Surveying a potential energy surface by eigenvector-following

We have developed a method to search potential energy surfaces which avoids some of the difficulties associated with trapping in local minima. Steps are directly taken between minima using eigenvector-following. Exploration of this space by low temperature Metropolis Monte Carlo is a useful global optimisation tool. This method successfully finds the lowest energy icosahedral minima of Lennard- Jones clusters from random starting configurations, but cannot find the global minimum in a reasonable time for difficult cases such as the 38-atom Lennard-Jones cluster where the face-centred-cubic truncated octahedron is lowest in energy. However, by performing searches at higher temperatures, we have found a pathway between the truncated octahedron and the lowest energy icosahedral minima. Such a pathway may be illustrative of some of the structural transformations that are observed for supported metal clusters by electron microscopy.     

SOME NOVEL Au-Ag SUPRACLUSTERS: THE SYNTHESES AND CHAR- ACTERIZATION OF 25-ATOM,37-ATOM,AND 38-ATOM CLUSTERS

<正> The reduction of mixtures of mononuclear Au(I)and Ag(I) phosphine halide complexes with sodium,boronhydride in different solvents gave rise to two types of 25-atom clusters,and 37-atom and 38-atom clusters. These clusters were formed by vertex-sharing of Au-centered icosahedral cluster units (Au7Ag6). The nuclearity of these clusters is given by (13n-e) , where n is the number of the cluster units and e is the edges of the polyhedron formed by centers of the icosahedral cluster units . The structures of these novel 25-atom,37-atom and 38-atom clusters can be described as two icosahedra sharing one vertex (2×13-1 = 25)or three icosahedra sharing three vertices in a triangle(3×13-3 = 36)plus capping atom(s).     

Adsorbate binding energies for ammonia on cobalt and nickel clusters

Equilibrium reactions of ammonia with cobalt and nickel clusters are analyzed to determine cluster-adsorbate binding energies. The temperature dependence of reaction equilibrium constantsK _eq are measured and ?ΔH ⁰ values obtained from plots of lnK _eq vs 1/T. We find that binding energies generally decrease with increasing ammonia coverage, and that for a given number of NH₃ molecules binding energies increase with increasing cluster size. The pattern of binding energies is found to be consistent with proposed geometrical structures for Co₁₉ and for clusters in the 55-atom size range. Cluster-ammonia binding energies are generally somewhat higher than for bulk metal surfaces, an expected result considering the character of the cluster surface and the nature of the NH₃-metal interaction.     

Electron affinity of Al13: a correlated electronic structure study

Neutral and anionic 13-atom aluminum clusters are studied with high-level, fully ab initio methods: second-order perturbation theory (MP2) and coupled cluster theory with singles, doubles, and perturbative triples (CCSD(T)). Energies and vibrational frequencies are reported for icosahedral and decahedral isomers, and are compared with density functional theory results. At the MP2 level of theory, with all of the basis sets employed, the icosahedral structure is energetically favored over the decahedral structure for both the neutral and anionic Al(13) clusters. Hessian calculations imply that only the icosahedral structures are potential energy minima. The CCSD(T)/aug-cc-pVTZ adiabatic electron affinity of Al(13) is found to be 3.57 eV, in excellent agreement with experiment.     

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.     

Global optimization and the energy landscapes of Dzugutov clusters

The global minima of clusters bound by a Dzugutov potential form non-compact polytetrahedral clusters mainly composed of interpenetrating and face-sharing 13-atom icosahedra. As the size increases, these icosahedral units first form linear arrays, then two-dimensional rings, then three-dimensional networks. Characterization of the energy landscapes of these clusters shows that they are particularly rough and generally exhibit a multiple-funnel topography. These results provide new insights into the structure and dynamics of bulk supercooled Dzugutov liquids and the form of the bulk phase diagram.     

Icosahedral to double-icosahedral shape transition of copper clusters

The lowest-energy isomers of Cu(N) clusters for N = 20-30 are identified using an unbiased search algorithm and density functional theory calculations. The low-energy structures over this size range are dominated by those based on a 13-atom icosahedral (I(h)) core and a 19-atom double icosahedron (DI(h)) core. A transition in the ground-state isomers from I(h)-based to DI(h)-based structures is predicted overt N = 21-23. We discuss this transition in the broader context of the growth pattern for Cu(N) over N = 2-30 that features regions of gradual evolution in which atoms successively add to the cluster surface, separated by sudden changes to a different structural organization and more compact shape. These transitions result from a competition between interatomic bonding energy and surface energy. The implications of this growth pattern for the further evolution of copper from microstructure to bulk are discussed.     

Pb12 2-: plumbaspherene

Although Si or Ge is not known to form empty cage clusters such as the fullerenes, we recently found a unique 12-atom icosahedral tin cluster, Sn12 2- (stannaspherene). Here we report photoelectron spectroscopy and theoretical evidence that Pb12 2- is also a highly stable icosahedral cage cluster and bonded by four delocalized radial pi bonds and nine delocalized on-sphere sigma bonds from the 6p orbitals of the Pb atoms. Following Sn12 2-, we coin a name, plumbaspherene, for the highly stable and nearly spherical Pb12 2- cluster, which is expected to be stable in solution and the solid state. Plumbaspherene has a diameter of approximately 6.3 A with an empty interior volume large enough to host most transition metal atoms, affording a new class of endohedral clusters.     

Nickel cluster structure determined from the adsorption of molecular nitrogen: Ni49-Ni71

The geometrical structures of nickel clusters in the size range from 49 to 71 atoms are studied by the chemical probe method. Saturation coverages of molecular nitrogen are determined for each cluster and from this data specific structures are proposed (except for Ni₆₆ and Ni₆₇). The results indicate that icosahedral packing is the dominant structural configuration throughout this size range, in agreement with earlier results based on water and ammonia adsorption. In addition, it seems that for clusters larger than Ni₅₄ the excessive strain in the surface of the 55-atom regular icosahedron often leads to rear-rangements of the surface atoms to relieve that strain. Ni₅₅, in particular, is found to have two isomers, the regular icosahedron and a structure in which a single apex atom is displaced to the center of an opposite face. Ni₇₁ occurs as a 55-atom regular icosahedron with a 16-atom cap. The results suggest that the atoms in the cap adopt an ABA configuration relative to the underlying icosahedron rather than an icosahedral arrangement. For some clusters the saturation with nitrogen causes a small degree of surface reconstruction that leads to the adsorption of additional nitrogen molecules.Work supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, under Contract No. W-31-109-Eng-38     

Heteroatomic deltahedral clusters: synthesis and structures of closo-[Bi3Ni(4)(CO)6]3-, closo-[Bi4Ni4(CO)6]2-, the open cluster [Bi3Ni6(CO)9]3-, and the intermetalloid closo-[Nix@[Bi6Ni6(CO)8)]4-

Reactions of ethylenediamine solutions of K4Bi5 with Ni(PPh3)2(CO)2 yielded four novel hetero-atomic Bi/Ni deltahedral clusters. Three of them, the 7-atom pentagonal bipyramidal [Bi3Ni4(CO)6]3-, the 8-atom dodecahedral [Bi4Ni4(CO)6]2-, and the Ni-centered or empty 12-atom icosahedral [Nix@[Bi6Ni6(CO)8]4-, are closo-species according to both electron count and shape. The centered icosahedral cluster resembles packing in intermetallic compounds and belongs to the emerging class of intermetalloid clusters. The shape of the fourth cluster, [Bi3Ni6(CO)9]3-, can be derived from the icosahedral Ni-centered [Ni@[Bi6Ni6(CO)8]4- by removal of three Bi- and one Ni-atoms of two neighboring triangular faces. The clusters were structurally characterized by single-crystal X-ray diffraction in compounds with potassium cations sequestered by 2,2,2-crypt or 18-crown-6 ether. They were also characterized in solution by electrospray mass spectrometry.     

Symmetry and ferromagnetic clusters

Isomers of pure Fe₁₃ and icosahedral Fe₁₂X clusters are studied using the all-electron linear-combination-of-Gaussian-type-orbital (LCGTO) local-density-functional (LDF) methods that allow the spin and geometry of the cluster to be determined self-consistently. The Fe₁₃ ground state is icosahedral. The icosahedral cluster also has the greatest magnetic moment because of increased symmetry-required orbital degeneracy for electrons of different spins. The central atom of the icosahedral iron cluster has been varied to optimize the spin of the cluster keeping the oribital contribution to the magnetic moment quenched. Varying the central atom under this constraint can alter the magnetic moment by more than 20%. Similar studies have begun on 55-atom icosahedral iron clusters.     

Structural transitions and melting in LJ(74-78) Lennard-Jones clusters from adaptive exchange Monte Carlo simulations

Phase changes in Lennard-Jones (LJ) clusters containing between 74 and 78 atoms are investigated by means of exchange Monte Carlo simulations in the canonical ensemble. The replica temperatures are self-adapted to facilitate the convergence. Although the 74- and 78-atom clusters have icosahedral global minima, the clusters with 75-77 atoms have decahedral ground-state structures and they undergo a structural transition to icosahedral minima before melting. The structural transitions are characterized by quenching and by looking at the Q4 and Q6 orientational bond order parameters. The transition temperatures are estimated to be 0.114, 0.065, and 0.074 reduced units for LJ75, LJ76, and LJ77, respectively. These values, their ordering and the associated latent heats are compared with other estimates based on the harmonic superposition approach.     

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.     

Dynamic factors in the reactions between the magic cluster Al(13)⁻ and HCl/HI

The icosahedral Al is a "magic" cluster with remarkable stability due to its high symmetry and closed valence shells. Its reactivity has provided a molecular model for understanding oxidation and dissolution processes in bulk metals. By first principles calculations, we demonstrated the importance of dynamic factors in the Al + HX reactions, with HX being either HCl or HI. There was a barrier to the dissociative adsorption of HX on the surface of an Al cluster, which involved charge transfer from Al. Furthermore, the H atom could be bonded to the cluster in multiple ways, similar to the top, bridge and hollow adsorption sites on Al(111) surface. With a large amount of energy (～40 kcal mol(-1)) deposited during the formation of Al(13)HX(-), the H atom could easily migrate among these sites, similar to the diffusion of hydrogen on metal surfaces. These factors were therefore important considerations in the formation and dissociation of Al(13)HX(-), and more generally in reactions involving other metal clusters.     

A genetic algorithm for the structural optimization of Morse clusters

This article describes the application of a genetic algorithm for the structural optimization of 19–50-atom clusters bound by medium-range and short-range Morse pair potentials. The GA is found to be efficient and reliable for finding the geometries corresponding to the previously published global minima [Doye JPK, Wales DJ (1997) J Chem Soc Faraday Trans 93: 4233]. Using the genetic algorithm, only a relatively small number of energy evaluations and minimizations are required to find the global minima. By contrast, a simple random search algorithm often cannot find the global minima of the larger clusters, even after many thousands of searches. Received: 27 October 1999 / Accepted: 7 December 1999 / Published online: 19 April 2000     

Melting phenomena: effect of composition for 55-atom Ag-Pd bimetallic clusters

Understanding the composition effect on the melting processes of bimetallic clusters is important for their applications. Here, we report the relationship between the melting point and the metal composition for the 55-atom icosahedral Ag-Pd bimetallic clusters by canonical Monte Carlo simulations, using the second-moment approximation of the tight-binding potentials (TB-SMA) for the metal-metal interactions. Abnormal melting phenomena for the systems of interest are found. Our simulation results reveal that the dependence of the melting point on the composition is not a monotonic change, but experiences three different stages. The melting temperatures of the Ag-Pd bimetallic clusters increase monotonically with the concentration of the Ag atoms first. Then, they reach a plateau presenting almost a constant value. Finally, they decrease sharply at a specific composition. The main reason for this change can be explained in terms of the relative stability of the Ag-Pd bimetallic clusters at different compositions. The results suggest that the more stable the cluster, the higher the melting point for the 55-atom icosahedral Ag-Pd bimetallic clusters at different compositions.     

Electronic Structure and Magnetic Properties of Rh13 Cluster with Three Possible Symmetries

1 INTRODUCTION Transition-metal (TM) clusters have been the sub- ject of widespread investigations in recent years be- cause of their promising practical applications in de- veloping new magnetic materials with large moment. As is well known that all 3d, 4d and 5d TM atoms have a finite magnetic moment due to the Hund’s- rule coupling in their unfilled d shells, but only 3d Fe, Co and Ni atoms are able to retain these mo- ments at a much reduced level in the bulk environ- ment. On the…     

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.     

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.     

Cluster size effects in vuv radiation spectra of argon and krypton supersonic jets

The relation between VUV radiation spectra of argon and krypton supersonic jets excited by an electron beam and the mean size of clusters in a jet is studied. For each atomic and molecular emission of argon in the 104–120 nm range and of krypton from 116 to 130 nm, the maximum intensity is found to occur when electrons collide with clusters of a definite mean size. It is found that self-localized excitons of atomic type or diatomic excimer molecular type with a small binding energy (several hundredths of an eV) are mainly formed in outer icosahedral shells of argon or krypton clusters and those of diatomic excimer molecular type with a large binding energy (several tenths of an eV) arise principally in inner shells.