A computational DFT analysis of OH chemisorption on catalytic Pt(111) nanoparticles

In this article, various energies and geometries of pure platinum nanoparticles and those of platinum nanoparticles with adsorbed OH were investigated. Fourteen different platinum clusters of 3–40 atoms were studied using spin-unrestricted density functional theory (DFT) with a double numerical plus polarization basis set. This range of sizes gave enough information for establishing the general trends that were the primary goal of the study. Three different shapes of platinum clusters were presented, and the effect of cluster size on binding energy, total energy, and HOMO–LUMO energy gap was investigated. Subsequently, same calculations were performed for those selected Pt clusters with OH adsorbate on the surface. The results show that the stability of both the pure clusters and the clusters with adsorbed OH molecule increases with an increase of cluster size. This fact indicates that direct influence of the size of Pt cluster on the reaction rate is possible, and the understanding of how cluster size would affect binding energy is important. As expected, the effect of cluster size on total energy of molecule was shown to be a linear function independent of cluster type. We also found that optimized (stable) Pt clusters were bigger in size than that of the initial clusters, or clusters with bulk geometry.     

Cluster generation from flowing plasma

The method of generation of cluster beams is analyzed in the regime when large clusters grow in a flow of a dense afterglow plasma and clusters are formed in a narrow region near the axis of this flow. This method gives a high intensity of the cluster beam in comparison with standard methods of cluster generation. Numerical parameters are evaluated for processes involving iridium clusters in an argon plasma.     

Cluster size and substrate temperature affecting thin film formation during copper cluster deposition on a Si （001） surface

The soft deposition of Cu clusters on a Si(001) surface was studied by molecular dynamics simulations.The embedded atom method,the Stillinger-Weber and the Lennar-Jones potentials were used to describe the interactions between the cluster atoms,between the substrate atoms,and between the cluster and the substrate atoms,respectively.The Cu13,Cu55,and Cu147 clusters were investigated at different substrate temperatures.We found that the substrate temperature had a significant effect on the Cu147 cluster.For smaller Cu13 and Cu55 clusters,the substrate temperature in the range of study appeared to have little effect on the mean center-of-mass height.The clusters showed better degrees of epitaxy at 800 K.With the same substrate temperature,the Cu55 cluster demonstrated the highest degree of epitaxy,followed by Cu147 and then Cu13 clusters.In addition,the Cu55 cluster showed the lowest mean center-of-mass height.These results suggested that the Cu55 cluster is a better choice for the thin-film formation among the clusters considered.Our studies may provide insight into the formation of desired Cu thin films on a Si substrate.     

Mesoscale and clusters of synchrony in networks of bursting neurons

We study the role of network architecture in the formation of synchronous clusters in synaptically coupled networks of bursting neurons. We give a simple combinatorial algorithm that finds the largest synchronous clusters from the network topology. We demonstrate that networks with a certain degree of internal symmetries are likely to have cluster decompositions with relatively large clusters, leading potentially to cluster synchronization at the mesoscale network level. We also address the asymptotic stability of cluster synchronization in excitatory networks of Hindmarsh-Rose bursting neurons and derive explicit thresholds for the coupling strength that guarantees stable cluster synchronization.     

An association theory for the formation of ion oligomers and its application to 1-1 electrolytes

A theory for modelling electrolyte solutions which includes the formation of ion clusters of different size has been developed in the framework of the primitive model. In primitive models the solvent is described as a dielectric continuum and the solvent–solute interactions are neglected. For the dielectric constant the value of the pure solvent has been used. The ion cluster distribution is calculated from the mass action law. The association constants are related to integrals over the cluster distribution functions which are calculated with the Kirkwood superposition approximation from low density pair distribution functions. The ion clusters are defined by a certain distance which rules if two ions belong to the same cluster. This so-called Bjerrum distance is chosen according to fundamental investigations of the structure of ion cluster. All ion clusters are modelled as hard spheres. For the free ions and charged clusters the mean spherical approximation expression for the Coulomb interaction is added. The co-volumes of the ion clusters have been taken from the investigation of the ion cluster structures, and are consistent with the definition of an ion cluster chosen here.     

Deformation of slow liquid and solid clusters upon deposition: A molecular-dynamics study of Al cluster impact on an Al surface

Using molecular-dynamics simulation, we investigate the self-deposition of Al_n clusters (n < 4000) on an Al substrate at velocities below the velocity of sound. Both cold crystalline and hot liquid clusters are studied. We examine the cluster deformation after impact on the surface, which we quantify by its height and base radius. At a given cluster velocity, the shape of deposited crystalline clusters is rather independent of the cluster size; only at small cluster sizes, n ? 40, the clusters are less strongly deformed. With increasing cluster size, liquid clusters are more strongly deformed than crystalline clusters. Faster projectiles become more strongly flattened by the deposition process. Even clusters depositing with vanishing velocity show a finite deformation, which is considerable for smaller clusters. At large cluster speed, clusters penetrate deeper into the (1 0 0) surface than into the (1 1 1) surface and also deform more strongly.     

Electron-beam-induced fluorescence of carbon dioxide clusters. II. Molecular beam with clusters

The fluorescence of CO₂ clusters excited by an electron beam in a molecular beam formed from a free jet expansion of carbon dioxide is investigated. Data on the fluorescence of the clusters are obtained by comparing the electron-beam-induced fluorescence with the signal appearing in an electronic-fluorescence detector as a result of reflection of the cluster beam from an obstacle placed after the electron beam, as well as with the intensity of the cluster beam. It is established that, unlike a jet expansion, for CO₂ clusters in a molecular beam the fluorescence yield from a cluster decreases significantly with increasing cluster size and is very small for clusters of large size. It is concluded on the basis of the results from an investigation of the fluorescence of CO₂ clusters that the electron-beam-induced fluorescence technique can be used for measurements in molecular beams with CO₂ clusters. Zh. Tekh. Fiz. 67, 63–71 (July 1997)     

Condensation of beryllium clusters

An original technique is proposed for describing the condensation of clusters in the situation where the interaction of a cluster with the surrounding clusters is very weak but cannot be ignored. It is demonstrated using beryllium clusters as an example that the proposed method is an efficient tool for calculating the energy band structure of clusters. It is shown that an increase in the number of beryllium atoms in a cluster leads to an increase in its stability.     

Overrun phenomenon and neutron yield in Coulomb explosion of deuterated alkane clusters driven by intense laser field

By using a simplified Coulomb explosion model, the laser-driven Coulomb explosion processes of three deuterated alkane clusters, i.e., deuterated methane(CD_4)_N, ethane(C_2D_6)_N and propane(C_3D_8)_N clusters are simulated numerically.The overrun phenomenon that the deuterons overtake the carbon ions inside the expanding clusters, as well as the dependence of the energetic deuterons and fusion neutron yield on cluster size, is discussed in detail. Researches show that the average kinetic energy of deuterons and neutron yield generated in the Coulomb explosion of(C_2D_6)_N cluster are higher than those of(CD_4)_N cluster with the same size, in qualitative agreement with the reported conclusions from the experiments of(C2 H6)_N and(CH4)_N clusters. It is indicated that(C_2D_6)_N clusters are superior to(CD_4)_N clusters as a target for the laser-induced nuclear fusion reaction to achieve a higher neutron yield. In addition, by comparing the relevant data of(C_3D_8)_N cluster with those of(C_2D_6)_N cluster with the same size, it is theoretically concluded that(C_3D_8)_N clusters with a larger competitive parameter might be a potential candidate for improving neutron generation. This will provide a theoretical basis for target selection in developing experimental schemes on laser-driven nuclear fusion in the future.     

Anions of xenon clusters bound by long-range electron correlations

In contrast with the single atom, atomic van der Waals clusters can form stable anions where the excess electron is bound due to long-range correlations with the electrons of the cluster. We report on extensive all-electron many-body ab initio studies on Xe clusters. Three-dimensional, planar, and linear structures of the clusters are investigated and compared. In particular, we find that the minimal number of Xe atoms in the cluster required to form a stable anion is 5 independently of the dimensionality of the cluster. We provide electron affinities for clusters made of 5, 6, and 7 atoms in all dimensions and find that the planar clusters form the most stable anions. The Dyson orbitals of the excess electrons are computed and analyzed.     

Quantum corrections to the semiclassical Hartree-Fock theory of a harmonically trapped Bose gas

An analytical approach is proposed to investigate the mechanism of implantation of size selected clusters into graphite, in order to explain the origin of linear variation of measured penetration depth with momentum or energy of incident cluster. In agreement with experimental observations, the cluster experiences, during its penetration, a force which consists in a component proportional with cluster velocity and a constant component. Expressions of these forces were obtained in the frame work of this approach. Regardless of whether the cluster breaks down into single atoms on the surface or not, there is evidence for existence of a wave generated under impact of cluster on the surface. Under the assumption that the cluster does not break up at impact on the surface, the penetration depth depends on the cross-section between the cluster and the surface, the cluster velocity and the properties of graphite. When the cluster fragments upon the impact on the surface, the generated wave is followed by a collective motion (??collective cascade??) of displaced atoms of target, including the constituents of cluster themselves, due to the transfer of cluster momentum. Thus, it is these displaced atoms which penetrate in the medium. During this collective penetration, some constituents of cluster can reach a certain depth which may be considered as the range of the deepest implanted constituents of cluster. It is shown that, the depth of penetration depends on the initial radius of cluster, its velocity and the properties of graphite. In addition, the depth varies non linearly with cluster velocity, for small clusters (n ?? 7), while for large clusters (n ?? 13), it varies (i) linearly with cluster velocity (or momentum) when the force proportional with speed of cluster is dominant. (ii) Linearly with the square of cluster velocity (or energy) if the constant force becomes dominant. It is shown that, a mechanism based on a collective motion of displaced atoms including the constituents of cluster themselves, induced by transfer of cluster momentum to the medium, permits to explain the behavior of measured depth of implanted clusters into graphite. This collective motion involves only one free parameter for all clusters of the same nature which are used as projectiles in the same experiment.     

Structure of unsupported bismuth nanoparticles

We present new results of electron diffraction experiments on unsupported nanometer-sized bismuth clusters. The high intensity cluster beam, necessary for electron diffraction, is provided by an inert-gas aggregation source. The cluster beam contains particles with average cluster sizes between 4.5 and 10 nm. When using Helium as a carrier gas we are able to observe a transition from crystalline clusters to a new structure, which we identify with that of amorphous or liquid clusters. Received 28 November 2000     

Rh_nBe(n=1～7)团簇结构和磁性的密度泛函研究

用密度泛函理论中的广义梯度近似方法研究了Rh_nBe(n=1～7)团簇的结构和磁性.结果表明:在Rh_n团簇上附加一个Be原子后,对Rh_n团簇的结构影响不大,与Be原子相配位的Rh原子间的键长发生了不同程度的增大.Rh_nBe与Rh_n团簇的稳定性变化趋势相一致,但Rh_nBe团簇更加稳定.Be原子均失去电子,磁矩相对较小.与Be原子相配位的Rh原子均是电子受体.团簇磁矩主要来自Rh原子的贡献;若Be原子呈正磁矩,则Rh_nBe团簇的总磁矩大于Rh_n团簇的磁矩,反之则小于Rh_n团簇的磁矩.     

RhnBe(n=1-7)团簇结构和磁性的密度泛函研究

用密度泛函理论中的广义梯度近似方法研究了RhnBe(n=1~7)团簇的结构和磁性。结果表明：在Rhn团簇上附加一个Be原子后,对Rhn团簇的结构影响不大,与Be原子相配位的Rh原子间的键长发生了不同程度的增大。RhnBe 与Rhn团簇的稳定性变化趋势相一致,但RhnBe团簇更加稳定。Be原子均失去电子,磁矩相对较小。与Be原子相配位的Rh原子均是电子受体。团簇磁矩主要来自Rh原子的贡献;若Be原子呈正磁矩,则RhnBe团簇的总磁矩大于Rhn团簇的磁矩,反之则小于Rhn团簇的磁矩。     

Neutralization of mass-selected cluster ions by charge transfer reactions

Mass-separated beams of clusters with a single, well-defined number of atoms or molecules are indispensable for studies of cluster properties. This paper presents a technique with the potential to generate such a beam which contains neutral clusters of one size only. For this purpose mass-selected cluster ions have been neutralized by charge transfer reactions in metal and sulphur vapors. Relative charge exchange cross sections were measured for different cluster sizes. They reveal pronounced variations of the electronic structure of these particles. Thus, the study of charge transfer processes is introduced as a method to probe the positions of electronic energy levels in neutral clusters.     

Localised spin modes of decorated magnetic clusters on a magnetic surface

A method for the calculation of the energies of spin modes of surface magnetic clusters on a magnetic surface, using broken translation symmetry in three dimensions (3D), is employed to determine the spin mode energies for a variety of planar clusters. The cluster is considered to be supported on a magnetically ordered substrate such that the localised spins of the cluster and the substrate interact via magnetic exchange. No electronic effects are considered. The analytical approach solves for the 3D evanescent crystal spin field in the bulk and the surface domains around the cluster. This spin field arises owing to the breakdown of magnetic translation symmetry caused by the surface cluster. The analytical approach can be applied to any cluster configuration, underlying the general character of the calculation. In particular, we consider here a 4-, 5-, and 9-atoms planar clusters supported on the surface of a ferromagnetic simple cubic lattice, the spin order being in the direction normal to surface boundary. The method is applied to calculate the spin mode energies of these planar clusters consisting of Gd atoms interacting via Anti-ferromagnetic exchange with an Fe(1 0 0) surface. These results are compared with the calculated energies of the spin modes of the free clusters, and also with those for the same planar clusters when the cluster-substrate exchange is considered hypothetically ferromagnetic.     

Cluster–surface interaction studied by time-resolved two-photon photoemission

n ⁺ clusters (n=2-9)deposited onto highly oriented pyrolytic graphite (HOPG) substrates at liquid nitrogen temperatures. The deposition was carried out with variable kinetic energies of the clusters. Clusters deposited with high kinetic energy (up to 60 eV/cluster) become fragmented upon impact. For low deposition energies (1–4 eV/cluster) the size dependence of the photoelectron spectra reveals a pronounced odd/even effect, which is well known for gas phase silver clusters. This indicates that the soft deposited clusters retain their size and identity on the sample. The phase of the odd/even effect suggests that transient negatively charged cluster ions serve as an intermediate step in the two-photon photoemission process. The lifetime of the anions rises with cluster size. This is attributed to an increasing electronic density of states for larger clusters. Received: 26 October 1998 / Revised version: 16 December 1998     

1-萘酚团簇的紫外光电离质谱研究

用飞行时间质谱仪和超声速脉冲分子束技术研究了紫外激光对1-萘酚(1HN)团簇的电离质谱.观测到(1HN)_n~+系列的团簇离子,且离子强度随团簇尺寸的增大而减小.电离激光的强度(在5μJ/pulse～100μJ/pulse范围内)对团簇离子强度的相对分布影响较小,说明软电离为产生团簇离子的主要过程,团簇离子的强度分布反映出电离前中性团簇的分布特征.增大电离区的进样气压可以产生更大尺寸的团簇离子,同时在(1HN)_n~+后面观测到新系列的团簇离子.这些新生离子与(H_2O)_m有关,考虑到1-萘酚团簇可以通过OH形成H键,推测该新生团簇离子通过团簇内的反应而产生.     

Late-stage coarsening of adlayers by dynamic cluster coalescence

We consider the late stages of adlayer coarsening when this process is dominated by cluster diffusion and coalescence. The growth rate of the average cluster size can be directly related to the cluster diffusion coefficient of individual clusters. The distribution of cluster sizes and the spatial correlations between clusters are examined as a function of coverage and cluster diffusion rate using Monte Carlo simulations. We also show how the Smoluchowski equation can give an approximate closed-form solution for the cluster size distribution during coarsening by coalescence. The coarsening of adlayers by cluster coalescence in a model that includes local inter-cluster interactions is also examined.