN METAL-SURFACES", Ann. Phys-paris.1, 257(1976).
[24]J. J. Zhao and R. H. Xie, "Genetic Algorithms for the Geometry Optimization of Atomic and Molecular Clusters", J. Comput. Theor. Nanosci.1,117 (2004).
[25]D. M. Deaven and K. M. Ho, "Molecular-Geometry Optimization with a Genetic Algorithm", Phys. Rev. Lett.75,288 (1995).
[26]D. J. Wales and H. A. Scheraga, "Review:Chemistry-Global optimization of clusters, crystals, and biomolecules", Science 285,1368 (1999).
[27]S. Yoo, J. J. Zhao, J. L. Wang, and X. C. Zeng, "Endohedral silicon fullerenes Si-N (27<= N<= 39)", J. Am. Chem. Soc.126,13845 (2004).
[28]J. L. Wang, J. L. Bai, J. Jellinek, and X. C. Zeng, "Gold-coated transition-metal anion Mn-13@Au-20 (-) with ultrahigh magnetic moment", J. Am. Chem. Soc. 129,4110(2007).
[29]F. Ding, A. Rosen, and K. Bolton, "Size dependence of the coalescence and melting of iron clusters:A molecular-dynamics study", Phys. Rev. B 70,075416 (2004).
[30]J. L. Wang, M. L. Yang, J. Jellinek, and G. H. Wang, "Dipole polarizabilities of medium-sized gold clusters", Phys. Rev. A 74,023202 (2006).
[31]G. L. Gutsev, R. H. O'Neal, B. C. Saha, M. D. Mochena, E. Johnson, and C. W. Bauschlicher, "Optical Properties of (GaAs)(n) Clusters (n=2-16)", J. Phys. Chem. A 112,10728(2008).
[32]W. E. Kaden, T. P. Wu, W. A. Kunkel, and S. L. Anderson, "Electronic Structure Controls Reactivity of Size-Selected Pd Clusters Adsorbed on TiO2 Surfaces", Science 326,826 (2009).
[33]T. Mitsui, M. K. Rose, E. Fomin, D. F. Ogletree, and M. Salmeron, "Water diffusion and clustering on Pd(111)", Science 297,1850 (2002).
[34]Y. Lei, F. Mehmood, S. Lee, J. Greeley, B. Lee, S. Seifert, R. E. Winans, J. W. Elam, R. J. Meyer, P. C. Redfern, D. Teschner, R. Schlogl, M. J. Pellin, L. A. Curtiss, and S. Vajda, "Increased Silver Activity for Direct Propylene Epoxidation via Subnanometer Size Effects", Science 328,224 (2010).
[35]B. Yoon, H. Hakkinen, U. Landman, A. S. Worz, J. M. Antonietti, S. Abbet, K. Judai, and U. Heiz, "Charging effects on bonding and catalyzed oxidation of CO on Au-8 clusters on MgO", Science 307,403 (2005).
[36]W. D. Luedtke and U. Landman, "Slip diffusion and Levy flights of an adsorbed gold nanocluster", Phys. Rev. Lett.82,3835 (1999).
[37]X. Q. Dai, Y. N. Tang, J. H. Zhao, and Y. W. Dai, "Absorption of Pt clusters and the induced magnetic properties of graphene", J. Phys-condens. Mat.22,316005 (2010).
[38]R. Schafer, S. Schlecht, J. Woenckhaus, and J. A. Becker, "Polarizabilities of isolated semiconductor clusters", Phys. Rev. Lett.76,471 (1996).
[39]I. Vasiliev, S. Ogut, and J. R. Chelikowsky, "Ab initio calculations for the polarizabilities of small semiconductor clusters", Phys. Rev. Lett.78,4805 (1997).
[40]Y. P. Feng, T. B. Boo, H. H. Kwong, C. K. Ong, A. Kumar, and S. Kabana, "Composition dependence of structural and electronic properties of GamAsn clusters from first principles", Phys. Rev. B 76,045336 (2007).
[41]S. Y. Yin, R. Moro, X. S. Xu, and W. A. de Heer, "Magnetic enhancement in cobalt-manganese alloy clusters", Phys. Rev. Lett.98,113401 (2007).
[42]F. Tao, M. E. Grass, Y. W. Zhang, D. R. Butcher, J. R. Renzas, Z. Liu, J. Y. Chung, B. S. Mun, M. Salmeron, and G. A. Somorjai, "Reaction-Driven Restructuring of Rh-Pd and Pt-Pd Core-Shell Nanoparticles", Science 322,932 (2008).
[43]Lucas Fernandez-Seivane and Jaime Ferrer, "Magnetic Anisotropies of Late Transition Metal Atomic Clusters", Phys. Rev. Lett.99,183401 (2007).
[44]G. Pastor, J. Dorantes-Davila, S. Pick, and H. Dreysse, "Magnetic Anisotropy of 3d Transition-Metal Clusters", Phys. Rev. Lett.75,326 (1995).
[45]B. Yoon and U. Landman, "Electric field control of structure, dimensionality, and reactivity of gold nanoclusters on metal-supported MgO films", Phys. Rev. Lett. 100,056102 (2008).
[46]X. Li, A. E. Kuznetsov, H. F. Zhang, A. I. Boldyrev, and L. S. Wang, "Observation of all-metal aromatic molecules", Science 291,859 (2001).
[47]D. K. Seo and J. D. Corbett, "Perspectives:Chemistry-Aromatic metal clusters", Science 291,841 (2001).
[48]Victor M. Medel, Jose Ulises Reveles, Shiv N. Khanna, Vikas Chauhan, Prasenjit Sen, and A. Welford Castleman, "Hund's rule in superatoms with transition metal impurities", Proc. Natl. Acad. Sci. U. S. A.108,10062 (2011).
[49]D. E. Bergeron, P. J. Roach, A. W. Castleman, N. Jones, and S. N. Khanna, "Al cluster superatoms as halogens in polyhalides and as alkaline earths in iodide salts", Science 307,231 (2005).
[50]A. W. Castleman and S. N. Khanna, "Clusters, Superatoms, and Building Blocks of New Materials", J. Phys. Chem. C 113,2664 (2009).
[51]R. P. Andres, R. S. Averback, W. L. Brown, L. E. Brus, W. A. Goddard, A. Kaldor, S. G. Louie, M. Moscovits, P. S. Peercy, S. J. Riley, R. W. Siegel, F. Spaepen, and Y. Wang, "RESEARCH OPPORTUNITIES ON CLUSTERS AND CLUSTER-ASSEMBLED MATERIALS-A DEPARTMENT OF ENERGY, COUNCIL ON MATERIALS SCIENCE PANEL REPORT", J. Mater. Res.4, 704(1989).
[52]M. Brust, D. Bethell, C. J. Kiely, and D. J. Schiffrin, "Self-assembled gold nanoparticle thin films with nonmetallic optical and electronic properties", Langmuir.14,5425(1998).
[53]P. Melinon, V. Paillard, V. Dupuis, A. Perez, P. Jensen, A. Hoareau, M. Broyer, J. L. Vialle, M. Pellarin, B. Baguenard, and J. Lerme, "FROM FREE CLUSTERS TO CLUSTER-ASSEMBLED MATERIALS", Int. J. Mod. Phys. B 9,339 (1995).
[54]J. Bansmann, S. H. Baker, C. Binns, J. A. Blackman, J. P. Bucher, J. Dorantes-Davila, 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.56,189 (2005).
[55]W. A. Deheer, "THE PHYSICS OF SIMPLE METAL-CLUSTERS EXPERIMENTAL ASPECTS AND SIMPLE-MODELS", Rev. Mod. Phys.65, 611(1993).
[56]王广厚,”原子团簇的稳定结构和幻数”,物理学进展20,52(2000).
[57]黄昆,韩汝琦,《固体物理学》,高等教育出版社,1983.
[58]冯端,金国钧,《凝聚态物理系》,高等教育出版社,2006.
[59]A. Vega, J. Dorantes-Davila, L. C. Balbas, and G. M. Pastor, "Calculated sp-electron and spd-hybridization effects on the magnetic properties of small Fe_{N} clusters", Phys. Rev. B 47,4742 (1993).
[60]Isabelle M. L. Billas, J. A. Becker, A. Chatelain, and Walt A. de Heer, "Magnetic moments of iron clusters with 25 to 700 atoms and their dependence on temperature", Phys. Rev. Lett.71,4067 (1993).
[61]Isabelle M.L. Billas, A. Chatelain, and Walt A. de Heer, "Magnetism from the Atom to the Bulk in Iron, Cobalt, and Nickel Clusters", Science 265,1682 (1994).
[62]Y. H. Luo, H. Q. Sun, J. J. Zhao, and G. H. Wang, "Structural dependence of electronic and magnetic properties of the Cr-13 cluster", Commun. Theor. Phys. 34,43 (2000).
[63]J. A. Alonso, "Electronic and atomic structure, and magnetism of transition-metal clusters", Chem. Rev.100,637 (2000).
[64]Brett I. Dunlap, "Symmetry and cluster magnetism", Phys. Rev. A 41,5691 (1990).
[65]Zhi-qiang Li and Bing-lin Gu, "Electronic-structure calculations of cobalt clusters", Phys. Rev. B 47,13611 (1993).
[66]H. L. Zhang, D. X. Tian, and J. J. Zhao, "Structural evolution of medium-sized Pd-n (n= 15-25) clusters from density functional theory", J. Chem. Phys.129, 114302(2008).
[67]K. D. Gross, D. Riegel, and R. Zeller, "Magnetic-moment formation and spin dynamics of isolated 4d ions in palladium", Phys. Rev. Lett.65,3044 (1990).
[68]D. Riegel, L. Buermann, K. D. Gross, M. Luszik-Bhadra, and S. N. Mishra, "Existence and Stability of Magnetic 3d Moments in Noble-and Transition-Metal Hosts", Phys. Rev. Lett.62,316 (1989).
[69]Martin Schmidt, Robert Kusche, Bernd von Issendorff, and Hellmut Haberland, "Irregular variations in the melting point of size-selected atomic clusters", Nature 393,238(1998).
[70]S. Chacko, Kavita Joshi, D. G. Kanhere, and S. A. Blundell, "Why Do Gallium Clusters Have a Higher Melting Point than the Bulk?", Phys. Rev. Lett.92, 135506(2004).
[71]Gary A. Breaux, Robert C. Benirschke, Toshiki Sugai, Brian S. Kinnear, and Martin F. Jarrold, "Hot and Solid Gallium Clusters:Too Small to Melt", Phys. Rev. Lett.91,215508(2003).
[72]B. Kalita and R. C. Deka, "Reaction Intermediates of CO Oxidation on Gas Phase Pd-4 Clusters:A Density Functional Study", J. Am. Chem. Soc.131, 13252(2009).
[73]C. Zhang, B. Yoon, and U. Landman, "Predicted oxidation of CO catalyzed by Au nanoclusters on a thin defect-free MgO film supported on a Mo(100) surface", J. Am. Chem. Soc.129,2228 (2007).
[74]B. Huber, P. Koskinen, H. Hakkinen, and M. Moseler, "Oxidation of magnesia-supported Pd-clusters leads to the ultimate limit of epitaxy with a catalytic function", Nat. Mater.5,44 (2006).
[75]K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, "Electric field effect in atomically thin carbon films", Science 306,666 (2004).
[76]A. K. Geim and K. S. Novoselov, "The rise of graphene", Nat. Mater.6,183 (2007).
[77]Changgu Lee, Xiaoding Wei, Jeffrey W. Kysar, and James Hone, "Measurement of the Elastic Properties and Intrinsic Strength of Monolayer Graphene", Science 321,385 (2008).
[78]R. R. Nair, P. Blake, A. N. Grigorenko, K. S. Novoselov, T. J. Booth, T. Stauber, N. M. R. Peres, and A. K. Geim, "Fine Structure Constant Defines Visual Transparency of Graphene", Science 320,1308 (2008).
[79]J. R. Williams, L. DiCarlo, and C. M. Marcus, "Quantum Hall Effect in a Gate-Controlled p-n Junction of Graphene", Science 317,638 (2007).
[80]D. A. Abanin and L. S. Levitov, "Quantized Transport in Graphene p-n Junctions in a Magnetic Field", Science 317,641 (2007).
[81]S. V. Morozov, K. S. Novoselov, M. I. Katsnelson, F. Schedin, D. C. Elias, J. A. Jaszczak, and A. K. Geim, "Giant intrinsic carrier mobilities in graphene and its bilayer", Phys. Rev. Lett.100,016602 (2008).
[82]H. Sahin and R. T. Senger, "First-principles calculations of spin-dependent conductance of graphene flakes", Phys. Rev. B 78,205423 (2008).
[83]Xiaolin Li, Xinran Wang, Li Zhang, Sangwon Lee, and Hongjie Dai, "Chemically Derived, Ultrasmooth Graphene Nanoribbon Semiconductors", Science 319,1229(2008).
[84]H. Sevincli, M. Topsakal, E. Durgun, and S. Ciraci, "Electronic and magnetic properties of 3d transition-metal atom adsorbed graphene and graphene nanoribbons", Phys. Rev. B 77,195434 (2008).
[85]Y. F. Li, Z. Zhou, P. W. Shen, and Z. F. Chen, "Spin Gapless Semiconductor-Metal-Half-Metal Properties in Nitrogen-Doped Zigzag Graphene Nanoribbons", Acs Nano 3,1952 (2009).
[86]N. Gorjizadeh, A. A. Farajian, K. Esfarjani, and Y. Kawazoe, "Spin and band-gap engineering in doped graphene nanoribbons", Phys. Rev. B 78,155427 (2008).
[87]S. Dutta, A. K. Manna, and S. K. Pati, "Intrinsic Half-Metallicity in Modified Graphene Nanoribbons", Phys. Rev. Lett.102,096601 (2009).
[88]D. W. Boukhvalov and M. I. Katsnelson, "Chemical Functionalization of Graphene with Defects", Nano Lett.8,4373 (2008).
[89]D. C. Elias, R. R. Nair, T. M. G. Mohiuddin, S. V. Morozov, P. Blake, M. P. Halsall, A. C. Ferrari, D. W. Boukhvalov, M. I. Katsnelson, A. K. Geim, and K. S. Novoselov, "Control of Graphene's Properties by Reversible Hydrogenation: Evidence for Graphane", Science 323,610 (2009).
[90]J. Zhou, Q. Wang, Q. Sun, X. S. Chen, Y. Kawazoe, and P. Jena, "Ferromagnetism in Semihydrogenated Graphene Sheet", Nano Lett.9,3867 (2009).
[91]M. H. Wu, Y. Pei, and X. C. Zeng, "Planar Tetracoordinate Carbon Strips in Edge Decorated Graphene Nanoribbon", J. Am. Chem. Soc.132,5554 (2010).
[92]E. J. Kan, Z. Y. Li, J. L. Yang, and J. G. Hou, "Half-metallicity in edge-modified zigzag graphene nanoribbons", J. Am. Chem. Soc.130,4224 (2008).
[93]Chuanhong Jin, Fang Lin, Kazu Suenaga, and Sumio Iijima, "Fabrication of a Freestanding Boron Nitride Single Layer and Its Defect Assignments", Phys. Rev. Lett.102,195505 (2009).
[94]B. Lalmi, H. Oughaddou, H. Enriquez, A. Kara, S. Vizzini, B. Ealet, and B. Aufray, "Epitaxial growth of a silicene sheet", Appl. Phys. Lett.97,223109 (2010).
[95]C. Tusche, H. L. Meyerheim, and J. Kirschner, "Observation of depolarized ZnO(0001) monolayers:Formation of unreconstructed planar sheets", Phys. Rev. Lett.99,026102(2007).
[96]H. Sahin, S. Cahangirov, M. Topsakal, E. Bekaroglu, E. Akturk, R. T. Senger, and S. Ciraci, "Monolayer honeycomb structures of group-IV elements and Ⅲ-Ⅴ binary compounds:First-principles calculations", Phys. Rev. B 80,155453 (2009).
[97]A. R. Botello-Mendez, F. Lopez-Urias, M. Terrones, and H. Terrones, "Magnetic behavior in zinc oxide zigzag nanoribbons", Nano Lett.8,1562 (2008).
[98]E. Kan, H. J. Xiang, F. Wu, C. Lee, J. L. Yang, and M. H. Whangbo, "Ferrimagnetism in zigzag graphene nanoribbons induced by main-group adatoms", Appl. Phys. Lett.96,102503 (2010).
[99]Q. Chen, J. L. Wang, L. Y. Zhu, S. D. Wang, and F. Ding, "Fluorination induced half metallicity in two-dimensional few zinc oxide layers", J. Chem. Phys.132, 204703 (2010).
[100]B. Xu, J. Yin, Y. D. Xia, X. G. Wan, and Z. G. Liu, "Ferromagnetic and antiferromagnetic properties of the semihydrogenated SiC sheet", Appl. Phys. Lett.96,143111 (2010).
[101]E. Bekaroglu, M. Topsakal, S. Cahangirov, and S. Ciraci, "First-principles study of defects and adatoms in silicon carbide honeycomb structures", Phys. Rev. B 81,075433 (2010).
[102]C. Ataca and S. Ciraci, "Functionalization of BN honeycomb structure by adsorption and substitution of foreign atoms", Phys. Rev. B 82,165402 (2010).
[103]Arun K Manna and Swapan K Pati, "Tunable Electronic and Magnetic Properties in B x N y C z Nanohybrids:Effect of Domain Segregation", The Journal of Physical Chemistry C 115,10842 (2011).
[104]Natalia Berseneva, Arkady Krasheninnikov, and Risto Nieminen, "Mechanisms of Postsynthesis Doping of Boron Nitride Nanostructures with Carbon from First-Principles Simulations", Phys. Rev. Lett.107,035501 (2011).
[105]Somnath Bhowmick, Abhishek K Singh, and Boris I Yakobson, "Quantum Dots and Nanoroads of Graphene Embedded in Hexagonal Boron Nitride", The Journal of Physical Chemistry C 115,9889 (2011).
[106]F. Diederich and M. Kivala, "All-Carbon Scaffolds by Rational Design", Adv. Mater.22,803(2010).
[107]Jian Zhou, Kun Lv, Qian Wang, X. S. Chen, Qiang Sun, and Puru Jena, "Electronic structures and bonding of graphyne sheet and its BN analog", The Journal of Chemical Physics 134,174701 (2011).
[1]E. Wimmer,《Prediction of Materials Properties》,1998.
[2]N. Metropolis and S. Ulam, "THE MONTE CARLO METHOD", J. Am. Stat. Assoc.44,335(1949).
[3]N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, "EQUATION OF STATE CALCULATIONS BY FAST COMPUTING MACHINES", J. Chem. Phys.21,1087 (1953).
[4]张跃,谷景华,尚家香,马岳,《计算材料学基础》,北京航空航天大学出版社,2007.
[5]D. Frenkel and B. Smit,《Understanding Molecular Simulations:From Algorithms to Applications》, (Academic Press,1996).
[6]R. D. Mountain and D. Thirumalai, "QUANTITATIVE MEASURE OF EFFICIENCY OF MONTE-CARLO SIMULATIONS", Physica A 210,453 (1994).
[7]D. J. Wales and J. P. K. Doye, "Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms", J. Phys. Chem. A 101,5111 (1997).
[8]D. J. Wales and M. P. Hodges, "Global minima of water clusters (H2O)(n), n<= 21, described by an empirical potential", Chem. Phys. Lett.286,65 (1998).
[9]D. J. Wales and H. A. Scheraga, "Review:Chemistry- Global optimization of clusters, crystals, and biomolecules", Science 285,1368 (1999).
[10]GMIN, http://www-wales.ch.cam.ac.uk/GMIN/
[11]B. J. Alder and T. E. Wainwright, "PHASE TRANSITION FOR A HARD SPHERE SYSTEM", J. Chem. Phys.27,1208 (1957).
[12]B. J. Alder and T. E. Wainwright, "STUDIES IN MOLECULAR DYNAMICS.1. GENERAL METHOD", J. Chem. Phys.31,459 (1959).
[13]唐景昌,徐伦彪,《固体理论导论》,浙江大学出报社,1997.
[14]L. Verlet, "COMPUTER EXPERIMENTS ON CLASSICAL FLUIDS.1. THERMODYNAMICAL PROPERTIES OF LENNARD-JONES MOLECULES", Phys. Rev.159,98 (1967).
[15]R. W. Hockney, "The potential calculation and some applications", Methods in Computational Physics 9,135 (1970).
[16]W. C. Swope, H. C. Andersen, P. H. Berens, and K. R. Wilson, "A COMPUTER-SIMULATION METHOD FOR THE CALCULATION OF EQUILIBRIUM-CONSTANTS FOR THE FORMATION OF PHYSICAL CLUSTERS OF MOLECULES-APPLICATION TO SMALL WATER CLUSTERS", J. Chem. Phys.76,637 (1982).
[17]D. Beeman, "SOME MULTISTEP METHODS FOR USE IN MOLECULAR-DYNAMICS CALCULATIONS", J. Comput. Phys.20,130 (1976).
[18]S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "OPTIMIZATION BY SIMULATED ANNEALING", Science 220,671 (1983).
[19]S. Geman and D. Geman, "STOCHASTIC RELAXATION, GIBBS DISTRIBUTIONS, AND THE BAYESIAN RESTORATION OF IMAGES", IEEE. T. Pattern. Anal.6,721 (1984).
[20]H. C. Andersen, "MOLECULAR-DYNAMICS SIMULATIONS AT CONSTANT PRESSURE AND-OR TEMPERATURE", J. Chem. Phys.72,2384 (1980).
[21]William G. Hoover, "Canonical dynamics:Equilibrium phase-space distributions", Phys. Rev. A 31,1695(1985).
[22]陈正隆,《分子模拟》,2002.
[23]D. M. Deaven and K. M. Ho, "Molecular-Geometry Optimization with a Genetic Algorithm", Phys. Rev. Lett.75,288 (1995).
[24]J. Maddox, "GENETICS HELPING MOLECULAR-DYNAMICS", Nature 376, 209(1995).
[25]J. J. Zhao and R. H. Xie, "Genetic Algorithms for the Geometry Optimization of Atomic and Molecular Clusters", J. Comput. Theor. Nanosci.1,117 (2004).
[26]J. A. Niesse and H. R. Mayne, "Global geometry optimization of atomic clusters using a modified genetic algorithm in space-fixed coordinates", J. Chem. Phys. 105,4700(1996).
[27]Sougata Pal, Rahul Sharma, Biplab Goswami, Pranab Sarkar, and S. P. Bhattacharyya, "A search for lowest energy structures of ZnS quantum dots: Genetic algorithm tight-binding study", The Journal of Chemical Physics 130, 214703 (2009).
[28]Jijun Zhao, Li Ma, and Bin Wen, "Lowest-energy endohedral fullerene structure of Si 60 from a genetic algorithm and density-functional theory", J. Phys.: Condens. Matter 19,226208 (2007).
[29]J. L. Wang, G. H. Wang, and J. J. Zhao, "Structure and electronic properties of Ge-n (n=2-25) clusters from density-functional theory", Phys. Rev. B 64,205411 (2001).
[30]J. L. Wang, G. H. Wang, and J. J. Zhao, "Density-functional study of Au-n (n= 2-20) clusters:Lowest-energy structures and electronic properties", Phys. Rev. B 66,035418(2002).
[31]B. L. Wang, S. Y. Yin, G. H. Wang, A. Buldum, and J. J. Zhao, "Novel structures and properties of gold nanowires", Phys. Rev. Lett.86,2046 (2001).
[32]B. L. Wang, S. Y. Yin, G. H. Wang, and J. J. Zhao, "Structures and electronic properties of ultrathin titanium nanowires", J. Phys.:Condens. Matter 13, L403 (2001).
[33]R. L. Johnston, "Evolving better nanoparticles:Genetic algorithms for optimising cluster geometries", Dalton Trans.,4193 (2003).
[34]Frank H. Stillinger and Thomas A. Weber, "Computer simulation of local order in condensed phases of silicon", Phys. Rev. B 31,5262 (1985).
[35]J. Tersoff, "Modeling solid-state chemistry:Interatomic potentials for multicomponent systems", Phys. Rev. B 39,5566 (1989).
[36]Donald W. Brenner, "Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films", Phys. Rev. B 42,9458 (1990).
[37]Fabrizio Cleri and Vittorio Rosato, "Tight-binding potentials for transition metals and alloys", Phys. Rev. B 48,22 (1993).
[38]Murray S. Daw and M. I. Baskes, "Semiempirical, Quantum Mechanical Calculation of Hydrogen Embrittlement in Metals", Phys. Rev. Lett.50,1285 (1983).
[39]M. S. Daw and M. I. Baskes, "EMBEDDED-ATOM METHOD-DERIVATION AND APPLICATION TO IMPURITIES, SURFACES, AND OTHER DEFECTS IN METALS", Phys. Rev. B 29,6443 (1984).
[40]F. Ercolessi, E. Tosatti, and M. Parrinello, "Au (100) Surface Reconstruction", Phys. Rev. Lett.57,719 (1986).
[41]Z. Q. Wang, D. Stroud, and A. J. Markworth, "Monte Carlo study of the liquid CdTe surface", Phys. Rev. B 40,3129 (1989).
[42]V. Rosato, M. Guillope, and B. Legrand, "THERMODYNAMICAL AND STRUCTURAL-PROPERTIES OF FCC TRANSITION-METALS USING A SIMPLE TIGHT-BINDING MODEL", Philos. Mag. A 59,321 (1989).
[43]I. L. Garzon and J. Jellinek, "MELTING OF GOLD MICROCLUSTERS", Zeitschrift Fur Physik D 20,235 (1991).
[44]L. Hui, F. Pederiva, B. L. Wang, J. L. Wang, and G. H. Wang, "How does the nickel nanowire melt?", Appl. Phys. Lett.86,011913 (2005).
[45]P. Hohenberg and W. Kohn, "INHOMOGENEOUS ELECTRON GAS", Phys. Rev.136, B864 (1964).
[46]R. A. Johnson, "Analytic nearest-neighbor model for fcc metals", Phys. Rev. B 37,3924 (1988).
[47]S. M. Foiles, M. I. Baskes, and M. S. Daw, "Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys", Phys. Rev. B 33, 7983 (1986).
[48]M. W. Finnis and J. E. Sinclair, "A SIMPLE EMPIRICAL N-BODY POTENTIAL FOR TRANSITION-METALS", Philos. Mag. A 50,45 (1984).
[49]R. A. Johnson and D. J. Oh, "ANALYTIC EMBEDDED ATOM METHOD MODEL FOR BCC METALS", J. Mater. Res.4,1195 (1989).
[50]S. L. Chen, J. C. Xu, and H. S. Zhang, "A new scheme of many-body potentials for hep metals", Comp. Mater. Sci.29,428 (2004).
[51]D. J. Oh and R. A. Johnson, "SIMPLE EMBEDDED ATOM METHOD MODEL FOR FCC AND HCP METALS", J. Mater. Res.3,471 (1988).
[52]M. I. Baskes, "Modified embedded-atom potentials for cubic materials and impurities", Phys. Rev. B 46,2727 (1992).
[53]欧阳义芳,钟夏平,”凝聚态物质计算和模拟中使用的相互作用势”,力学进展36,321(2006).
[54]D. R. Hartree, "The wave mechanics of an atom with a non-Coulomb central field Part I theory and methods", Proc. Cambridge Philos. Soc 24,89 (1928).
[55]J. C. Slater and G. F. Koster, "Simplified LCAO Method for the Periodic Potential Problem", Phys. Rev.94,1498 (1954).
[56]L. H. Thomas, "The calculation of atomic fields", Proc. Cambridge Philos. Soc 23,542 (1927).
[57]E. Fermi, "Un Metodo Statistico per la Determinazione di alcune Prioprieta dell'Atomo", Rend. Acad. Maz. Lancei 6,602 (1927).
[58]W. Kohn and L. J. Sham, "Self-Consistent Equations Including Exchange and Correlation Effects", Phys. Rev.140, A1133 (1965).
[59]冯端,金国钧,《凝聚态物理系》,高等教育出版社,2006.
[60]W. Kohn, "Density Functional and Density Matrix Method Scaling Linearly with the Number of Atoms", Phys. Rev. Lett.76,3168 (1996).
[61]D. M. Ceperley and B. J. Alder, "GROUND-STATE OF THE ELECTRON-GAS BY A STOCHASTIC METHOD", Phys. Rev. Lett.45,566 (1980).
[62]J. P. Perdew and A. Zunger, "SELF-INTERACTION CORRECTION TO DENSITY-FUNCTIONAL APPROXIMATIONS FOR MANY-ELECTRON SYSTEMS", Phys. Rev. B 23,5048 (1981).
[63]John P. Perdew and Yue Wang, "Accurate and simple analytic representation of the electron-gas correlation energy", Phys. Rev. B 45,13244 (1992).
[64]John P. Perdew, J. A. Chevary, S. H. Vosko, Koblar A. Jackson, Mark R. Pederson, D. J. Singh, and Carlos Fiolhais, "Atoms, molecules, solids, and surfaces:Applications of the generalized gradient approximation for exchange and correlation", Phys. Rev. B 46,6671 (1992).
[65]A. I. Liechtenstein, V. I. Anisimov, and J. Zaanen, "Density-functional theory and strong interactions:Orbital ordering in Mott-Hubbard insulators", Phys. Rev. B 52, R5467 (1995).
[66]E. Wimmer, 《All electron methods》,2001.
[1]X. Michalet, F. F. Pinaud, L. A. Bentolila, J. M. Tsay, S. Doose, J. J. Li, G. Sundaresan, A. M. Wu, S. S. Gambhir, and S. Weiss, "Quantum dots for live cells, in vivo imaging, and diagnostics", Science 307,538 (2005).
[2]T. Calarco, A. Datta, P. Fedichev, E. Pazy, and P. Zoller, "Spin-based all-optical quantum computation with quantum dots:Understanding and suppressing decoherence", Phys. Rev. A 68,012310 (2003).
[3]Y. Z. Lan, W. D. Cheng, D. S. Wu, J. Shen, S. P. Huang, H. Zhang, Y. J. Gong, and F. F. Li, "A theoretical investigation of hyperpolarizability for small GanAsm (n+m=4-10) clusters", J. Chem. Phys.124,094302 (2006).
[4]P. Karamanis, D. Begue, and C. Pouchan, "Ab initio finite field (hyper)polarizability computations on stoichiometric gallium arsenide clusters GanAsn (n=2-9)", J. Chem. Phys.127,094706 (2007).
[5]S. C. O'brien, Y Liu, Q. Zhang, J. R. Heath, F. K. Tittel, R. F. Curl, and R. E. Smalley, "Supersonic Cluster Beams of Iii-V Semiconductors-Gaxasy", J. Chem. Phys.84,4074 (1986).
[6]R. Schafer, S. Schlecht, J. Woenckhaus, and J. A. Becker, "Polarizabilities of isolated semiconductor clusters", Phys. Rev. Lett.76,471 (1996).
[7]R. Schafer and J. A. Becker, "Photoabsorption spectroscopy on isolated GaNAsM clusters", Phys. Rev. B 54,10296 (1996).
[8]J. J. BelBruno, "Bonding and energetics in small clusters of gallium and arsenic", Heteroatom Chem.14,189 (2003).
[9]L. Lou, L. Wang, L. P. F. Chibante, R. T. Laaksonen, P. Nordlander, and R. E. Smalley, "Electronic-Structure of Small Gaas Clusters", J. Chem. Phys.94,8015 (1991).
[10]I. Vasiliev, S. Ogut, and J. R. Chelikowsky, "Ab initio calculations for the polarizabilities of small semiconductor clusters", Phys. Rev. Lett.78,4805 (1997).
[11]Y. P. Feng, T. B. Boo, H. H. Kwong, C. K. Ong, A. Kumar, and S. Kabana, "Composition dependence of structural and electronic properties of GamAsn clusters from first principles", Phys. Rev. B 76,045336 (2007).
[12]G. L. Gutsev, E. Johnson, M. D. Mochena, and C. W. Bauschlicher, "The structure and energetics of (GaAS)(n), (GaAs)(n)(-), and (GaAs)(n)(+) (n=2-15)", J. Chem. Phys.128,144707 (2008).
[13]G. L. Gutsev, R. H. O'Neal, B. C. Saha, M. D. Mochena, E. Johnson, and C. W. Bauschlicher, "Optical Properties of (GaAs)(n) Clusters (n=2-16)", J. Phys. Chem. A112,10728(2008).
[14]J. J. Zhao, R. H. Xie, X. L. Zhou, X. S. Chen, and W. Lu, "Formation of stable fullerenelike GanAsn clusters (6<= n<= 9):Gradient-corrected density-functional theory and a genetic global optimization approach", Phys. Rev. B 74,035319 (2006).
[15]Z. Q. Wang and D. Stroud, "MONTE-CARLO STUDY OF LIQUID GAAS-BULK AND SURFACE-PROPERTIES", Phys. Rev. B 42,5353 (1990).
[16]D. M. Deaven and K. M. Ho, "Molecular-Geometry Optimization with a Genetic Algorithm", Phys. Rev. Lett.75,288 (1995).
[17]J. J. Zhao and R. H. Xie, "Genetic Algorithms for the Geometry Optimization of Atomic and Molecular Clusters", J. Comput. Theor. Nanosci.1,117 (2004).
[18]D. J. Wales and J. P. K. Doye, "Global optimization by basin-hopping and the lowest energy structures of Lennard-Jones clusters containing up to 110 atoms", J. Phys.Chem.A 101,5111 (1997).
[19]Frank H. Stillinger and Thomas A. Weber, "Computer simulation of local order in condensed phases of silicon", Phys. Rev. B 31,5262 (1985).
[20]B. Delley, "AN ALL-ELECTRON NUMERICAL-METHOD FOR SOLVING THE LOCAL DENSITY FUNCTIONAL FOR POLYATOMIC-MOLECULES", J. Chem. Phys.92,508 (1990).
[21]John P. Perdew and Yue Wang, "Accurate and simple analytic representation of the electron-gas correlation energy", Phys. Rev. B 45,13244 (1992).
[22]John P. Perdew, J. A. Chevary, S. H. Vosko, Koblar A. Jackson, Mark R. Pederson, D. J. Singh, and Carlos Fiolhais, "Atoms, molecules, solids, and surfaces:Applications of the generalized gradient approximation for exchange and correlation", Phys. Rev. B 46,6671 (1992).
[23]J. P. Perdew, K. Burke, and M. Ernzerhof, "Generalized gradient approximation made simple", Phys. Rev. Lett.77,3865 (1996).
[24]G.W. Trucks M.J. Frisch, H.B. Schlegel, G.E. Scuseria,M.A. Robb, J.R. Cheeseman,, J.A. Montgomery V.G. Zakrzewski, Jr., R.E. Stratmann, J.C. Burant, S. Dapprich,, A.D. Daniels J.M. Millam, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V., M. Cossi Barone, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J., G.A. Petersson Ochterski, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D., K. Raghavachari Rabuck, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul,, G. Liu B.B. Stefanov, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M., P.M.W. Gill Challacombe, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C., M. Head-Gordon Gonzalez, E.S. Replogle, J.A. Pople, GAUSSIAN 03, Gaussian,, and Pittsburgh Inc., PA,2003., "GAUSSIAN 03, Gaussian, Inc., Pittsburgh, PA,2003.".
[25]A. D. Becke, "DENSITY-FUNCTIONAL EXCHANGE-ENERGY APPROXIMATION WITH CORRECT ASYMPTOTIC-BEHAVIOR", Phys. Rev. A 38,3098 (1988).
[26]J. P. Perdew, K. Burke, and Y. Wang, "Generalized gradient approximation for the exchange-correlation hole of a many-electron system", Phys. Rev. B 54,16533 (1996).
[27]L. A. Curtiss, M. P. Mcgrath, J. P. Blaudeau, N. E. Davis, R. C. Binning, and L. Radom, "Extension of Gaussian-2 Theory to Molecules Containing 3rd-Row Atoms Ga-Kr", J. Chem. Phys.103,6104 (1995).
[28]B. L. Wang, S. Y. Yin, G. H. Wang, A. Buldum, and J. J. Zhao, "Novel structures and properties of gold nanowires", Phys. Rev. Lett.86,2046 (2001).
[29]A. D. McLean and Yoshimin.M, "THEORY OF MOLECULAR POLARIZABILITIES", J. Chem. Phys.47,1927 (1967).
[30]S. Schlecht, R. Schafer, J. Woenckhaus, and J. A. Becker, "ELECTRIC-DIPOLE POLARIZABILITIES OF ISOLATED GALLIUM-ARSENIDE CLUSTERS", Chem. Phys. Lett.246,315 (1995).
[31]K. E. Laidig and R. F. W. Bader, "PROPERTIES OF ATOMS IN MOLECULES-ATOMIC POLARIZABILITIES", J. Chem. Phys.93,7213 (1990).
[32]K. R. S. Chandrakumar, T. K. Ghanty, and S. K. Ghosh, "Relationship between ionization potential, polarizability, and softness:A case study of lithium and sodium metal clusters", J. Phys. Chem. A 108,6661 (2004).
[33]J. L. Wang, M. L. Yang, J. Jellinek, and G. H. Wang, "Dipole polarizabilities of medium-sized gold clusters", Phys. Rev. A 74,023202 (2006).
[34]R. F. W. Bader, M. T. Carroll, J. R. Cheeseman, and C. Chang, "PROPERTIES OF ATOMS IN MOLECULES-ATOMIC VOLUMES", J. Am. Chem. Soc.109, 7968 (1987).
[35]B. J. Orr and J. F. Ward, "Perturbation Theory of Non-Linear Optical Polarization of an Isolated System", Mol. Phys.20,513(1971).
[1]O. M. Wilson, M. R. Knecht, J. C. Garcia-Martinez, and R. M. Crooks, "Effect of Pd nanoparticle size on the catalytic hydrogenation of allyl alcohol", J. Am. Chem. Soc.128,4510 (2006).
[2]B. Kalita and R. C. Deka, "Reaction Intermediates of CO Oxidation on Gas Phase Pd-4 Clusters:A Density Functional Study", J. Am. Chem. Soc.131,13252 (2009).
[3]A. S. Worz, K. Judai, S. Abbet, and U. Heiz, "Cluster size-dependent mechanisms of the CO+NO reaction on small Pd-n (n<= 30) clusters on oxide surfaces", J. Am. Chem. Soc.125,7964 (2003).
[4]G. Gantefor and W. Eberhardt, "Localization of 3d and 4d electrons in small clusters:The "roots" of magnetism", Phys. Rev. Lett.76,4975 (1996).
[5]T. Taniyama, E. Ohta, and T. Sato, "Observation of 4d ferromagnetism in free-standing Pd fine particles", Europhys. Lett.38,195 (1997).
[6]T. Shinohara, T. Sato, and T. Taniyama, "Surface ferromagnetism of Pd fine particles", Phys. Rev. Lett.91,197201 (2003).
[7]V. Kumar and Y. Kawazoe, "Icosahedral growth, magnetic behavior, and adsorbate-induced metal-nonmetal transition in palladium clusters", Phys. Rev. B 66,144413 (2002).
[8]M. Moseler, H. Hakkinen, R. N. Barnett, and U. Landman, "Structure and magnetism of neutral and anionic palladium clusters", Phys. Rev. Lett.86,2545 (2001).
[9]H. L. Zhang, D. X. Tian, and J. J. Zhao, "Structural evolution of medium-sized Pd-n (n=15-25) clusters from density functional theory", J. Chem. Phys.129, 114302(2008).
[10]A. J. Cox, J. G. Louderback, S. E. Apsel, and L. A. Bloomfield, "MAGNETISM IN 4D-TRANSITION METAL-CLUSTERS", Phys. Rev. B 49,12295 (1994).
[11]D. C. Douglass, J. P. Bucher, and L. A. Bloomfield, "MAGNETIC STUDIES OF FREE NONFERROMAGNETIC CLUSTERS", Phys. Rev. B 45,6341 (1992).
[12]T. Futschek, M. Marsman, and J. Hafner, "Structural and magnetic isomers of small Pd and Rh clusters:an ab initio density functional study", J. Phys.: Condens. Matter 17,5927 (2005).
[13]J. Rogan, G. Garcia, M. Ramirez, V. Munoz, J. A. Valdivia, X. Andrade, R. Ramirez, and M. Kiwi, "The structure and properties of small Pd clusters", Nanotechnology 19,205701 (2008).
[14]C. M. Chang and M. Y. Chou, "Alternative low-symmetry structure for 13-atom metal clusters", Phys. Rev. Lett.93,133401 (2004).
[15]Andreas M Koster, Patrizia Calaminici, Emilio Orgaz, Debesh R Roy, Jose Ulises Reveles, and Shiv N Khanna, "On the Ground State of Pd(13).", J. Am. Chem. Soc.133,12192(2011).
[16]M. J. Piotrowski, P. Piquini, and J. L. F. Da Silva, "Density functional theory investigation of 3d,4d, and 5d 13-atom metal clusters", Phys. Rev. B 81,155446 (2010).
[17]C. Jing, Y. Yang, S. X. Cao, and J. C. Zhang, "Electronic structure and magnetism of Mnl-xPdx alloys", Mod. Phys. Lett. B 20,305 (2006).
[18]S. Nigam, C. Majumder, and S. K. Kulshreshtha, "Geometry and electronic and magnetic properties of MPdl2 clusters (M=Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, and Pd) from first principles", Phys. Rev. B 76,195430 (2007).
[19]D. M. Deaven and K. M. Ho, "Molecular-Geometry Optimization with a Genetic Algorithm", Phys. Rev. Lett.75,288 (1995).
[20]Bin Shan, Ligen Wang, Sang Yang, Jangsuk Hyun, Neeti Kapur, Yujun Zhao, John Nicholas, and Kyeongjae Cho, "First-principles-based embedded atom method for PdAu nanoparticles", Phys. Rev. B 80,1 (2009).
[21]W. Q. Zhang, Q. F. Ge, and L. C. Wang, "Structure effects on the energetic, electronic, and magnetic properties of palladium nanoparticles", J. Chem. Phys. 118,5793 (2003).
[22]J. Rogan, G. Garcia, J. A. Valdivia, W. Orellana, A. H. Romero, R. Ramirez, and M. Kiwi, "Small Pd clusters:A comparison of phenomenological and ab initio approaches", Phys. Rev. B 72,115421 (2005).
[23]N. F. Shen, J. L. Wang, and L. Y. Zhu, "Ab initio study of magnetic properties of bimetallic Con-1Mn and Con-1V clusters", Chem. Phys. Lett.467,114 (2008).
[24]K. Huber and G. Herzberg,{Molecular Spectra and Molecular Structure. IV. Constants of Diatomic Molecules》, (Van Nostrand Reinhold,1979).
[25]M. D. Morse, "CLUSTERS OF TRANSITION-METAL ATOMS", Chem. Rev. 86,1049(1986).
[26]K. D. Bier, T. L. Haslett, A. D. Kirkwood, and M. Moskovits, "THE RESONANCE RAMAN AND VISIBLE ABSORBANCE SPECTRA OF MATRIX-ISOLATED MN-2 AND MN-3", J. Chem. Phys.89,6 (1988).
[27]G. Kresse and J. Furthmuller, "Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set", Phys. Rev. B 54,11169 (1996).
[28]G. Kresse and J. Hafner, "NORM-CONSERVING AND ULTRASOFT PSEUDOPOTENTIALS FOR FIRST-ROW AND TRANSITION-ELEMENTS", J. Phys.:Condens. Matter 6,8245 (1994).
[29]P. E. Blochl, "PROJECTOR AUGMENTED-WAVE METHOD", Phys. Rev. B 50, 17953 (1994).
[30]G. Kresse and D. Joubert, "From ultrasoft pseudopotentials to the projector augmented-wave method", Phys. Rev. B 59,1758 (1999).
[31]J. P. Perdew, K. Burke, and M. Ernzerhof, "Generalized gradient approximation made simple", Phys. Rev. Lett.77,3865 (1996).
[32]F. Aguilera-Granja, A. Vega, J. Rogan, W. Orellana, and G. Garcia, "Magnetic properties of Pd atomic clusters from different theoretical approaches", Eur. Phys. J. D 44,125(2007).
[33]P. Blonski and J. Hafner, "Magneto-structural properties and magnetic anisotropy of small transition-metal clusters:a first-principles study", J. Phys.:Condens. Matter 23,136001 (2011).
[34]V. Kumar and Y. Kawazoe, "Magnetism in clusters of non-magnetic elements:Pd, Rh, and Ru-Magnetism in clusters of non-magnetic elements", Eur. Phys. J. D 24,81 (2003).
[35]H. Chen, N. E. Brener, and J. Callaway, "Electronic-Structure, Optical and Magnetic-Properties of Fcc Palladium", Phys. Rev. B 40,1443 (1989).
[36]M. Brack, "THE PHYSICS OF SIMPLE METAL-CLUSTERS SELF-CONSISTENT JELLIUM MODEL AND SEMICLASSICAL APPROACHES", Rev. Mod. Phys.65,677 (1993).
[37]Mark B. Knickelbein, "Experimental Observation of Superparamagnetism in Manganese Clusters", Phys. Rev. Lett.86,5255 (2001).
[38]Mark B. Knickelbein, "Magnetic ordering in manganese clusters", Phys. Rev. B 70,014424 (2004).
[39]L. Vitos, B. Johansson, and J. Kollar, "Size-dependent paramagnetic-ferromagnetic phase transition in palladium clusters", Phys. Rev. B 62, R11957 (2000).
[40]P. Bobadova-Parvanova, K. A. Jackson, S. Srinivas, and M. Horoi, "Density-functional investigations of the spin ordering in Fel3 clusters", Phys. Rev. B 66,195402(2002).
[1]F. A. Ponce and D. P. Bour, "Nltride-based semiconductors for blue and green light-emitting devices", Nature 386,351 (1997).
[2]S. Nakamura, "The roles of structural imperfections in InGaN-Based blue light-emitting diodes and laser diodes", Science 281,956 (1998).
[3]H. Morkoc, S. Strite, G. B. Gao, M. E. Lin, B. Sverdlov, and M. Burns, "LARGE-BAND-GAP SIC,Ⅳ-Ⅴ NITRIDE, AND Ⅱ-Ⅵ ZNSE-BASED SEMICONDUCTOR-DEVICE TECHNOLOGIES", J. Appl. Phys.76,1363 (1994).
[4]J. M. de Almeida, T. Kar, and P. Piquini, "AlN, GaN, AlxGal-xN nanotubes and GaN/AlxGal-xN nanotube heterojunctions", Phys. Lett. A 374,877 (2010).
[5]J. Goldberger, R. R. He, Y. F. Zhang, S. W. Lee, H. Q. Yan, H. J. Choi, and P. D. Yang, "Single-crystal gallium nitride nanotubes", Nature 422,599 (2003).
[6]L. Yang, X. Zhang, R. Huang, G. Y. Zhang, and X. An, "Synthesis of single crystalline GaN nanoribbons on sapphire(0001) substrates", Solid State Commun. 130,769 (2004).
[7]X. Xiang, C. B. Cao, F. L. Huang, R. T. Lv, and H. S. Zhu, "Synthesis and characterization of crystalline gallium nitride nanoribbon rings", J. Cryst. Growth 263,25 (2004).
[8]S. Y. Bae, H. W. Seo, J. Park, H. Yang, and S. A. Song, "Synthesis and structure of gallium nitride nanobelts", Chem. Phys. Lett.365,525 (2002).
[9]Jian Yu Huang, He Zheng, S X Mao, Qiming Li, and George T Wang, "In Situ Nanomechanics of GaN Nanowires.", Nano Lett.11,1618 (2011).
[10]H.Sahin, S. Cahangirov, M. Topsakal, E. Bekaroglu, E. Akturk, R. T. Senger, and S. Ciraci, "Monolayer honeycomb structures of group-Ⅳ elements and Ⅲ-Ⅴ binary compounds:First-principles calculations", Phys. Rev. B 80,155453 (2009).
[11]H. M. Li, J. Dai, J. Li, S. Zhang, J. Zhou, L. J. Zhang, W. S. Chu, D. L. Chen, H. R. Zhao, J. L. Yang, and Z. Y. Wu, "Electronic Structures and Magnetic Properties of GaN Sheets and Nanoribbons", J. Phys. Chem. C 114,11390 (2010).
[12]E. Kan, H. J. Xiang, F. Wu, C. Lee, J. L. Yang, and M. H. Whangbo, "Ferrimagnetism in zigzag graphene nanoribbons induced by main-group adatoms", Appl. Phys. Lett.96,102503 (2010).
[13]Q. Chen, J. L. Wang, L. Y. Zhu, S. D. Wang, and F. Ding, "Fluorination induced half metallicity in two-dimensional few zinc oxide layers", J. Chem. Phys.132, 204703 (2010).
[14]C. Ataca and S. Ciraci, "Functionalization of BN honeycomb structure by adsorption and substitution of foreign atoms", Phys. Rev. B 82,165402 (2010).
[15]A. R. Botello-Mendez, F. Lopez-Urias, M. Terrones, and H. Terrones, "Magnetic behavior in zinc oxide zigzag nanoribbons", Nano Lett.8,1562 (2008).
[16]G. Kresse and J. Furthmuller, "Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set", Phys. Rev. B 54,11169 (1996).
[17]G. Kresse and J. Hafner, "NORM-CONSERVING AND ULTRASOFT PSEUDOPOTENTIALS FOR FIRST-ROW AND TRANSITION-ELEMENTS", J. Phys.:Condens. Matter 6,8245 (1994).
[18]P. E. Blochl, "PROJECTOR AUGMENTED-WAVE METHOD", Phys. Rev. B 50, 17953(1994).
[19]G. Kresse and D. Joubert, "From ultrasoft pseudopotentials to the projector augmented-wave method", Phys. Rev. B 59,1758 (1999).
[20]J. P. Perdew, K. Burke, and M. Ernzerhof, "Generalized gradient approximation made simple", Phys. Rev. Lett.77,3865 (1996).
[21]Hendrik J. Monkhorst and James D. Pack, "Special points for Brillouin-zone integrations", Phys. Rev. B 13,5188 (1976).
[22]Quantum ESPRESSO, http://www.quantum-espresso.org/.
[23]F. D. Murnaghan, "Finite Deformations of an Elastic Solid", Am. J. Math.59, 235(1937).
[24]Roy Papiya Bose and Roy Sushil Bose, "Applicability of isothermal three-parameter equations of state of solids-a reappraisal", J. Phys.:Condens. Matter 17,6193(2005).
[25]J. Zhou, Q. Wang, Q. Sun, X. S. Chen, Y. Kawazoe, and P. Jena, "Ferromagnetism in Semihydrogenated Graphene Sheet", Nano Lett.9,3867 (2009).
[26]G. Bouzerar, J. Kudrnovsky, L. Bergqvist, and P. Bruno, "Ferromagnetism in diluted magnetic semiconductors:A comparison between ab initio mean-field, RPA, and Monte Carlo treatments", Phys. Rev. B 68 (2003).
[27]Jian Zhou and Qiang Sun, "Magnetism of phthalocyanine-based organometallic single porous sheet.", J. Am. Chem. Soc.133,15113 (2011).
[28]N. F. Shen, J. L. Wang, and L. Y. Zhu, "Ab initio study of magnetic properties of bimetallic Con-IMn and Con-1V clusters", Chem. Phys. Lett.467,114 (2008).