Formation and stability of high-spin alkali clusters

Helium nanodroplet isolation has been applied to agglomerate alkali clusters at temperatures of 380 mK. The very weak binding to the surface of the droplets allows a selection of only weakly bound, high-spin states. Here we show that larger clusters of alkali atoms in high-spin states can be formed. The lack of strong bonds from pairing electrons makes these systems nonmetallic, van der Waals-like complexes of metal atoms. We find that sodium and potassium readily form such clusters containing up to 25 atoms. In contrast, this process is suppressed for rubidium and cesium. Apparently, for these heavy alkalis, larger high-spin aggregates are not stable and depolarize spontaneously upon cluster formation.     

Dipole moment of a small water cluster. The effect of size,temperature, and electric field

A molecular dynamics simulation of neutral clusters (H₂O) _{n ≤ 21} has been performed in the framework of the flexible polarized model. The formation and evolution of the dipole moment of the cluster have been investigated with a change in the size and temperature of the cluster and an external electric field. It has been shown that at low electric fields corresponding to the experiments on the deflection of clusters in the transverse inhomogeneous electrostatic field (Moro et al., 2006), the induced polarization of the cluster is determined by the orientational polarizability of the “rigid” cluster, rather than by the intracluster reorientation of the molecules. The calculated dependence of the effective polarizability of the cluster in the low field on n qualitatively reproduces the experimental results, but the calculated polarizability is numerically much higher than the experimental value by, e.g., a factor of 4 for n ≈ 20.     

Damping of the high-spin neutron hole orbitals of the207Pb

The neutron strength functions of the high-spin 1g _7/2 and 1h _11/2 hole states of the²⁰⁷Pb have been deduced within the formalism of the hole-core vibrational coupling scheme. The attenuation of the shell-model strengths of these two high-spin hole states have been compared with the distribution of the neutron strength functions of the discrete 1h _9/2 and 1i _13/2 states. The theoretical results have been discussed in the light of the recent experimental findings on the neutron hole orbitals of the²⁰⁷Pb nucleus. Side by the side the implication of the present research works has been reviewed on the basis of the other existing theoretical calculations on the high-spin neutron hole states of the²⁰⁷Pb.     

Charged clusters in liquid helium

The appropriateness of the experimental study of charged clusters in liquid helium has been supported. The interaction potential of negative ions (electron bubbles) with inert clusters formed by Ne, Ar, Kr, and Xe atoms or H₂ and N₂ molecules has been found. Small clusters levitate at a distance of 13–16 Å above the negative ion. The scalings laws for the properties of charged inert clusters have been discovered and grounded; the number of quantum levels and states of such clusters has been determined. The mobility measurement of charged clusters may provide a new technique of probing the properties of impurity nanoparticles in helium.     

On the origin of atomistic mechanism of rapid diffusion in alkali halide nanoclusters

To elucidate the atomistic diffusion mechanism responsible for the rapid diffusion in alkali halide nano particles, called Spontaneous Mixing, we execute molecular dynamics simulations with empirical models for KCl-KBr, NaCl-NaBr, RbCl-RbBr and KBr-KI. We successfully reproduce essential features of the rapid diffusion phenomenon. It is numerically confirmed that the rate of the diffusion clearly depends on the size and temperature of the clusters, which is consistent with experiments. A quite conspicuous feature is that the surface melting and collective motions of ions are inhibited in alkali halide clusters. This result indicates that the Surface Peeling Mechanism, which is responsible for the spontaneous alloying of binary metals, does not play a dominant role for the spontaneous mixing in alkali halide nanoclusters. Detailed analysis of atomic motion inside the clusters reveals that the Vacancy Mechanism is the most important mechanism for the rapid diffusion in alkali halide clusters. This is also confirmed by evaluation of the vacancy formation energy: the formation energy notably decreases with the cluster size, which makes vacancy formation easier and diffusion more rapid in small alkali halide clusters.     

Heteronuclear and homonuclear high-spin alkali trimers on helium nanodroplets

The electronic excitation spectra of all possible homo- and heteronuclear high-spin (quartet) trimers of K and Rb (KxRb(3-x), x=0...3) assembled on the surface of superfluid helium droplets, are measured in the spectral range from 10,600 to 17,400 cm(-1). A regular series of corresponding bands is observed, reflecting the similar electronic structure of all these trimers. For the assignment and separation of overlapping bands, we determine x directly, with mass-selected beam depletion, and indirectly with a V-type double-resonance scheme. The assignment is confirmed by high-level ab initio calculations of the electronic structure of the bare trimers. The level structure is rationalized in terms of harmonic-oscillator states of the three valence electrons in a quantum-dot-like confining potential. We predict that three should be a magic number for high-spin alkali clusters.     

Shape dependence of optical properties of sodium clusters

We develop an analytical approach to calculate the aspect ratios of free alkali metal clusters using measured surface plasmon frequencies. The method is based on the concept of small deviations from a spherical shape and can be applied to clusters with spheroidal, icosahedral and other shapes. Results of experimental data as well as of numerical calculations for the surface plasmon resonance frequencies in small spheroidal sodium clusters containing less than 50 atoms are reproduced accurately through a quite simple formula which links the aspect ratio of the cluster to the observable surface plasmon frequencies. The developed approach allows also to reveal the dependence of the dielectric function of alkali metal on the number of atoms in the cluster.     

Formation of an ensemble of nanoclusters under rapid deposition of atoms on a surface

The results of an experimental study of the formation of nanometer-size Au clusters on NaCl(100) and HOPG(0001) surfaces under pulsed laser deposition are presented. No clusters of small sizes (d ≤ 1 nm) have been found in the cluster size distribution. The distribution itself at d < 5 nm has the form of a percolation distribution. It has been established that the perimeter of clusters with sizes d < 5 nm has a fractal structure. The fractal dimension of clusters is different for NaCl(100) and HOPG(0001) surfaces with different symmetries; it decreases with increasing cluster size from D _f ≈ 1.2–1.4 at d ≈ 1.5 nm to D _f ≈ 1 at d ≈ 5 nm. A physical mechanism of nanocluster formation is suggested. Under pulsed laser deposition, the attainable densities of adatoms are close to the percolation threshold in the region of thermodynamically unstable states and many-particle correlation regions are formed in a spatially inhomogeneous adsorbate. Clusters are formed on the surface from many-particle correlation regions in several diffusion jumps. The suggested mechanism allows the fractal dimension of the clusters forming on surfaces with different symmetries, its dependence on cluster size, and the cluster size distribution functions to be calculated.     

Study of clusters of interest for liquid ionic alloys

Calculations are reported of the total energies and related quantities of sequences of small clusters of the form A_m Pb_n, where A is an alkali atom, n <6 and m < 9. The object of this study is to shed light on the stoichiometry and the possible formation of complexes in A-Pb liquid alloys. The calculations are performed using empty core pseudopotentials and the spherical average approximation for the cluster. The results are insensitive to the choice of alkali atom apart from a smooth trend with the progression from Li to Cs. The calculated total energies suggest that clusters with compositions A₄Pb and A₄Pb₄ are very stable against a change in the number of Pb or A atoms and support the possibility of these clusters forming in the liquid alloys. This stability arises from an electronic shell-closing effect.     

Formation of excited states in high-Z helium like systems

High-Z helium like ions represent the simplest multi electron systems for studying the interplay between electron–electron correlations, relativistic as well as quantum electrodynamical effects in strong fields. In contrast to the adjacent lithium like ions, however, almost no experimental information is available about the excited states in the high-Z domain of the helium sequence. Here, we present a theoretical analysis of the X ray production and decay dynamics of the excited states in helium like uranium. Emphasis has been paid particularly to the formation of the ³P₀ and ³P₂ levels by using electron capture into hydrogen like U⁹¹⁺. Both states are of interest for precise measurements on high-Z helium like ions in the future. This revised version was published online in August 2006 with corrections to the Cover Date.     

MINDO/3 calculation of the electronic structure of silicon nitride

The electronic structure of silicon nitride has been calculated by the semiempirical quantumchemical method MINDO/3 in the cluster approximation. The effect of cluster size and of boundary conditions on the partial density of one-electron states is analyzed. The results of the calculation are compared with experimental data on amorphous silicon nitride. The origin of a peak in the upper part of the valence band, which is seen in the SiL2,3 spectrum but not reproduced in the calculations is discussed. Fiz. Tverd. Tela (St. Petersburg) 39, 1342–1347 (August 1997)     

Structural,energetic and magnetic properties of small Ti<Subscript>n</Subscript> (n = 2–13) clusters: a density functional study

The structural, energetic, and magnetic properties of Ti _n clusters (n = 2 to 13 atoms) have been studied using Density Functional Theory (DFT), applying the pseudopotential LCAO method and the generalized gradient approximation for the exchange-correlation functional. The binding energy and the dissociation energy were calculated using the PBE and BLYP approximations for the exchange-correlation potential, in order to evaluate the performance of this functionals in predicting the energetic properties of small Ti clusters. The experimentally observed trend in the dissociation energy of Ti _n as a function of the cluster size is reproduced by both PBE and BLYP calculations. The effects of structural distortion on the magnetism of clusters were studied comparing the ground state structure against non-distorted clusters. It was found that the structural distortion has no effect on the total magnetic moment. For all studied clusters using the BLYP functional, with exception of Ti₆ and Ti₇, magnetism is predicted.     

FeBN(N≤6)团簇的结构与磁性

利用密度泛函理论中的广义梯度近似(GGA)，在考虑自旋多重度后，预测了FeB_N(N≤6)团簇的基态结构.结果表明基态团簇的自旋多重度分别为4，3，2，1，2和1，其中FeB₄团簇比较稳定.同时对FeB_N(N≤6)基态团簇的磁性做了系统地研究，发现除了FeB₅团簇外，FeB_N(N≤6)团簇的总磁矩和Fe原子磁矩随团簇尺寸的增大而减小. 关键词： N团簇')" href="#">FeB_N团簇 自旋多重度 磁矩     

Ab initio study of formation, migration and binding properties of helium-vacancy clusters in aluminum

Ab initio calculations based on density functional theory have been performed to study the dissolution and migration of helium, and the stability of small helium-vacancy clusters He_nV_m (n, m=0-4) in aluminum. The results indicate that the octahedral configuration is more stable than the tetrahedral. Interstitial helium atoms are predicted to have attractive interactions and jump between two octahedral sites via an intermediate tetrahedral site with low migration energy. The binding energies of an interstitial He atom and an isolated vacancy to a He_nV_m cluster are also obtained from the calculated formation energies of the clusters. We find that the di- and tri-vacancy clusters are not stable, but He atoms can increase the stability of vacancy clusters.     

The problem of the structure (state of helium) in small He<Subscript><Emphasis Type="Italic">N</Emphasis></Subscript>-CO clusters

A second-order perturbation theory, developed for calculating the energy levels of the He-CO binary complex, is applied to small He _N -CO clusters with N = 2−4, the helium atoms being considered as a single bound object. The interaction potential between the CO molecule and HeN is represented as a linear expansion in Legendre polynomials, in which the free rotation limit is chosen as the zero approximation and the angular dependence of the interaction is considered as a small perturbation. By fitting calculated rotational transitions to experimental values it was possible to determine the optimal parameters of the potential and to achieve good agreement (to within less than 1%) between calculated and experimental energy levels. As a result, the shape of the angular anisotropy of the interaction potential is obtained for various clusters. It turns out that the minimum of the potential energy is smoothly shifted from an angle between the axes of the CO molecule and the cluster of θ = 100° in He-CO to θ = 180° (the oxygen end) in He₃-CO and He₄-CO clusters. Under the assumption that the distribution of helium atoms with respect to the cluster axis is cylindrically symmetric, the structure of the cluster can be represented as a pyramid with the CO molecule at the vertex.     

Direct observation of the non-supported metal nanoparticle electron density of states by X-ray photoelectron spectroscopy

Synchrotron-based X-ray photoelectron spectroscopy on copper and silver cluster beams created by a magnetron-based gas-aggregation source has allowed mapping the electron density of states (DOS) of free metallic nanoparticles. The cluster DOS profiles obtained in the experiments strongly resemble the infinite solid DOS shapes, but the extracted cluster work-functions are lower than those for the bulk metal. The latter observation is explained by the initial negative charge on most of the clusters, created by the source.     

Growth of tellurium clusters in presence of metal impurities

The growth of small tellurium clusters in helium and the influence of a metal impurity (dysprosium atoms) on the cluster size distribution are investigated in a double laser vaporization source. A model describing the role of the carrier gas as collision partner is presented, emphasizing the crucial influence of the gas pressure on cluster formation. Changes in cluster reactivity due to dysprosium addition are discussed in terms of ionic structures Dy ^{3 +}(Te _N)^{3 -} containing a radical electron. Received 28 November 2000     

Hartree-Fock interaction between a helium atom and lithium metal: A test for the effective medium theory

The interaction of a helium atom with 6 and 10 atom clusters of lithium has been calculated using the unrestricted Hartree-Fock method, Hartree-Fock method with correlation corrections, and the effective medium theory. Inside the cluster the helium embedding energy is found to be proportional to the electron density of the cluster. The proportionality constant obtained by the Hartree-Fock method is in fair agreement with that calculated in the homogeneous electron gas using the local density approximation. Outside the cluster, in the region compatible with the helium diffraction experiments, the self-consistent calculations give much larger repulsion than the effective medium theory.     

Experimental and theoretical studies of interactions between Si<Subscript>7</Subscript> clusters

The possibility of using magic Si₇ clusters to form a cluster material was studied experimentally and theoretically. In experiments Si₇ clusters were deposited on carbon surfaces, and the electronic structure and chemical properties of the deposited clusters were measured using X-ray photoelectron spectroscopy (XPS). A non bulk-like electronic structure of Si₇ was found in the Si 2p core level spectra. Si₇ is suggested to form a more stable structure than the non-magic Si₈ cluster and Si atoms upon deposition on carbon surfaces. Theoretically it was possible to study the interaction between the clusters without the effect of a surface. Density functional theory (DFT) calculations of potential curves of two free Si₇ clusters approaching each other in various orientations hint at the formation of cluster materials rather than the fusion of clusters forming bulk-like structures.