Statistical measures and magic numbers in metal clusters

In this work, a shell model for metal clusters up to 220 valence electrons is used to obtain the fractional occupation probabilities of the electronic orbitals. Then, the calculation of a statistical measure of complexity and the Fisher-Shannon information is carried out. An increase of both magnitudes with the number of valence electrons is observed. The shell structure is reflected by the behavior of the statistical complexity. The magic numbers are indicated by the Fisher-Shannon information. So, as in the case of atomic nuclei, the study of statistical indicators also unveil the existence of magic numbers in metal clusters.     

Mapping the magic numbers in binary Lennard-Jones clusters

Using a global optimization approach that directly searches for the composition of greatest stability, we have been able to find the particularly stable structures for binary Lennard-Jones clusters with up to 100 atoms for a range of Lennard-Jones parameters. In particular, we have shown that just having atoms of different sizes leads to a remarkable stabilization of polytetrahedral structures, including both polyicosahedral clusters and at larger sizes structures with disclination lines.     

Different magic number behaviors in supported metal clusters

Two different magic number behaviors in supported metal clusters, which contain several to hundreds of atoms, are revealed on a series of fcc(001) metal surfaces based on the calculations with the tight-binding potential. The magic number sequence persists on some surfaces while gradually disappears on the others with the increasing cluster size. A theory is proposed to explain these behaviors in terms of atomic interactions. We find in surprise that the different magic number behaviors are triggered by the relatively weak adatom–adatom interactions between next nearest-neighbor (NNN) atoms, although the closed shell of the magic cluster is enhanced by nearest-neighbor interactions. For an attractive NNN interaction, the closed shell of the magic cluster is gradually destabilized and eventually broken, leading to the disappearance of the magic number sequence with increasing cluster size. For a repulsive one, the closed shell and magic number sequence persists. Besides, our theory also allows a good understanding of the equilibrium shape of Cu islands on the Cu(001) surface.     

Diffraction of neutral helium clusters: evidence for "magic numbers"

The size distributions of neutral 4He clusters in cryogenic jet beams, analyzed by diffraction from a 100 nm period transmission grating, reveal magic numbers at N=10-11, 14, 22, 26-27, and 44 atoms. Whereas magic numbers in nuclei and clusters are attributed to enhanced stabilities, this is not expected for quantum fluid He clusters on the basis of numerous calculations. These magic numbers occur at threshold sizes for which the quantized excitations calculated with the diffusion Monte Carlo method are stabilized, thereby providing the first experimental confirmation for the energy levels of 4He clusters.     

Geometric magic numbers of sodium clusters: Interpretation of the melting behaviour

Putative global minima of sodium clusters with up to 380 atoms have been located for two model interatomic potentials in order to identify the structures responsible for the size-dependence of the thermodynamic properties in experiments. Structures based upon the Mackay icosahedra predominate for both potentials, and the magic numbers for the Murrell-Mottram model show excellent agreement with the sizes at which maxima in the latent heat and entropy change at melting have been found in experiment. In particular, the magic numbers at sizes intermediate between the complete Mackay icosahedra are due to unusual twisted icosahedral structures.     

Stability and magic numbers of hetero-atomic clusters of simple metals

The main trends in the magic numbers observed for a class of simple-metal hetero-atomic clusters M_xN (M = Na or K; N = monovalent or divalent impurity; X = number of host atoms) is explained using an extension of the jellium model of clusters. The appearance of a “new” magic number, n = 10 (n = number of valence electrons), and the growing importance of n = 20 over n = 18, as Δ₊ increases (Δ₊ is the difference in the density of the jellium backgrounds of the two metals) are explained by an inversion of the order of the energy levels with respect to that of pure clusters.     

Tetrahedra packings — Observation of magic numbers for clusters from antimony-tetramers

Sb_n-clusters have been generated by condensation of tetramer units in LN₂-cooled He-gas. Electronic time-of-flight spectra show resolved mass peaks of clusters from tetramers up to n = 240 with pronounced size dependent structure. The observed magic numbers $\text{n}{}^1\text{= 8, 36, 52}\text{and}\text{84}$ are explained by a tetrahedra packing model.     

Structures of inert atomic clusters and their magic numbers of geometry

The optimal configurations of all atoms in atomic microclusters of an inert element have been obtained from their arbitrary positions and shapes by means of a Lennard-Jones interaction potential between atoms in the clusters, calculating the binding energies of the clusters with the numbers of atoms N ⩽ 14, which have shown the magic numbers of geometry in accordance with the experimental results. The structural pictures of such clusters are also presented.     

Equilibrium geometries,magic numbers and electronic structure of small carbon clusters

A carbon tetramer in the form of a distorted tetrahedron has been discovered to exist in a metastable spin-triplet excited state with an activation barrier of 0.5 eV. This state is 2.5 eV above the spin-singlet rhombus shaped ground state. These results are based on fully self-consistent all electron molecular orbital calculations. We also illustrate the processes leading to the carbon trimer as a “magic number”. Implications of the present discovery for future industrial applications are pointed out.     

Temperature dependence of the sputtering yield of surface metal clusters

The method of molecular dynamics has been used to investigate the influence of thermal oscillations of atoms on the sputtering of surface metal nanoclusters. The sputtering of a copper cluster consisting of 75 atoms from the (100) surface of a copper substrate by 200-eV argon ions for the target being at an equilibrium temperature of 0 and 300 K has been simulated. For each temperature, the sputtering yields have been predicted for both the substrate and the cluster and the polar and azimuthal angular distributions of sputtered atoms have been obtained. The procedure of simulation of two-object cluster-substrate systems at equilibrium temperatures other than 0 K is discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 20–25, July, 2007.     

Polarizability effect in metallic clusters

Langevin approach implemented in the inelastic cross-sections measured for the low-energy electrons colliding with metallic clusters points out that statical form of the polarizability dominate at energies less than 1.25 eV. The dynamical form comes into play at energies around 1.3 eV. The form of the polarizabilities indicates that polarizability of the metallic clusters is energy-dependent.     

Preferred clusters in metallic glasses

In this work,we present a feasible scheme based on framework of the sophisticated Voronoi tessellation method in order to evaluate what clusters should be preferred for building blocks in any given metallic glass,by analysing the fivefold-symmetry axes as well as the degree of structural regularity in various clusters.This scheme is well proved by a group of experiments and calculations,which may have broad implications for exploration of obtaining explicit and proper structural pictures,and understanding the structural origin of the unique properties and glass forming ability in these novel amorphous alloys.     

C/N/O centred metal clusters: super valence bonding and magic structure with 26 valence electrons

By using genetic algorithm combined with B3LYP and QCISD methods, this paper investigates the stabilities and electronic structures of Al₆OM_m (M?=?Na, K; m?=?2,4,6) and a few other Al_nXNa_m (X?=?C, N, O) clusters. The results show that the nonmetal doped metal clusters with 26 valence electrons have enhanced stabilities and large energy gaps. This paper extends the Jellium model for the application to the nonmetal doped metal clusters and explains the electronic origin of this strong magic structure. The nonmetal X atom is situated in the centre of the magic clusters. The 2s/2p orbitals of the central atom interact strongly with the superatomic 1S/1P orbitals and form bonding and antibonding orbitals. The bonding orbitals make the C/N/O atoms form s²p⁶ shell closure, and the antibonding orbitals make the metal moieties form closed 2S²2P⁶ shells. The 26 valence electrons form closed s²p⁶S²P⁶D¹⁰ shells, and this electronic configuration can be taken as the combination of the octet rule and 18-electron rule. The octahedral Al₆O^2? core is a superatomic anion with great stability, and it can be used as building blocks to assemble Zintl phase materials by interaction with alkali metals.     

Van der Waals coefficients for alkali metal clusters and their size dependence

In this paper we employ the hydrodynamic formulation of time-dependent density functional theory to obtain the van der Waals coefficientsC ₆ andC ₈ of alkali metal clusters of various sizes including very large clusters. Such calculations become computationally very demanding in the orbital-based Kohn-Sham formalism, but are quite simple in the hydrodynamic approach. We show that for interactions between the clusters of the same sizes,C ₆ andC ₈ scale as the sixth and the eighth power of the cluster radius, respectively, and approach their classically predicted values for the large size clusters.