First principles study of the stability and electronic structure of the icosahedral La13, La(-1) (13), and La(+1) (13) clusters

The structural stability and electronic-structure of icosahedral La(13), La(-1) (13), and La(+1) (13) clusters have been studied by DMOL cluster method based on density-functional theory. The ground state of all-electron with relativity results is shown to be a distorted D(2h) icosahedron by the Jahn-Teller effect. However, the binding energies of D(3d) and D(5d) are very close to that of the D(2h) structure for La(13), La(-1) (13), and La(+1) (13) clusters. The effective core potential results show that the true ground state is D(5d) structure. The clusters have small magnetic moments and the symmetry of cluster is an important factor in determining the magnetic moments of the clusters. The effects of interatomic spacing and coordination on atomic magnetic moment are discussed. Further, 5d electrons dominate the hybrid orbitals below the Fermi level in the neutral cluster and contribute the main spin of clusters.     

Rotational diffusivity of fractal clusters

The rotational diffusion behavior of fractal clusters generated through an off-lattice cluster-cluster aggregation algorithm in both diffusion-limited cluster aggregation and reaction-limited cluster aggregation conditions is investigated. The extended Kirkwood-Riseman theory (Garcia de la Torre et al., Macromolecules, 1987) is used to estimate the cluster rotational diffusion tensor. The three eigenvalues of this tensor, which correspond to the three main rotational diffusivity values of the cluster, have been computed for each generated cluster. Once the eigenvalues have been sorted in ascending order, each of them has been averaged over several thousands of clusters. It is found that one of the three main average rotational diffusivities is substantially larger than the other two, indicating significant anisotropy of fractal clusters. Moreover, a rotational hydrodynamic radius Rh,r has been determined on the basis of the mean value of the three average rotational diffusivities, which is about 25% larger than the mean translational hydrodynamic radius Rh calculated through the same Kirkwood-Riseman theory. Finally, the obtained Rh,r values have been applied to interpret dynamic light scattering data from aggregating colloidal systems and to investigate the reliability of the assumption, Rh = Rh,r, typically made in the literature.     

Properties of small antiferromagnetic Ising clusters

Magnetic properties of small antiferromagnetic clusters have been studied by using the Ising model with nearest-neighbour interactions. The number of atoms in the clusters varied between 6 and 30. Several cluster geometries were analysed in detail with the result that there is no generic phase diagram. In an external magnetic field magnetisation can increase with increasing temperature in a considerable temperature range. Magnetisation was found to strongly depend on both the overall geometry of the cluster and on the symmetry of the underlaying lattice structure.     

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.     

Theoretical Study of Structural Symmetry in Ternary Clusters

The geometrical symmetry presents an intriguing theoretical problem in many kinds of clusters. The diversity of geometrical structures is associated with cluster sizes, different model functions and potential parameters, and ternary clusters are investigated to study the relationship between geometrical symmetry and homotopic symmetry. Ternary Lennard-Jones model potential is studied with different parameters, and the putative global minimum structures of A₁₃B₃₀C₁₂ clusters are optimized using an adaptive immune optimization algorithm. The results show that there mainly exist five geometrical symmetry structures, i.e., Mackay icosahedral, fivefold partial Mackay icosahedral, sixfold pancake, partial double Mackay icosahedral, and amorphous structures. Furthermore, the number of bonds is used to distinguish the geometrical symmetry. The importance of geometrical symmetry and homotopic symmetry determined by potential parameters is discussed. It was found that in the optimization it is more important to generate geometrical symmetry than to optimize homotopic symmetry.     

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.     

First-principles study on MRh12 (M = Rh, Fe, Co, AND Ni) clusters

In this paper, a first-principles study on the stability, electronic and magnetic properties of MRh₁₂ (M = Rh, Fe, Co and Ni) clusters is performed. By optimizing the geometrical structure, we find that MRh₁₂ clusters change from a perfect icosahedron to a distorted structure and have an obvious bond length contraction as compared with the corresponding bulk phase; FeRh₁₂, CoRh₁₂, and NiRh₁₂ clusters are more energetically stable than the RhRh₁₂ cluster. The effect of the impurity M on the density of states, valence band width, HOMO and LUMO for MRh₁₂ clusters is not significant, but when the central Rh atom is substituted with M, the magnetic moment of MRh₁₂ reduces dramatically. The Mulliken population analysis indicates that there are more charge transfers from other orbitals to Rh4d and M3d orbitals, and the spd hybrid effect in d orbitals of MRh₁₂ clusters is stronger than that in the RhRh₁₂ cluster. this situation means that the unpaired d electrons have more chance to be paired, and the magnetic moments of MRh₁₂ clusters can be reduced reasonably.     

Joint photoelectron and theoretical study of (Rh(m)Co(n))⁻ (m=1-5, n=1-2) cluster anions and their neutral counterparts

Anion photoelectron spectroscopic experiments and calculations based on density functional theory have been used to investigate and uniquely identify the structural, electronic, and magnetic properties of both neutral and anionic (Rh(m)Co(n)) and (Rh(m)Co(n))(-) (m=1-5, n=1-2) clusters, respectively. Negative ion photoelectron spectra are presented for electron binding energies up to 3.493 eV. The calculated electron affinities and vertical detachment energies are in good agreement with the measured values. Computational results for geometric structures and magnetic moments of both cluster anions and their neutrals are presented.     

Giant magnetic moment of the core-shell Co13@Mn20 clusters: first-principles calculations

The core-shell clusters Co(13)@TM(20) with TM = Mn, Fe, Co, and Ni are investigated within first-principles simulations in the framework of density-functional theory. Huge magnetic moments have been found in the Co(13)@TM(20) clusters especially for the Co(13)@Mn(20) cluster with a giant magnetic moment of 113 μ(B). The large magnetic moments are mainly due to the special core-shell structure and the weak interaction between the TM and other atoms.     

Density functional based calculations for Fen (n⩽32)

We investigate magnetic and structural properties of iron clusters up to Fe₃₂, well extending into the size range accessible by experiment. A density-functional based tight-binding scheme fully incorporating the effects of spin polarisation and charge transfer in a self-consistent manner has been used. The potential hypersurfaces have been scanned by an unconstrained search using a genetic algorithm. Results for smaller clusters up to Fe₁₇ are validated against more sophisticated density functional theory calculations. Our magnetic moment data show a strong change around Fe₁₃ being unique in this size range. For the larger cluster sizes a smooth decrease of the clusters average spin magnetic moments is found in good agreement with experimental data.     

Flattening of rhodium vertices in mixed rhodium-nickel carbonyl clusters: relationships to borane and zintl ion structures

The flattened deltahedra and related polyhedra found in hypoelectronic bare group 13 metal cluster anions are also found in some anionic mixed rhodium-nickel carbonyl clusters. In all cases the rhodium vertices rather than the nickel vertices are involved in the flattening process so that the rhodium vertices contribute four internal orbitals and the nickel vertices three internal orbitals to the skeletal bonding of the cluster. Thus, the 11-vertex cluster Rh(5)Ni(6)(CO)(21)(3-) has a D(3h) triflattened pentacapped trigonal prismatic structure similar to that found in the In(11)(7-) anion of the intermetallic K(8)In(11). Similarly the polyhedra in the 11-vertex cluster RhNi(10)(CO)(19)(3-) and the 9-vertex cluster Rh(3)Ni(6)(CO)(17)(3-) are both derived from a 10-vertex isocloso polyhedron by capping (for RhNi(10)(CO)(19)(3-)) or vertex removal (for Rh(3)Ni(6)(CO)(17)(3-)) followed by flattening all of the rhodium vertices. A D(3h) icosahedron with flattened rhodium vertices is found in the 12-vertex cluster Rh(3)Ni(9)(CO)(22)(3-).     

Oxidation state and symmetry of magnesia-supported Pd13O(x) nanocatalysts influence activation barriers of CO oxidation

Combining temperature-programmed reaction measurements, isotopic labeling experiments, and first-principles spin density functional theory, the dependence of the reaction temperature of catalyzed carbon monoxide oxidation on the oxidation state of Pd(13) clusters deposited on MgO surfaces grown on Mo(100) is explored. It is shown that molecular oxygen dissociates easily on the supported Pd(13) cluster, leading to facile partial oxidation to form Pd(13)O(4) clusters with C(4v) symmetry. Increasing the oxidation temperature to 370 K results in nonsymmetric Pd(13)O(6) clusters. The higher symmetry, partially oxidized cluster is characterized by a relatively high activation energy for catalyzed combustion of the first CO molecule via a reaction of an adsorbed CO molecule with one of the oxygen atoms of the Pd(13)O(4) cluster. Subsequent reactions on the resulting lower-symmetry Pd(13)O(x) (x < 4) clusters entail lower activation energies. The nonsymmetric Pd(13)O(6) clusters show lower temperature-catalyzed CO combustion, already starting at cryogenic temperature.     

Nitric oxide decomposition on small rhodium clusters, Rh(n)+/-

The decomposition of nitric oxide on small charged rhodium clusters Rh(n)(+/-) (6 < n < 30) has been investigated by Fourier transform ion cyclotron resonance mass spectrometry. For both cationic and anionic naked clusters, the rates of reaction with NO increase smoothly with cluster size in the range studied without the dramatic size-dependent fluctuations often associated with the reactions of transition-metal clusters. The cationic clusters react significantly faster than the anions and both exhibit rate constants exceeding collision rates calculated by average dipole orientation theory. Both the approximate magnitude and the trends in reactivity are modeled well by the surface charge capture model recently proposed by Kummerl?we and Beyer. All clusters studied here exhibit pseudo-first-order kinetics with no sign of biexponential kinetics often interpreted as evidence for multiple isomeric structures. Experiments involving prolonged exposure to NO have revealed interesting size-dependent trends in the mechanism and efficiency of NO decomposition: For most small clusters (n < 17), once two NO molecules are coadsorbed on a cluster, N(2) is evolved, generating the corresponding dioxide cluster. By analogy with experiments on extended surfaces, this observation is interpreted in terms of the dissociative adsorption of NO in the early stages of reaction, generating N atoms that are mobile on the surface of the cluster. For clusters where n < 13, this chemistry, which occurs independently of the cluster charge, repeats until a size-dependent, limiting oxygen coverage is achieved. Following this, NO is observed to adsorb on the oxide cluster without further N(2) evolution. For n = 14-16 no single end-point is observed and reaction products are based on a small range of oxide structures. By contrast, no evidence for N(2) production is observed for clusters n = 13 and n > 16, for which simple sequential NO adsorption dominates the chemistry. Interestingly, there is no evidence for the production of N(2)O or NO(2) on any of the clusters studied. A simple general mechanism is proposed that accounts for all observations. The detailed decomposition mechanisms for each cluster exhibit size (and, by implication, structure) dependent features with Rh(13)(+/-) particularly anomalous by comparison with neighboring clusters.     

Magic carbon clusters in the chemical vapor deposition growth of graphene

Ground-state structures of supported C clusters, C(N) (N = 16, ..., 26), on four selected transition metal surfaces [Rh(111), Ru(0001), Ni(111), and Cu(111)] are systematically explored by ab initio calculations. It is found that the core-shell structured C(21), which is a fraction of C(60) possessing three isolated pentagons and C(3v) symmetry, is a very stable magic cluster on all these metal surfaces. Comparison with experimental scanning tunneling microscopy images, dI/dV curves, and cluster heights proves that C(21) is the experimentally observed dominating C precursor in graphene chemical vapor deposition (CVD) growth. The exceptional stability of the C(21) cluster is attributed to its high symmetry, core-shell geometry, and strong binding between edge C atoms and the metal surfaces. Besides, the high barrier of two C(21) clusters' dimerization explains its temperature-dependent behavior in graphene CVD growth.     

Dramatic size effects and evidence of structural isomers in the reactions of rhodium clusters, Rhn+/-, with nitrous oxide

The reactions of gas phase rhodium clusters, Rhn+/- (n<30), with nitrous oxide, N2O, have been investigated under single collision conditions by Fourier transform ion cyclotron resonance mass spectrometry. The only significant reaction observed is the sequential generation of oxides. Absolute rate constants for the reactions of all clusters have been determined and, in the case of the cationic clusters especially, they exhibit large fluctuations as a function of cluster size with local minima observed for n=5, 19, 28. Striking similarities are observed with the variation in rate constants for these clusters in reactions with small hydrocarbons (C. Adlhart and E. Uggerud, J. Chem. Phys., 2005, 123, 214709). Corresponding size effects are also observed but are less marked in the reactions of the anionic clusters. The reactions of several clusters exhibit marked deviations from simple pseudo-first-order kinetics suggesting the presence of multiple isomeric forms: Rh11+, Rh12+ and Rh8- exhibit characteristic biexponential decays which are interpreted in terms of the existence of different structural forms of the cluster which have markedly different reactivity. By contrast, Rh6+, Rh7+ and Rh8+ show rates which apparently increase with time, probably due to collisional activation. Thermalisation of the clusters prior to reaction by exposure to pulses of argon results in changes to the kinetics of these anomalous systems which can be explained in terms of collision induced isomerisation.     

Synthesis and electrochemistry of new Rh-centered and conjuncto rhodium carbonyl clusters. X-ray structure of [NEt(4)](3)[Rh(15)(CO)(27)], [NEt(4)](3)[Rh(15)(CO)(25)(MeCN)(2)] x 2MeCN, and [NEt(4)](3)[Rh(17)(CO)(37)

A reinvestigation of the redox chemistry of [Rh7(CO)16]3- resulted in the finding of new alternative syntheses for a series of previously reported Rh-centered carbonyl clusters, i.e., [H4-nRh14(CO)25]n- (n = 3 and 4) and [Rh17(CO)30]3-, as well as new species such as a different isomer of [Rh15(CO)27]3-, the carbonyl-substituted [Rh15(CO)25(MeCN)2]3-, and the conjuncto [Rh17(CO)37]3- clusters. All of the above clusters are suggested to derive from oxidation of [Rh7(CO)16]3- with H+, arising from dissociation either of [M(H2O)n]2+ aquo complexes or nonoxidizing acids. The nature of the previously reported species has been confirmed by IR, electrospray ionization mass spectrometry, and complete X-ray diffraction studies. Only the molecular structures of the new clusters are reported in some details. The ready conversion of [Rh7(CO)16]3- in [HRh14(CO)25]3- upon oxidation has been confirmed by electrochemical techniques. In addition, electrochemical studies point out that the close-packed [H3Rh13(CO)24]2- dianion undergoes a reversible monoelectronic reduction followed by an irreversible reduction. The irreversibility of the second reduction is probably a consequence of H2 elimination from a purported [H3Rh13(CO)24]4- species. Conversely, the body-centered-cubic [HRh14(CO)25]3- and [Rh15(CO)27]3- trianions display several well-defined redox changes with features of electrochemical reversibility, even at low scan rate. The major conclusion of this work is that mild experimental conditions and a tailored oxidizing reagent may enable more selective conversion of [Rh7(CO)16]3- into a higher-nuclearity rhodium carbonyl cluster. It is also shown that isonuclear Rh clusters may display isomeric metal frameworks [i.e., [Rh15(CO)27]3-], as well as almost identical metal frames stabilized by a different number of carbonyl groups [i.e., [Rh15(CO)27]3- and [Rh15(CO)30]3-]. Other isonuclear Rh clusters stabilized by a different number of CO ligands more expectedly exhibit completely different metal geometries [i.e., [Rh17(CO)30]3- and [Rh17(CO)37]3-]. The first pair of isonuclear and isoskeletal clusters is particularly astonishing in that [Rh15(CO)30]3- features six valence electrons more than [Rh15(CO)27]3-. Finally, the electrochemical studies seem to suggest that interstitial Rh atoms are less effective than Ni and Pt interstitial atoms in promoting redox properties and inducing molecular capacitor behavior in carbonyl clusters.     

钯团簇形成和增长机理的Monte Carlo研究

利用Monte Carlo（MC）方法和Lennard-Jones加Axilord-Teller （LJ＋AT）势能函数,研究了气相中钯团簇的形成过程和增长机理.发现具有二十面体结构的Pd13团簇可以在气相中自发形成,较大的团簇通过在Pd13二十面体结构的表面添加原子组成四面体的方式形成.通过分析团簇结构和能量之间的关系,发现除了Pd13和Pd55以外,Pd19和Pd39团簇也具有五次对称性,都是比较稳定的结构.     

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.     

Size and structure dependence of carbon monoxide chemisorption on cobalt clusters

We have carried out a series of ab initio calculations to investigate changes in the structural and magnetic properties of pristine cobalt clusters upon CO chemisorption. Our results show that binding energies of CO to 13-55 atom (0.5-1.5 nm) cobalt nanoparticles and preferred chemisorption sites depend on the cluster structure (whether fcc or icosahedral), size, and surface coverage. In addition, we find a strong influence of CO on the magnetism of the cluster, leading to magnetic moments smaller than in the bulk, at variance with pristine clusters which have magnetic moments larger than the bulk. Our findings suggest important changes in catalytic properties of cobalt at the nanoscale. Our theory suggests that at the nanoscale cluster size and surface coverage might control catalysis.