Structural fluctuation of Au55 and Au147 clusters: Substrate effect

Structural fluctuation of Au₅₅ and Au₁₄₇ clusters with and without the substrate interaction are examined using model potentials and the transition state theory. It is shown that, for Au₅₅ both with and without the substrate interaction, the cuboctahedral structure (COCT) has a lifetime too short to be observed with an electron microscope while the icosahedral structure (IC) has a lifetime long enough. On the other hand, for Au₁₄₇ without the substrate interaction, both COCT and IC have lifetimes long enough but the lifetime of IC is too long for both of them to be observed in an observation period, say in several minutes. However, the lifetime is so much reduced by the substrate interaction that both the structures can be observed in an observation period. These results are compared with the experimental facts.     

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.     

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.     

Theoretical studies on carbon and silicon clusters: comparison of the structures and stabilities of neutral and ionic forms

Optimized molecular geometries and electronic structures are determined for neutral, positively charged, and negatively charged carbon and silicon clusters containing up to ten atoms. The effects of polarization functions and electron correlation are included in these claculations. Carbon clusters have linear or monocyclic ground state geometries whereas silicon clusters containing five or more atoms have three-dimensional ground state structures. Neutral C₄, C₆ and C₈ all have linear and monocyclic isomers of comparable stability whereas the ionic forms appear to be generally more stable as linear geometrical arrangements. In the case of neutral and positively charged carbon clusters, the odd-numbered clusters are significantly more stable than the adjacent even-numbered clusters whereas the opposite order of stability occurs for the negative ions. This is due to the large values of the electron affinities of the linear forms of even-numbered clusters such as C₄ and C₆. The relative stabilities of silicon clusters does not change with the charge state of the clusters.     

Stability and migration of large oxygen clusters in UO(2+x): density functional theory calculations

Using ab initio molecular dynamics simulations and nudged elastic band calculations we examine the finite temperature stability, transition pathways, and migration mechanisms of large oxygen clusters in UO(2+x). Here we specifically consider the recently proposed split quad-interstitial and cuboctahedral oxygen clusters. It is shown that isolated cuboctahedral clusters may transform into more stable configurations that are closely linked to the split quad-interstitial. The split quad-interstitial is stable with respect to single interstitials occupying the empty octahedral holes of the UO(2) lattice. In order to better understand discrepancies between theory and experiments, the simulated atomic pair distribution functions for the split quad-interstitial structures are analyzed with respect to the distribution function for U(4)O(9) previously obtained from neutron diffraction data. Our nudged elastic band calculations suggest that the split quad-interstitial may migrate by translating one of its constituent di-interstitial clusters via a barrier that is lower than the corresponding barrier for individual interstitials, but higher than the barrier for the most stable di-interstitial cluster.     

Structure and energetics of two- and three-dimensional neutral, cationic, and anionic gold clusters Au(5< or = n < or =9)Z (Z=0,+/-1)

Low-energy structures are found on the potential energy surfaces of the neutral, cationic, and anionic gold clusters Au(5< or = n < or =9)Z (Z=0,+/-1) and on the neutral potential energy surface of Au(9). These structures provide insights on the two to three dimensional (2D-->3D) transition in small neutral and charged gold clusters. It is demonstrated that the size threshold for the 2D-3D coexistence is lower for cationic than neutral gold clusters: the 2D-3D coexistence develops for Au(5) (+) and Au(7) (+) on the cationic potential energy surfaces while only for Au(9) on the neutral. Two metastable long-lived dianions of gold clusters are also reported.     

The determination of electrochemical reactivity and sustainability on individual hyper-stoichiometric UO2+x grains by Raman microspectroscopy and scanning electrochemical microscopy

Using scanning electrochemical microscopy and Raman microspectroscopy, we have successfully observed four distinct defect structures in hyper-stoichiometric UO_2+x and demonstrated the relationships between the defect structures and their ability to sustain cathodic reduction processes. When only random point defects are present, the initially inert surface is enhanced by oxidation of the UO_2+x. However, when the UO_2+x is already extensively oxidized and cuboctahedral clusters are present, further oxidation reduces the surface reactivity. At intermediate levels of stoichiometry corresponding to Willis clusters the surface appears to be reversibly oxidizable.     

Halo-like structures studied by atomic force microscopy

Nanometer-sized clusters of copper have been produced in a hollow cathode sputtering source and deposited on SiO_x. Halo-like structures consisting of micrometer sized protrusions in the silicon oxide surface surrounded by thin rings of smaller particles are observed. The area in between seems to be depleted of particles. We propose that the halo-like structures are a result of electrostatic forces acting between the incoming charged clusters and charged regions on the surface. A simple computer simulation supports this suggestion.     

Transition between icosahedral and cuboctahedral nanoclusters of lead

We have used ab initio methods to study the possible transition between icosahedral (ico) and cuboctahedral (fcc) structures in lead nanoclusters of sizes up to 309 atoms. Spontaneous fcc-to-ico transition in Pb(13) was observed in the ab initio molecular dynamics (MD) simulations at various temperatures. The transition path can be described predominantly by an angular variable s, which can, generally be applied to the similar transitions in clusters of larger sizes and was observed to follow the Mackay model. We have calculated the two-dimensional energy surface that describes the transition in Pb(13) and found a barrierless fcc-to-ico transition path, which is consistent with the observed spontaneous transition in the ab initio MD simulations. The atomic displacements in the transition were identified as one of the vibrational eigenmodes of these two Pb(13) clusters. For clusters of larger sizes (Pb(n), where n = 55, 147, and 309), the possible transitions following similar paths were determined not to be barrierless and the sizes of the barriers were determined by the ab initio elastic band method.     

Dehydrogenation of ammonia by early transition metals: formation of metal nitride clusters

The dehydrogenation of NH₃ by Ti, Zr, and Nb cations, produced in a laser-induced plasma reactor, is found to form both neutral and cationic clusters. Depending on the conditions, either the production of neutral metal nitride clusters is favored or, the formation of cationic `precursor' metal nitride clusters containing additional intact NH₃ is observed. The neutral clusters are formed when full dehydrogenation of the NH₃ is achieved, while the cationic precursor species are formed under conditions where a large fraction of the NH₃ remains intact. Metastable dissociation studies show that intact NH₃ molecules are bound to the developing transition metal nitride clusters.     

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.     

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.     

Unimolecular dissociation of trivalent metal cluster ions (Al n + , Ga n + , In n + ): evidence for a transition from covalent to metallic bonding

Unimolecular dissociation of aluminum, gallium and indium clusters is investigated. Small sizes dissociate into two channels: either the evaporation of a neutral or a charged monomer. Above a given size n _c, only dissociation of a neutral atom subsists. The evaporation of a charged monomer is characteristic of trivalent metal clusters and is consistent with the size evolution of the ionization potential towards the atomic value. The experiments are interpreted in the framework of the statistical R.R.K. model. For smaller sizes (n < n _c), as two evaporation processes are in competition, we have evaluated cluster relative dissociation energies and ionization potentials. The competition between the two evaporation channels is well mirrored by the evolution of the ionization potentials independently measured by near-threshold photoionization experiments. For gallium, our measurements have revealed that the covalent to metal transition occurs for larger sizes (n = 30–50 atoms) than for aluminum clusters.     

Structural transformations in silver nanoparticles

A molecular dynamics simulation was performed for silver clusters of 147, 309, and 561 atoms with the initial cuboctahedral habit in the temperature range 0–1000 K with an embedded atom potential for silver. Structural transitions of the silver clusters to complex twins (icosahedral habit) with coherent (111)/(111) boundaries over all edges of icosahedra were found, which started at temperatures of 50 K, 350 K, and 700 K, respectively. To analyze the structural transformations in nanoparticles, an algorithm is proposed based on a simplicial Delaunay decomposition (Delaunay triangulation). It was found that after the transition of silver nanoparticles to complex twins, the atomic motion becomes vibrational; the atoms vibrate around the sites that correspond to the vertices of the regular polyhedra. In the case of the 147-atom silver nanoparticle, the polyhedra are arranged in the following sequence, starting from the center of mass: icosahedron (12 atoms), icosododecahedron (30 atoms), icosahedron (12 atoms), dodecahedron (20 atoms), truncated icosahedron (60 atoms, isostructural with fullerene C₆₀), icosahedron (12 atoms), and one atom at the center of mass.     

Superconducting lead cluster films with particle size dependent reduction ofT c

To investigate films of metal clusters, a neutral lead cluster beam, generated by inert gas aggregation, is characterized via time-of-flight mass spectroscopy and subsequently used for growing a thin film (d=100 Å) on a cold sapphire substrate. In an annealing program the temperature dependence of the electrical resistance of the film is determined by the dc 4-probe technique. Directly after deposition a superconducting transition atT _c =5.6 K is observed which is shifted to higher temperatures with increasing annealing temperature (T _c =6.5 K after annealing at room temperature).     

A localized-orbital Hartree-Fock description of alkali metal clusters

We propose a new variational method, based on the ab initio Hartree-Fock methods, for the purpose of calculating efficiently both the equilibrium geometry and stability of alkali metal microclusters. Applying this method to neutral and cationic lithium clusters, up to Li₃₆, we find that the calculated stable cluster size corresponds to the observed magic numbers. Our results also indicate that both neutral and cationic clusters exhibit very similar dependence on the number of electrons both in stability and cluster shape, which is quite similar to the one obtained by the shell model. Furthermore, we find that lithium clusters larger than Li₂₆ have an ordered structure while clusters smaller than this do not. This is suggestive of the occurrence of a structural transition to a solid-like phase.     

Relativistic computational investigation: the geometries and electronic properties of TaSi(n)+ (n = 1-13, 16) clusters

The equilibrium geometries, stabilities, and electronic properties of the TaSi(n)+ (n = 1-13, 16) clusters are investigated systematically by using the relativistic density functional method with generalized gradient approximation. The small-sized TaSi(n)+ clusters with slight geometrical adjustments basically keep the frameworks that are analogous to the neutrals while the medium-sized charged clusters significantly deform the neutral geometries, which are confirmed by the calculated AIP and VIP values. Furthermore, the optimized geometries of the charged clusters agree with the experimental results of Hiura and co-workers (Hiura, H.; Miyazaki, T.; Kanayama, T. Phys. Rev. Lett. 2001, 86, 1733). The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gaps of the charged clusters are generally increased as the cluster size goes from n = 1 to 13; and the large HOMO-LUMO gaps of charged clusters resulting from the positive charge indicate that their chemical stabilities are stronger than their neutral counterparts, especially for n = 4, 6, and 7 clusters. Additionally, the contributions of the d orbitals of the Ta atom to the HOMO and LUMO reveal that the chemical activity of the d orbitals of the Ta atom decreases gradually as the number of silicon atoms increases. This interesting finding is in good agreement with the recent experimental results on the reactive activities of the H2O and transition-metal silicon clusters (Koyasu, K.; Akutsu, M.; Mitsui, M.; Nakajima, A. J. Am. Chem. Soc. 2005, 127, 4998). Generally, the positive charge significantly influences the electronic and geometric structures of the charged clusters. Finally, the most stable neutral and charged TaSi16 clusters are found to be fullerene-like structures and the HOMO-LUMO gap in charged form is detectable experimentally.     

Size effects in the solid phase transition of SF6 clusters

The structure of SF₆ clusters produced in a free jet expansion is studied by electron diffraction methods. A solid phase transition is known to occur when clusters are warmed up by changing several experimental conditions in the expansion of a Ne + SF₆ mixture. In the present study, the total stagnation pressure and the SF₆ mole fraction are varied in order to understand how these parameters influence the structural state of the clusters and further to observe the phase transition for different cluster sizes. When the stagnation pressurep ₀ is larger than about 10 bar, a given mole fraction results in clusters with identical structure and probably identical temperature. Whenp ₀ is decreased below 10 bar, identical structures are found for lower and lower mole fractions. This structural behaviour suggests that for small clusters, containing less than about 500 molecules, the transition steps occur at temperatures lower than those observed for larger clusters. The possibility of detecting a temperature variation in the diffraction patterns of small cubic clusters is discussed.     

Structural and Magnetic Properties of CoGen− (n=2–11) Clusters: Photoelectron Spectroscopy and Density Functional Calculations

A series of cobalt‐doped germanium clusters, CoGe_n^?/0 (n=2–11), are investigated by using anion photoelectron spectroscopy combined with density functional theory calculations. For both anionic and neutral CoGe_n (n=2–11) clusters, the critical size of the transition from exo‐ to endohedral structures is n=9. Natural population analysis shows that there is electron transfer from the Ge_n framework to the Co atom at n=7–11 for both anionic and neutral CoGe_n clusters. The magnetic moments of the anionic and neutral CoGe_n clusters decrease to the lowest values at n=10 and 11. The transfer of electrons from the Ge_n framework to the Co atom and the minimization of the magnetic moments are related to the evolution of CoGe_n structures from exo‐ to endohedral.     

Interplay between charge and vibrational delocalization in cationic helium clusters

The stable structures and low temperature thermodynamics of cationic helium clusters are investigated theoretically using a diatomics-in-molecules model for the potential energy surfaces and a computational framework in which both electronic and nuclear degrees of freedom are treated on a quantum mechanical footing. While the charge is generally carried by two atoms, vibrational delocalization significantly spreads out the charge over multiple isomers for clusters containing five or more helium atoms. Our calculations indicate that large clusters are essentially fluid with a well-defined solvation shell around the charged core.