5d过渡金属原子中心镶嵌Ag团簇M@Ag12(M＝Hf～Hg) Ih和Oh构型的密度泛函理论研究

采用相对论密度泛函理论方法对Ih和Oh构型M@Ag12 (M＝Hf～Hg)的几何和电子结构进行了系统的研究. 研究表明, 原子半径之和与团簇的电子结构共同决定了M—Ag键长的大小. M@Ag12的成键能来自中心原子的嵌入能和Ag12笼子的形变能. 最高占据轨道为成键轨道的团簇比反键轨道的团簇的稳定性强. 我们发现在此系列中, Ih构型不一定总比Oh构型稳定. Hf@Ag12, Ir@Ag12, Au@Ag12和Hg@Ag12的Oh构型比Ih构型稳定.     

Binding energy of large icosahedral and cuboctahedral Lennard-Jones clusters

It is widely believed that the lowest energy configurations for small rare gas clusters have icosahedral symmetry. This contrasts with the bulk crystal structures which have cuboctahedral fcc symmetry. It is of interest to understand the transition between this finite and bulk behavior. To model this transition in rare gas clusters we have undertaken optimization studies within the Lennard-Jones pair potential model. Using a combination of Monte Carlo and Partan Search optimization methods, the lowest energy relaxed structures of Lennard-Jones clusters having icosahedral and cuboctahedral symmetry were found. Studies were performed for complete shell clusters ranging in size from one shell having 13 atoms to 14 shells having 10,179 atoms. It was found that the icosahedral structures are lower in energy than the cuboctahedral structures for cluster sizes having 13 shells or fewer. Additional studies were performed using the more accurate Aziz-Chen [HFD-C] pair potential parameterized for argon. The conclusions appear to be relatively insensitive to the form of the potential.     

CO oxidation on Pt nanoclusters, size and coverage effects: a density functional theory study

CO oxidation on Pt nanoclusters of approximately 1 nm in size was studied using density functional theory (DFT). Reaction barriers on various sites of a cuboctahedral 55-atom cluster and of several two-layer plane clusters representing (111) and (100) facets of the 147-atom cluster have been calculated at various coverage. The effect of atomic structure of various clusters was discussed. It was concluded that the 147-atom cuboctahedral cluster reveals properties of the Pt single crystal surfaces, while a 55-atom cluster cannot be fully described in terms of Pt single crystal surfaces. It was found that CO oxidation may occur faster at higher coverage and that for cluster sizes up to a few nanometers in size, larger platinum clusters can be more efficient in CO oxidation than the smaller clusters. The size effect was found to depend upon coverage.     

Structural transitions and melting of copper clusters

Molecular dynamics is used to study the melting and structural transitions of small copper clusters. The melting temperature is found to be proportional to the average coordination number. Small icosahedral clusters melt at slightly higher temperatures than the cubic structures. Small cuboctahedral clusters are not stable but transform via a nondiffusive transition to icosahedral structure.     

Theory of the structural fluctuation of Au55 clusters

Stabilities and structural fluctuations of both neutral and charged Au₅₅ clusters are examined and discussed in relation to recent experimental observations of small gold particles with an electron microscope. Transition probabilities between the icosahedral and cuboctahedral structures are calculated according to the transition state theory using a model potential consisting of attractive many-body, repulsive pairwise and Coulomb parts. It is shown that for a neutral cluster the cuboctahedral structure has too short life time to be observed around room temperature and that, on the other hand, for more than 6-fold multiply charged clusters, both structures have life times of the order of 0.1 s around room temperature and, therefore, the transition between them can be observed.     

Chemical identification of icosahedral structure for cobalt and nickel clusters

Reactions of bare and hydrogenated cobalt and nickel clusters with ammonia and with water are used to determine cluster geometrical structure. Saturation measurements determine the total number of ammonia binding sites on cluster surfaces. A pattern of minima in the number of such sites is found to correlate with the sequence of closed shells and subshells expected for icosahedral packing in the 50- to 120-atom size range (50- to 200-atom range for hydrogenated clusters). In many cases there are 12 sites at the minima, the number that would be expected for preferred ammonia binding sites on closed (sub)shells of icosahedral clusters. The equilibrium adsorption of a single water molecule provides a sensitive measure of changes in cluster-water binding energy. A pattern of binding energy maxima is found, once again correlating with icosahedral structure, but for clusters having one metal atom more than the closed (sub)shells. In general, hydrogenation enhances the patterns of minima and maxima. These observations are explained in terms of the expected nature of ammonia and water binding to icosahedral clusters.     

Mackay,Anti-Mackay,Double-Mackay,Pseudo-Mackay,and Related Icosahedral Shell Clusters

Mackay introduced two important crystallographic concepts in a short paper published 40 years ago. One is the icosahedral shell structure (iss) consisting of concentric icosahedra displaying fivefold rotational symmetry. The number of atoms contained within these icosahedral shells and subshells agrees well with the magic numbers in rare gas clusters, (C₆₀) _N molecules, and some metal clusters determined by mass spectroscopy or simulated on energy considerations. The cluster of 55 atoms within the second icosahedral shell occurs frequently and has been called Mackay icosahedron, or simply MI, which occurs not only in various clusters, but also in intermetallic compounds and quasicrystals. The second concept is the hierarchic icosahedral structures caused by the presence of a stacking fault in the fcc packing of the successive triangular faces in the iss. For instance, a fault occurs after the ABC layers resulting an ABCB packing. This is, in fact, a hierarchic icosahedral structure of a core icosahedron connected to 12 outer icosahedra by vertex sharing, or an icosahedron of icosahedra (double MI. Contrary to Mackay's iss, a faulted hierarchic icosahedral shell is, in fact, a twinlike face capping of the underlying triangles; it is, therefore, called an anti-Mackay cluster. The hierarchic icosahedral structure in an Al-Mn-Pd icosahedral quasicrystal has a core of body-centered cube rather than an icosahedron and, therefore, is called a pseudo-Mackay cluster. The hierarchic icosahedral structures have been studied separately in the past in the fields of clusters, nanoparticles, intermetallic compounds, and quasicrystals, but the underlying geometry should be the same. In the following a unified geometrical analysis is presented.     

Geometrical and electronic structure of small copper nanoclusters: XANES and DFT analysis

The geometrical and electronic structure of small copper nanoclusters was studied by density functional theory (DFT) and analysis of X-ray absorption spectra. It was shown that the icosahedral geometry of small copper nanoclusters of 13 atoms was energetically more stable than cuboctahedral geometry. The binding energies in these structures were compared; the theoretical XANES spectra were compared with experiment. The paper gives the results of ab initio calculations of the electronic structure of copper clusters differing in size.     

Electronic shells and shells of atoms in metallic clusters

Intensity anomalies (magic numbers) have been observed in the mass spectra of sodium clusters containing up to 22 000 atoms. For small clusters (Na _n ,n≤1500) the anomalies appear to be due to the filling of electronic shells (groups of subshells having the same energy). The shells can be characterized rather well by a pseudoquantum-number, indicating the possible existence of a symmetry higher than spherical. The mass spectra of larger clusters (1500≤n≤22 000) are well explained by the completion of icosahedral or cuboctahedral shells of atoms. The fact that the two types of shells (electron and atom) occur in distinct and non-overlapping size intervals might indicate the existence of a “liquid” to “solid” transition in going from small to large clusters.     

Structural transition from icosahedra to decahedra of large Lennard-Jones clusters

The lowest icosahedral and decahedral energies of LJ1001-1610 clusters are obtained using a greedy search method (GSM) based on lattice construction. By comparing the lowest energies of icosahedral and decahedral clusters with the same atoms, the structural transition of LJ clusters is studied. Results show that the critical size from icosahedra to decahedra is located at N = 1034. When the cluster size is larger than 1034, the optimal structures are decahedra except the LJ1367-1422 clusters near the magic number, 1402, of icosahedra. However, the energies of icosahedra near the next magic number, 2044, are higher than that of decahedra, which implies that decahedra will be the optimal structure when the cluster size is larger than 1422, even for those clusters near the magic numbers of icosahedra.     

Clusters as crystal fragments of silicon bulk

Silicon clusters of 13 to 43 atoms were studied with the semi-empirical method SINDO1. Crystalline structures of face-centered cubic (fcc), hexagonal close packed (hcp) and diamond type and noncrystalline structures of icosahedral type were compared. Noncrystalline structures are most stable for clusters up to 13 atoms. Clusters with 19 and more atoms of the fcc structure are preferable to the less dense diamond structure. With more than 35 Si atoms, the diamond structure is favored over the hcp structure. The binding energy of fcc and hcp structures decreases and that of the diamond structure increases with increasing cluster size. A similar trend is observed for the HOMO-LUMO energy gap which is taken as a measure of the band gap.     

On the ground state of Pd13

First-principles electronic structure calculations within a gradient corrected density functional formalism have been carried out to investigate the electronic structure and magnetic properties of Pd(13) clusters. It is shown that a bilayer ground-state structure that can be regarded as a relaxed bulk fragment is most compatible with the experimental results from Stern-Gerlach measurements. An icosahedral structure, considered to be the ground state in numerous previous studies, is shown to be around 0.14 eV above the ground state. A detailed analysis of the molecular orbitals reveals the near degeneracy of the bilayer or icosahedral structures is rooted in the stabilization by p- or d-like cluster orbitals. The importance of low-lying spin states in controlling the electronic and magnetic properties of the cluster is highlighted.     

Melting and freezing characteristics and structural properties of supported and unsupported gold nanoclusters

Molecular dynamics simulations in conjunction with MEAM potential models have been used to study the melting and freezing behavior and structural properties of both supported and unsupported Au nanoclusters within a size range of 2 to 5 nm. In contrast to results from previous simulations regarding the melting of free Au nanoclusters, we observed a structural transformation from the initial FCC configuration to an icosahedral structure at elevated temperatures followed by a transition to a quasimolten state in the vicinity of the melting point. During the freezing of Au liquid clusters, the quasimolten state reappeared in the vicinity of the freezing point, playing the role of a transitional region between the liquid and solid phases. In essence, the melting and freezing processes involved the same structural changes which may suggest that the formation of icosahedral structures at high temperatures is intrinsic to the thermodynamics of the clusters, rather than reflecting a kinetic phenomenon. When Au nanoclusters were deposited on a silica surface, they transformed into icosahedral structures at high temperatures, slightly deformed due to stress arising from the Au-silica interface. Unlike free Au nanoclusters, an icosahedral solid-liquid coexistence state was found in the vicinity of the melting point, where the cluster consisted of coexisting solid and liquid fractions but retained an icosahedral shape at all times. These results demonstrated that the structural stability in the structures of small Au nanoclusters can be enhanced through interaction with the substrate. Supported Au nanoclusters demonstrated a structural transformation from decahedral to icosahedral motifs during Au island growth, in contrast to the predictions of the minimum-energy growth sequence: icosahedral structures appear first at very small cluster sizes, followed by decahedral structures, and finally FCC structures recovered at very large cluster sizes. The simulations also showed that island shapes are strongly influenced by the substrate, more specifically, the structural characteristic of a Au island is not only a function of size, but also depends on the contact area with the surface, which is controlled by the wetting of the cluster to the substrate.     

Ground state, growth, and electronic properties of small lanthanum clusters

The DMol cluster method based on density-functional theory has been employed to study the structural stability and electronic structure of La(n) (n=2-14) clusters. The ground states have been found out for lanthanum clusters. The Jahn-Teller effect plays an important role in this process because there are many isomers near the ground state. The magnetism is not sensitive to interatomic spacing when the change of interatomic spacing is in a small range. Lanthanum clusters grow in an icosahedral pattern. The results of the mean binding energy, of the second derivative of binding energy, and of the formation energy show strong odd-even alternation and that 7- and 13-atom clusters are magic. Further, the HOMO-LUMO gap, the mean nearest bond lengths, and the mean magnetic moments suggest that the convergence to bulk is slow and it shows an oscillatory behavior for small lanthanum clusters.     

Computer simulations of HREM images of metal clusters

Multislice calculations have been performed for Ag, Pd and Au clusters in the size range of 5.0 nm diameter of cuboctahedral, icosahedral and decahedral structures. It could be shown that tilt series are necessary for the classification of the structures. Particularly for arbitrary orientations, i.e. deviations from main directions such as 2-, 3- and 5-fold axes, the performance of computer simulations is mandatory. The influence of absorption is also studied for the case of a 100 kV microscope by introducing a complex potential.     

Correlating the crystal structure of a thiol-protected Au25 cluster and optical properties

The total structure determination of thiol-protected Au clusters has long been a major issue in cluster research. Herein, we report an unusual single crystal structure of a 25-gold-atom cluster (1.27 nm diameter, surface-to-surface distance) protected by eighteen phenylethanethiol ligands. The Au25 cluster features a centered icosahedral Au13 core capped by twelve gold atoms that are situated in six pairs around the three mutually perpendicular 2-fold axes of the icosahedron. The thiolate ligands bind to the Au25 core in an exclusive bridging mode. This highly symmetric structure is distinctly different from recent predictions of density functional theory, and it also violates the empirical golden rule "cluster of clusters", which would predict a biicosahedral structure via vertex sharing of two icosahedral M13 building blocks as previously established in various 25-atom metal clusters protected by phosphine ligands. These results point to the importance of the ligand-gold core interactions. The Au25(SR)18 clusters exhibit multiple molecular-like absorption bands, and we find the results are in good correspondence with time-dependent density functional theory calculations for the observed structure.     

Structural stability of boron clusters with octahedral and tetrahedral symmetries

The structural stability of cagelike boron clusters with octahedral and tetrahedral symmetries has been investigated by means of first-principles calculations. Twenty-eight cluster models, ranging from B(10) to B(66), were systematically constructed using regular and semiregular polyhedra as prototypes. The binding energies per atom were, on the whole, slightly lower than those of icosahedral clusters B(80) and B(100), which are supposed to be the most stable in the icosahedral group. The larger clusters did not always have higher binding energies. Isothermal molecular dynamics simulations were performed to determine the deformation temperatures at which clusters began to break or change their structures. We found eight clusters that had nonzero deformation temperatures, indicating that they are in metastable states. The octahedral cluster B(18) had the highest deformation temperature among these, similar to that of icosahedral B(80) and B(100). The analysis of the electronic structure of B(18) showed that it attained this high stability owing to Jahn-Teller distortion.     

First principles study of the carbon-(silicon-) doped La13 clusters

The structural stability and physical properties have been studied for carbon-(silicon-) doped La(13) clusters using DMOL method based on density-functional theory. Doped La(13) clusters prefer to be icosahedron. Substitutional doping with a carbon or silicon impurity makes some clusters closed electronic shell, especially in icosahedral isomers. Substitutional doping of icosahedral La(13) clusters is found to be favorable at surface sites of clusters, especially for Si-doped La(13) cluster, which is very likely to be formed during the doping process. In addition, the structural distortions due to the doping are discussed.     

On the solid- and liquidlike nature of quantum clusters in their ground state

The ground state of pristine clusters of (paraH(2))(N) and (orthoD(2))(N) of size ranging from N=11 to 55 is examined by means of the variational path integral method. The chemical potential is calculated for two different interaction models and it is shown that the location of magic numbers indeed depends on the chosen interaction potential. Density profiles are calculated and reveal the difference between the two isotopes with regards to shell structure. The magnitude of relative pair distance and position fluctuations is used to asses the rigidity of these finite-size quantum systems. A comparison of generic and specific distance fluctuations as a function of cluster size is proposed as a probe of the appearance of rigidity in the clusters. It is found that smaller (paraH(2))(N) clusters are fluidlike and start to display increased rigidity for clusters of size N> or =26, whereas (orthoD(2))(N) clusters of N=13 and N> or =19 are rigid. Small clusters exhibit structures loosely based on an anti-Mackay icosahedral motif. An anti-Mackay to Mackay transition at N=41-42 is suggested.     

First-principles study of the electronic structures of icosahedral TiN (N=13,19,43,55) clusters

We have studied the electronic structures of icosahedral Ti(N) clusters (N=13, 19, 43, and 55) by using a real-space first-principles cluster method with generalized gradient approximation for exchange-correlation potential. The hexagonal close-packed and fcc close-packed clusters have been studied additionally for comparisons. It is found that the icosahedral structures are the most stable ones except for Ti(43), where fcc close-packed structure is favorable in energy. We present and discuss the variation of bond length, the features of the highest occupied molecular orbitals and the lowest unoccupied molecular orbital, the evolution of density of states, and the magnetic moment in detail. The results are in good agreement with the predictions from the collision-induced dissociation and size-selected anion photoelectron spectroscopy experiments.