Surface tensions and stress tensors of liquid and solid clusters by molecular dynamics

Surface tension and pressure (stress) tensors of Lennard-Jones clusters, in the size range 200 ~ 2700 atoms/cluster, formed from evaporating liquid droplets were calculated in a Molecular Dynamics simulation. Icosahedral clusters have a much larger surface tension than decahedral, fcc, and hcp ones, meanwhile asymmetric icosahedral clusters have a lower surface tension. Fcc and hcp clusters have a very small surface tension. Decahedral clusters have a surface tension closer to that of fcc and hcp ones than to that of icosahedral ones, though both icosahedral and decahedral structures have five fold symmetry axis. Binary component clusters have a higher surface tension than single component ones.     

CO2 motion in carbon dioxide deuterohydrate determined by applying maximum entropy method to neutron powder diffraction data

Crystal structures of carbon dioxide deuterohydrate were studied by neutron powder diffraction at temperatures from 10 to 200 K. Maps of scattering length density distribution were obtained using a maximum entropy method (MEM), which clarified the motion of CO₂ molecules in the hydrate. In small cages, the carbon atom of the CO₂ molecule is at the center of the cage, and the oxygen atoms of CO₂ revolve freely around the carbon atom. In large cages, the carbon atom also is at the center of the cage, but the oxygen atoms tend to revolve around the carbon atom along the plane parallel to the hexagonal facets of the cage.     

Molecular dynamics simulations of the freezing of gold nanoparticles

A set of molten gold clusters, each with 1157 gold atoms, was studied by molecular dynamics simulations as the clusters underwent freezing at three different temperatures. Most of the clusters attained an icosahedral structure upon freezing, a structure found to be stable to mild annealing. Other structures observed were imperfect truncated decahedral, truncated octahedral and hexagonal close packed structures. The role of kinetics in the process of cluster solidification is discussed. Received 6 November 2000     

利用Gupta势结合遗传算法研究ConCu55－n(n=0—55)混合团簇的结构演化及基态能量

采用半经验的Gupta多体势结合遗传算法对Co_nCu_55－n(n=0—55)混合团簇的基态结构和能量进行了研究,发现这些混合团簇的基态结构是在Co₅₅,Cu₅₅单质团簇(Mackay二十面体)的基础之上发生的畸变;从n=0(Cu₅₅)开始,Co原子从中心到表面,从棱到顶点依次、连续替换Cu原子;基态结构与键能较大键的数目及其平均键长有关;Co₁₃Cu₄₂具有最稳定的结构,13个Co原子全部位于团簇内部形成Mackay二十面体对整个团簇的稳定性有显著影响. 关键词： 团簇 结构和能量 Gupta势 遗传算法     

The structure of 55-atom Cu–Au bimetallic clusters: Monte Carlo study

We have investigated segregation phenomena in Cu–Au bimetallic clusters with decahedral structures at 100 K and 300 K, based on the second-moment approximation of the tight-binding (TB-SMA) potentials by using Monte Carlo method. The simulation results indicate that there are three regions (split, three-shell onion-like and core-shell region) at 100 K and two regions (split and core-shell) at 300 K with the structure of decahedral clusters, as the chemical potential difference Δμ changes. It is found that the structure of decahedral clusters undergoes a division into smaller clusters in the split region. In the core-shell structure, Au atoms are enriched in surface and Cu atoms occupy the core of the clusters because of the different surface energy of Cu and Au. The Au atoms are enriched in the surface shell, and the Cu atoms are in the middle shell, while a single Au atom is located in the center to form the three-shell onion-like structure. The structure and binding energy of smaller clusters after splitting are also discussed. The Au atoms generally lie on the surface of the smaller clusters after splitting.     

A density functional theoretic study of novel silicon-carbon fullerene-like nanostructures: Si40C20, Si60C20, Si36C24, and Si60C24

Fullerene-like silicon nanostructures with twenty and twenty-four carbon atoms on the surface of the Si₆₀ cage by substitution, as well as inside the cage at various orientations have been studied within the generalized gradient approximation to density functional theory. Full geometry optimizations have been performed without any symmetry constraints using the Gaussian 03 suite of programs and the LANL2DZ basis set. Thus, for the silicon atom, the Hay-Wadt pseudopotential with the associated basis set is used for the core electrons and the valence electrons, respectively. For the carbon atom, the Dunning/Huzinaga double zeta basis set is employed. Electronic and geometric properties of these nanostructures are presented and discussed in detail. Optimized silicon-carbon fullerene like nanostructures are found to have increased stability compared to the bare Si₆₀ cage and the stability depends on the number and the orientation of carbon atoms, as well as on the nature of silicon-carbon and carbon-carbon bonding.     

Probing the structural,electronic and magnetic properties of small Au4M (M = Sc–Zn) clusters

Density-functional method PW91 has been selected to investigate the structural, electronic and magnetic properties of Au₄M (M =Sc–Zn) clusters. Geometry optimisations show that the M atoms in the ground-state Au₄M clusters favour the most highly coordinated position. The ground-state Au₄M clusters possess a solid structure for M = Sc and Ti and a planar structure for M = V–Zn. The characteristic frequency of the doped clusters is much greater than that of pure gold cluster. The relative stability and chemical activity are analysed by means of the averaged binding energy and highest occupied molecular orbital and lowest unoccupied molecular orbital energy gap for the lowest energy Au₄M clusters. It is found that the dopant atoms can enhance the thermal stability of the host cluster except for Zn atom. The Au₄Ti, Au₄Mn and Au₄Zn clusters have relatively higher chemical stability. The vertical detachment energy, electron affinity and photoelectron spectrum are calculated and simulated theoretically for all the ground-state structures. The magnetism calculations reveal that the total magnetic moment of Au₄M cluster is mainly localised on the M atom and vary from 0 to 5 μ_B by substituting an Au atom in Au₅ cluster with different transition-metal atoms.     

第一性原理计算ZrnFe(n=2—13)团簇的基态结构及其磁性

从第一性原理出发，利用密度泛函理论中的广义梯度近似对Zr_nFe(n=2—13)团簇进行了结构优化、能量和频率计算.在充分考虑自旋多重度的前提下，对每一具体尺寸的团簇，得到了多个平衡构型，并根据能量高低确定了团簇的基态结构.综合团簇的结合能、二阶能量差分以及团簇的最高占据轨道和最低未占据轨道间的能隙可知Zr₅Fe，Zr₇Fe和Zr₁₂Fe团簇的稳定性相对较高，Zr₁₂Fe团簇的结构是具有I_h对称性的正二十面体，而且Zr₁₂Fe的稳定性在所有团簇中是最高的.另外，不仅Zr₅Fe，Zr₇Fe和Zr₁₂Fe团簇的稳定性相对较高，而且它们均为磁性团簇(而Zr_n团簇的磁矩在n≥5时已经发生了淬灭)，由此可知通过选择合适的掺杂元素可能得到高稳定的磁性团簇.从Mulliken布居分析结果可知，除了在Zr₁₂Fe团簇中Fe原子失去少量电荷外，其他团簇中Fe原子均从Zr原子那里得到了一定量电荷，即Fe原子在Zr_nFe(n=2—13，n≠12)团簇中是电子受体.     

碱金属钠原子修饰硅原子团簇的结构及储氢性能研究

提出碱金属钠原子修饰笼形Si_6团簇的结构模型,采用密度泛函理论(DFT)研究钠原子修饰笼形Si_6团簇的结构及储氢性能.研究结果表明,氢分子与笼形Si_6团簇表面相互作用很弱,氢分子在其表面容易脱附.采用钠原子修饰笼形Si_6团簇后可有效避免氢分子的脱附,并且钠原子在笼形Si_6团簇的表面不发生团聚,有利于氢分子在其表面吸附和循环利用.研究发现在两个钠原子修饰笼形Si_6团簇的结构中,每个钠原子可以有效吸附六个氢分子.计算得到Na2Si_6团簇结构储氢的质量分数高达10.08 wt%,且氢分子的平均吸附能约为0.837 kcal/mol.可见,实现钠原子修饰笼形Si_6团簇结构在常温常压条件下储氢是有可能的.     

Melting Behaviour of Core-Shell Structured Ag-Rh Bimetallic Clusters

The melting behaviour of four typical core-shell structured 309-atom Ag-Rh bimetallic clusters, with decahedral and icosahedral geometric configurations, is investigated by using molecular dynamics simulation, based on the Sutton-Chen potential. The initial atomic configurations are obtained from semi-grand canonical ensemble Monte Carlo simulations. It is found that the melting point temperature Tm increases with the mole fraction of Rh in the bimetallic clusters, and Tm of Ag-Rh icosahedral clusters is higher than those of Ag-Rh decahedral clusters with the same Rh mole fraction. It is also found that the Ag atoms lie on the surface of Ag-Rh bimetallic clusters even after melting.     

Hydrogenated silicon fullerenes: effects of H on the stability of metal-encapsulated silicon clusters

Ab initio calculations of H interaction on Si12M, Si18M2 (M=Cr, Mo, and W), and Zr@Si(16) fullerene (f) show relatively weak binding of H in agreement with experimental results of H free Si12M and Si18M2 clusters. Adsorption of H enhances sp(3) bonding between the Si atoms, weakens the M-Si cage interactions, and leads to distortions in the cages. Si12CrH12 has 4 mu(B) magnetic moment in contrast to zero for Si12Cr. Removal of the M atom leads to stable empty cages of Si12H12, f-Si16H16, and f-Si20H20 with large highest occupied-lowest unoccupied molecular orbital gaps of 2.5-3.0 eV, making them attractive for optoelectronic applications.     

Formation of metallofullerenes by laser ablation of externally doped fullerenes C60Mx (M=Sm, Pt and Ni)

Photofragmentation of metal fullerides C₆₀M_x (M=Sm, Pt and Ni) has been studied by excimer laser ablation–TOF mass spectrometry. Metallofullerenes of the type C_nM (n<60) have been observed in both the positive and negative ionic modes, with C₅₉M being the most prominent species. It is supposed that the metal atom is incorporated into the network of the fullerene cage to replace one carbon atom of the cage, forming substitutional metallofullerene. The occurrence of the C₅₉M, C₅₈M, C₅₇M clusters in the mass spectra is confirmed by the coincidence of the intensity distribution of the mass peaks with the isotopic abundance pattern calculated from the natural abundance of isotopes of C and M. Odd-numbered high-carbon clusters are observed in our laser ablation study of all the metal fullerides in the negative ion channel. The evolution of the mass spectra of these samples with laser irradiation shots indicates that the transformation process from an externally doped fullerene to the substitutionally doped fullerene involves the loss of metal carbide, MC. The structures of metallofullerenes C_2n+1M and C_2nM with even and odd total numbers of atoms respectively are discussed. Formation mechanisms with the participation of odd-numbered all-carbon fullerene clusters as intermediates are supposed. Received: 18 June 2001 / Accepted: 28 September 2001 / Published online: 2 May 2002     

Chirality, defects, and disorder in gold clusters

Theoretical and experimental information on the shape and morphology of bare and passivated gold clusters is fundamental to predict and understand their electronic, optical, and other physical and chemical properties. An effective theoretical approach to determine the lowest-energy configuration (global minimum) and the structures of low energy isomers (local minima) of clusters is to combine genetic algorithms and many-body potentials (to perform global structural optimizations), and first-principles density functional theory (to confirm the stability and energy ordering of the local minima). The main trend emerging from structural optimizations of bare Au clusters in the size range of 12-212 atoms indicates that many topologically interesting low-symmetry, disordered structures exist with energy near or below the lowest-energy ordered isomer. For example, chiral structures have been obtained as the lowest-energy isomers of bare Au₂₈ and Au₅₅ clusters, whereas in the size-range of 75-212 atoms, defective Marks decahedral structures are nearly degenerate in energy with the ordered symmetrical isomers. For methylthiol-passivated gold nanoclusters [Au₂₈(SCH₃)₁₆ and Au₃₈(SCH₃)₂₄], density functional structural relaxations have shown that the ligands are not only playing the role of passivating molecules, but their effect is strong enough to distort the metal cluster structure. In this work, a theoretical approach to characterize and quantify chirality in clusters, based on the Hausdorff chirality measure, is described. After calculating the index of chirality in bare and passivated gold clusters, it is found that the thiol monolayer induces or increases the degree of chirality of the metallic core. We also report simulated high-resolution transmission electron microscopy (HRTEM) images which show that defects in decahedral gold nanoclusters, with size between 1-2 nm, can be detected using currently available experimental HRTEM techniques.     

Structures, stabilities and ordering in Ni-Al nanoalloy clusters

A detailed study is made of the structures and relative stabilities of nickel and aluminium clusters and nickel-aluminium "nanoalloy" clusters, with up to 55 atoms, modelled by the many-body Gupta potential. Random search and genetic algorithms are used to find the lowest energy isomers (both geometrical and permutational). For the pure Al and Ni clusters, the lowest energy structures are identical for most nuclearities but different structures are found for clusters with 15-18 atoms -- the Al clusters having non-icosahedral structures. For these nuclearities, we investigate the effect of doping Al atoms into pure Ni clusters and vice versa, finding that the replacement of a single atom by a dopant atom is often sufficient to change the cluster geometry. The lowest energy isomers of nanoalloy clusters with the approximate composition "Ni₃Al" generally have structures based on icosahedral packing, though truncated octahedral (fcc packing) motifs are also observed. In agreement with previous studies, the atom ordering in the mixed Ni-Al clusters is found to depend on the maximization of the number of Ni-Al interactions, the minimization of the cluster surface energy, and atom size effects.Received: 17 January 2003, Published online: 17 July 2003PACS: 36.40.Mr Spectroscopy and geometrical structure of clusters - 61.46.+w Nanoscale materials: clusters, nanoparticles, nanotubes, and nanocrystals - 61.66.Dk AlloysM.S. Bailey: Present address: Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, NY 14853-1301, USA.     

Cluster formulae for metallic glasses derived from devitrification phases

Bulk metallic glasses are known to have a composition formula [cluster](glue atom)_1,3 within the framework of the cluster-plus-glue-atom model. The key issue in applying the cluster formula is the determination of the right clusters and glue atoms. As examples, alloy phases in the glass-forming systems Al–Ni–Zr and B–Co–Si are analysed from the viewpoint of nearest coordination polyhedral clusters. These alloy phases are described by [effective cluster](glue atom) _x , where the effective cluster refers to true cluster composition after taking account of cluster-sharing in the phase structure. For each alloy phase, a principal cluster can be identified that features the local short-range order of that phase. It is pointed out that the principal clusters can express compositions with high glass-forming abilities, as verified by our experiments in Al–Ni–Zr and B–Co–Si–Ta.     

Stuffed fullerene structures for medium-sized silicon clusters

The structural properties of medium-sized silicon clusters (Si₄₀, Si₄₅ and Si₅₀) have been studied using an unbiased global genetic algorithm search incorporated with a tight-binding model, followed by gradient-corrected density functional calculations. Stuffed fullerene cages are obtained as energetically favorite structures. The stuffing/cage ratio (m/n for Si_m@Si_n) can be understood by a space filling picture. The present results, along with our recent works on Si_N (N=27-39) clusters [20], suggest that stuffed fullerene cages are the preferred structural growth pattern of medium-sized silicon clusters.     

Geometries,stabilities and electronic properties of small-sized Pd2-doped Sin (n = 1–11) clusters

The geometries, growth patterns, relative stabilities and electronic properties of small-sized Pd₂Si_n and Si_n+2 (n = 1–11) clusters are systematically studied using the hybrid density functional theory method B3LYP. The optimised structures revealed that the lowest energy Pd₂Si_n clusters are not similar to those of pure Si_n clusters. When n = 9, one Pd atom in Pd₂Si₉ completely falls into the centre of the Si outer frame, forming metal-encapsulated Si cages. On the basis of the optimised structures, the averaged binding energy, fragmentation energy, second-order energy difference and highest occupied–lowest unoccupied molecular orbital energy gap are calculated. It is found that the Pd₂Si₅ and Pd₂Si₇ clusters have stronger relative stabilities among the Pd₂Si_n clusters. Additionally, the stabilities of Si_n+2 clusters have been reduced by the doping of Pd impurity. The natural population and natural electronic configuration analysis indicated that the Pd atoms possess negative charges for n = 1–11 and there exist the spd hybridisation in the Pd atom. Finally, the chemical hardness, chemical potential, electrostatic potential and polarisability are discussed.     

Ab-initio molecular dynamical study of a single transition metal atom on fullerene C<Subscript>60</Subscript>: the case of Ta

We report the first-principles Car-Parrinello molecular dynamics study of the behaviour of a single transition metal Ta atom on fullerene C₆₀, at different temperatures, and for both neutral and charged clusters. We seek to characterise the motion of the lone Ta metal atom on the C₆₀ surface, contrasting its behaviour both with that of three Ta atoms, as well as with a single alkali metal atom on the cage surface. Our earlier simulations on C₆₀Ta₃ had revealed that the Ta atoms on the surface of the fullerene are affected by a rather high mobility, and that the motion of these atoms is highly correlated due to Ta-atom-Ta-atom attraction. Earlier, experimental studies of a single metal atom (K, Rb) on the surface of a C₆₀ molecule had led to the inference that at room temperature the metal atom skates freely over the surface, the first direct evidence for which was presented by us in earlier first principles molecular dynamical simulations.     

Metal-encapsulated caged clusters of germanium with large gaps and different growth behavior than silicon

Metal ( M)-encapsulated caged clusters of Ge are studied using the ab initio pseudopotential plane-wave method and the generalized gradient approximation for the exchange-correlation energy. Depending upon the size of the M atom, we find Frank-Kasper polyhedral M@Ge(16) for M= Ti, Zr, Hf, and capped decahedral or cubic M@Ge(14) and M@Ge(15) clusters for several M atoms. The growth behavior differs from the one found in M@Si(n) clusters. The highest-occupied-lowest-unoccupied molecular orbital gaps are, however, similarly large or even higher in some cases. Cr@Ge(16) and Fe@Ge(15) are magnetic. The weak interaction between the clusters makes such species attractive for cluster assembled materials.     

小尺寸铜团簇冷却与并合过程中结构变化的原子尺度研究

研究Cu_N（N=57,58,59）熔融铜团簇在冷却过程以及300 K时两个具有二十面体结构Cu₅₅团簇在并合过程中的结构变化.对这些小尺寸团簇的结构变化采用基于嵌入原子方法的正则系综分子动力学进行计算机模拟.通过对模拟结果的分析表明,小团簇的冷却和并合过程存在阶段变化的特点.降温过程中Cu_N（N=57,58,59）团簇的原子运动及其微观结构变化表现出较大差异,由此导致这三类团簇内原子排布的不同,其中Cu₅₉团簇结构的有序程度最低.在两个Cu₅₅团簇并合早期阶段,这两个团簇相接触后发生变形导致原子位置出现较大改变,在随后的并合过程中,原子扩散引起原子局部位置调整导致所并合体系的结构发生变化.远离两个团簇接触区的原子仍保持其并合前的结构. 关键词： 团簇 分子动力学 计算机模拟 表面