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Showing papers on "Cluster (physics) published in 1988"


Proceedings ArticleDOI
01 Jan 1988
TL;DR: This work gives a polynomial time approximation scheme that estimates the optimal number of clusters under the second measure of cluster size within factors arbitrarily close to 1 for a fixed cluster size.
Abstract: In a clustering problem, the aim is to partition a given set of n points in d-dimensional space into k groups, called clusters, so that points within each cluster are near each other. Two objective functions frequently used to measure the performance of a clustering algorithm are, for any L4 metric, (a) the maximum distance between pairs of points in the same cluster, and (b) the maximum distance between points in each cluster and a chosen cluster center; we refer to either measure as the cluster size.We show that one cannot approximate the optimal cluster size for a fixed number of clusters within a factor close to 2 in polynomial time, for two or more dimensions, unless P=NP. We also present an algorithm that achieves this factor of 2 in time O(n log k), and show that this running time is optimal in the algebraic decision tree model. For a fixed cluster size, on the other hand, we give a polynomial time approximation scheme that estimates the optimal number of clusters under the second measure of cluster size within factors arbitrarily close to 1. Our approach is extended to provide approximation algorithms for the restricted centers, suppliers, and weighted suppliers problems that run in optimal O(n log k) time and achieve optimal or nearly optimal approximation bounds.

485 citations


Journal ArticleDOI
TL;DR: In this paper, the laser-induced fragmentation behavior of positive carbon cluster ions was investigated by tandem time-of-flight techniques for the jet-cooled clusters up to 80 atoms in size.
Abstract: The laser-induced fragmentation behavior of positive carbon cluster ions has been investigated by tandem time-of-flight techniques for the jet-cooled clusters up to 80 atoms in size. Two distinct photophysical regimes were found. The first applies to clusters with 34 atoms or more, all of which dissociate to produce even numbered fragments. Large even clusters fragment by the loss of the high energy species C2, odd ones lose a C atom. The second regime applies to clusters composed of 31 or less atoms, all of which fragment by the loss of C3. These two regimes are sharply separated by C + 32 which fragments to produce small cluster ions in the 10–19 atom size range. Fragmentation of the large clusters occurs on a microsecond or faster time scale only at very high levels of excitation (>12.8 eV). These photophysical results are interpreted as consequences of the large even clusters having edgeless, spheroidal cage structures while the small ones have linear chain or ring structures.

437 citations


Journal ArticleDOI
TL;DR: In this article, the Hartree-Fock (HF) level of theory with the polarized 6−31G* basis set was used to study the structures and energies of intermediate-sized silicon clusters.
Abstract: Ab initio calculations have been performed to study the structures and energies of intermediate‐sized silicon clusters (Sin, n=7–10). All geometries have been optimized at the Hartree–Fock (HF) level of theory with the polarized 6‐31G* basis set. The harmonic vibrational frequencies have been evaluated at the HF/6‐31G* level of theory. Electron correlation effects have been included by means of fourth order Mo/ller–Plesset perturbation theory. The most stable structure for Si7 is a pentagonal bipyramid and the lowest energy calculated structures for Si8–Si10 correspond to capped octahedral or prismatic geometrical arrangements. The evolution of the cluster geometries with increasing size is discussed. Clusters containing four, six, seven, and ten atoms have been identified as ‘‘magic numbers’’ for small silicon clusters, both theoretically and experimentally. The hybridization and bonding in small silicon clusters is discussed. Our results are used to interpret the recent photoelectron spectra of negative...

374 citations


Journal ArticleDOI
TL;DR: In this article, electron attachment and localization in small water clusters (H2O)n (n=8−128) were studied using path-integral molecular dynamics simulations and the electron-water molecule interaction was described via a pseudopotential which includes Coulomb, polarization, exclusion and exchange contributions.
Abstract: Electron attachment and localization in small water clusters (H2O)n (n=8–128) is studied using path‐integral molecular dynamics simulations. The electron‐water molecule interaction is described via a pseudopotential which includes Coulomb, polarization, exclusion and exchange contributions. Different electron localization modes are found depending on cluster size. For small and intermediate size clusters (n=8–32), the energetically favored localization mode involves a surface state and the calculated excess electron binding energies are in agreement with experimentally measured values. In larger clusters, n=64, 128, internal localization (solvation) is energetically favored. In both cases the localization of the excess electron is accompanied by large cluster molecular reorganization. The cluster size dependence of the localization mode, the energetics, structure, and excess electron distributions in the negative molecular anions (H2O)−n, and the dependence on temperature are explored.

236 citations


Journal ArticleDOI
TL;DR: In this article, the authors examined the bonding properties of small boron cluster cations (BZTl3+) by measurement of appearance potentials and fragmentation patterns for collision-induced dissociation (CID) with Xe.
Abstract: Bonding in small boron cluster cations (BZTl3+) is examined by measurement of appearance potentials and fragmentation patterns for collision-induced dissociation (CID) with Xe. Cluster stabilities are generally found to increase with increasing cluster size; however, there are large fluctuations from the overall trend. The lowest energy fragmentation channel for all size cluster ions is loss of a single atom. Clusters smaller than six atoms preferentially lose B', while for the larger clusters the charge remains on the BW1+ fragment. The results are used to estimate cluster ionization potentials and geometries. Comparison of measured stabilities with "magic" numbers in the cluster ion size distribution and with total CID cross sections shows that neither is a reliable indicator of stability. We also report on ab initio calculations for both neutral and ionic BI4. The results include cluster geometries, ionization potentials, charge distributions, dissociation energies, and bonding character. The results for IPS, geometries, and De)s are compared with experiment.

235 citations


Journal ArticleDOI
G. K. Wertheim1, S. B. DiCenzo1
TL;DR: In this article, the coverage dependence of the core-electron photoemission intensity and binding energy for simple, noble, and transition-metal clusters supported on amorphous carbon was examined.
Abstract: Examination of the coverage dependence of the core-electron photoemission intensity and binding energy for simple, noble, and transition-metal clusters supported on amorphous carbon reveals three distinct, cluster-size-dependent regimes. In very small clusters, containing fewer than \ensuremath{\sim}30 atoms, the final-state hole is screened by the polarization of the neighboring atoms, and the binding energy depends only weakly on cluster size. In larger, metallic clusters the hole is screened by conduction electrons, with the missing charge appearing at the surface of the cluster. In this regime, the core-electron binding-energy shifts vary inversely with the one-third power of the coverage, confirming that they are dominated by the Coulomb energy of the charged final-state cluster. In the third regime the clusters begin to coalesce, forming a contiguous metallic layer in which the binding energy rapidly approaches that of the bulk metal.

207 citations


Journal ArticleDOI
TL;DR: In this article, a modified cluster analysis method was developed to identify spatial patterns of planetary flow regimes, and to study transitions between them, applied first to a simple deterministic model and second to Northern Hemisphere (NH) 500 mb data.
Abstract: A modified cluster analysis method was developed to identify spatial patterns of planetary flow regimes, and to study transitions between them. This method was applied first to a simple deterministic model and second to Northern Hemisphere (NH) 500 mb data. The dynamical model is governed by the fully-nonlinear, equivalent-barotropic vorticity equation on the sphere. Clusters of point in the model's phase space are associated with either a few persistent or with many transient events. Two stationary clusters have patterns similar to unstable stationary model solutions, zonal, or blocked. Transient clusters of wave trains serve as way stations between the stationary ones. For the NH data, cluster analysis was performed in the subspace of the first seven empirical orthogonal functions (EOFs). Stationary clusters are found in the low-frequency band of more than 10 days, and transient clusters in the bandpass frequency window between 2.5 and 6 days. In the low-frequency band three pairs of clusters determine, respectively, EOFs 1, 2, and 3. They exhibit well-known regional features, such as blocking, the Pacific/North American (PNA) pattern and wave trains. Both model and low-pass data show strong bimodality. Clusters in the bandpass window show wave-train patterns in the two jet exit regions. They are related, as in the model, to transitions between stationary clusters.

205 citations


Journal ArticleDOI
TL;DR: In this article, a simple and efficient algorithm for sampling physical cluster statistics in Monte Carlo simulations of continuum morphology models is described, which produces a variety of information including the pair connectedness function, cluster size distribution, and mean cluster size.
Abstract: We describe a simple and efficient algorithm for sampling physical cluster statistics in Monte Carlo simulations of continuum morphology models. The algorithm produces a variety of information including the pair connectedness function, cluster size distribution, and mean cluster size. The approach can be applied to any system, given a definition of a physical cluster for that system. Results are presented for two types of models commonly used in studies of percolation phenomena; randomly centered spheres and the concentric shell (extended sphere) model. The simulation results are used to assess the accuracy of the predictions of the Percus–Yevick closure of the Ornstein–Zernike equation for the pair connectedness function.

176 citations


Journal ArticleDOI
TL;DR: In this article, reaction rates and saturation values were determined for H2 dissociative chemisorption on positive niobium cluster ions in an FT-ICR apparatus.
Abstract: Reaction rates and saturation values were determined for H2 dissociative chemisorption on positive niobium cluster ions in an FT‐ICR apparatus. Clusters with 8,10,12, and 16 atoms were found to be particularly unreactive, in remarkable agreement with the reactivity patterns observed previously for neutral niobium clusters. Saturation coverage for most clusters was found to occur near a hydrogen/niobium ratio of 1.3, although some clusters (8–12,16, and 19) reached effectively inert compositions at considerably lower coverages. Several examples were found of clusters having two isomeric forms with different reactivities. One form of Nb+19 was found to readily react with H2, whereas a second form representing one‐third of the original sample of 19 atom clusters was completely inert to H2 chemisorption under the same FT‐ICR conditions. The geometrical shape of these niobium clusters must therefore have a critical effect on reactivity.

175 citations


Journal ArticleDOI
TL;DR: In this paper, a new rule for calculating chemisorption energies using the cluster model was proposed, based on the realization that relatively large clusters (50 atoms and more) often need to be prepared for bonding by making an excitation to a proper bonding state (such a state will always be easily accessible in an infinite cluster).

175 citations



Journal ArticleDOI
TL;DR: Observation d'un transition de phase solide-fluide d'agregats d'argon en fonction de la temperature, par mesure du profil de raie spectrale d'une molecule de benzene dopee dans l'argon.
Abstract: Larger argon atomic clusters undergo a size-specific transition from rigid to fluid forms as the cluster temperature is varied The observed nature of this phase change, detected by measurement of the spectral line shape of a benzene dopant molecule, favors the phase-coexistence model of the cluster melting transition

Journal ArticleDOI
TL;DR: In this article, the authors introduced a two-point cluster function C2(r1,r2) which reflects information about clustering in general continuum-percolation models.
Abstract: We introduce a two‐point cluster function C2(r1,r2) which reflects information about clustering in general continuum–percolation models. Specifically, for any two‐phase disordered medium, C2(r1,r2) gives the probability of finding both points r1 and r2 in the same cluster of one of the phases. For distributions of identical inclusions whose coordiantes are fully specified by center‐of‐mass positions (e.g., disks, spheres, oriented squares, cubes, ellipses, or ellipsoids, etc.), we obtain a series representation of C2 which enables one to compute the two‐point cluster function. Some general asymptotic properties of C2 for such models are discussed. The two‐point cluster function is then computed for the adhesive‐sphere model of Baxter. The two‐point cluster function for arbitrary media provides a better signature of the microstructure than does a commonly employed two‐point correlation function defined in the text.

Journal ArticleDOI
TL;DR: In this article, structural changes in iron clusters in the Fe13 to Fe23 size range were found for several chemical properties, including reactivity with hydrogen and binding energies of ammonia and water.
Abstract: Evidence is presented for structural changes in iron clusters in the Fe13 to Fe23 size range. Abrupt changes with cluster size are found for several chemical properties, including reactivity with hydrogen and binding energies of ammonia and water. These changes often come at the same cluster sizes, pointing to a common origin—fundamental changes in the structure of the bare iron clusters. In addition, changes in structure as a consequence of adsorbate binding are suggested. The experimental observations leading to these conclusions are detailed, and possible structures for clusters in this size range are proposed.

Journal ArticleDOI
TL;DR: In this paper, the reaction of transition metal halides with silylated compounds such as E(SiMe3)2 (E = S, Se, Te) and E′R(SiME3) 2 (R = Ph, Me, Et; E′ = P, As, Sb).
Abstract: In both physics and chemistry, increased attention is being paid to metal clusters. One reason for this attitude is furnished by the surprising results that have been obtained from studies of the preparation, structural characterization and physical and chemical properties of the clusters. Whereas investigations of cluster reactivity are at present generally limited to three- or four-membered clusters, successful syntheses of clusters with many more metal atoms have recently been designed. These substances occupy an intermediate position between solid state chemistry and the chemistry of metal complexes. This review presents a versatile method for synthesizing metal clusters: the reaction of complexes of transition metal halides with silylated compounds such as E(SiMe3)2 (E = S, Se, Te) and E′R(SiMe3)2 (R = Ph, Me, Et; E′ = P, As, Sb). Although some of the compounds thus formed have already been prepared by other routes, the method affords ready access to both small and large transition metal clusters with unusual structures and valence electron concentrations; a variety of reactions in the ligand sphere are also possible.

Journal ArticleDOI
TL;DR: In this article, the effects of ionizing laser intensity and frequency, vaporization and condensation conditions, and graphite substrate composition (pure and metal loaded) on the carbon cluster ion signals were investigated.
Abstract: We have performed a series of experiments in which the conditions necessary for synthesis and detection of carbon clusters have been systematically investigated. The effects of ionizing laser intensity and frequency, vaporization and condensation conditions, and graphite substrate composition (pure and metal loaded) on the carbon cluster ion signals show that ‘‘special’’ conditions are needed to observe locally enhanced ion signals on particular clusters (e.g., a large C+60 signal). We present evidence for two sources of carbon clusters, one source which produces mostly smaller (n 32) carbon clusters. In addition we find that several, not just one, metal atom can be attached to C60. Lastly we propose that large variations in ion signals may be explained in terms of the electronic properties of the carbon clusters.

Journal ArticleDOI
TL;DR: In this article, negative aluminum clusters in the size range of 3-32 atoms were used for ultraviolet photoelectron spectroscopy (UPS) and the electron affinities (EA) of the neutral clusters were peaked at cluster sizes of 6, 13, 19, and 23.

Journal ArticleDOI
TL;DR: In this paper, mass analysis of the ionic photofragments shows that in some cases the photodissociated Br−2 has recombined and in other cases a Br atom has escaped from the cluster.
Abstract: Photofragmentation studies of mass selected Br−2⋅(CO2)n, n≤24, cluster ions are presented. The heterogeneous cluster ions are synthesized in a supersonic expansion crossed with an electron beam. These ionic clusters are mass analyzed in a time‐of‐flight mass spectrometer prior to photodissociation of the Br−2 absorber in the cluster. Mass analysis of the ionic photofragments shows that in some cases the photodissociated Br−2 has recombined and in other cases a Br atom has escaped from the cluster. The branching ratio for recombination depends on both the size of the initial cluster ion and the photodissociation wavelength. The photofragmentation data are consistent with a recombination mechanism dominated by attractive forces in the smaller clusters and repulsive interactions in the larger clusters.

Journal ArticleDOI
01 Jul 1988-Science
TL;DR: Results serve to elucidate at the molecular level the course of change of a system to be followed from the gas to the condensed state, thereby enabling a spanning of the states of matter.
Abstract: Gas-phase clusters, which are weakly bound aggregates comprised of either atoms or molecules, often display properties that lie between those of the gaseous and condensed states. Interesting questions arise concerning how large a cluster must be before it will display bulk properties. Currently there is extensive research activity directed toward studies of their formation and varying properties and reactivity as a function of the degree of aggregation. Results serve to elucidate at the molecular level the course of change of a system to be followed from the gas to the condensed state, thereby enabling a spanning of the states of matter.


Book
23 May 1988
TL;DR: The literature concerning cluster complexes which contain both main group element and transition metal vertices is reviewed in this paper, with a focus on structural properties and relationships between mixed clusters and Zintl ions.
Abstract: The literature concerning cluster complexes which contain both main group element and transition metal vertices is reviewed. Synthetic methods and general reactivity patterns are summarized. Emphasis is placed on structural. Comparisons of cluster geometries for a wide variety of element combinations. Relationships between these mixed clusters and the main group element clusters known as Zintl ions are discussed.

Journal ArticleDOI
TL;DR: In this article, the authors proposed to remove the ligand sphere together with the outer shell of metal atoms to generate the inner naked M13 nuclei, which are metastable and build up novel structures.

Journal ArticleDOI
TL;DR: In this article, the authors presented images that show columns or layers of cluster molecules with a distance of 2.1± 0.1 nm, including the ligand shell and of the naked cluster.

Book
01 Jan 1988
TL;DR: The ionized cluster beam (ICB) deposition and epitaxial process is an ion-assisted technique by which high quality films of metals, dielectrics and active semiconductor materials can be formed at a low substrate temperature in a technical-grade vacuum system as discussed by the authors.
Abstract: The ionized cluster beam (ICB) deposition and epitaxial process is an ion-assisted technique by which high quality films of metals, dielectrics and active semiconductor materials can be formed at a low substrate temperature in a technical-grade vacuum system. In the ICB process, film material is vaporized from a confinement crucible under conditions which result in the formation of aggregate clusters of atoms held together by weak forces. Clusters can be ionized by electron impact and subsequently accelerated by high potentials. Through selection of available parameters, it is possible to control the average energy of depositing species over the range from thermal ejection to above 100 eV per atom. It is within this range that optimum conditions for film growth are generally achieved. In the ICB deposition, characteristics of the deposition are mainly caused by both the structural characteristic of the clusters and the effects of ionization and acceleration of the clusters.


Journal ArticleDOI
TL;DR: In this article, a method for predicting the perturbed infrared spectrum of a solvated chromophore such as SF6 in a mixed van der Waals cluster is developed and applied to a realistic model for SF6-(AR)n clusters with n=1-100.
Abstract: A method for predicting the perturbed infrared spectrum of a solvated chromophore such as SF6 in a mixed van der Waals cluster is developed and applied to a realistic model for SF6–(AR)n clusters with n=1–100. The dominant contribution to the band shift arises from the interaction of an induced dipole on the perturber with the oscillating instantaneous dipole of the vibrationally distorted SF6. Spectra generated by Monte Carlo averaging these frequency shifts over a canonical distribution of cluster configurations and over a plausible assumed cluster size distribution are in near‐quantitative agreement with experiment. For the smaller clusters (n≲18), features of the simulations point to the presence of two distinct classes of cluster structure, one in which the chromophore is wrapped in a unimolecular layer of atoms, and a second in which the solvent atoms have multilayered structures. However, the question of whether the infrared spectra can provide evidence for the presence of the kind of phase coexist...

Journal ArticleDOI
TL;DR: In this paper, a system of weights corresponding to the precision of open cluster data is described, and some properties of open clusters can be studied more accurately than was possible earlier using these weights.
Abstract: A system of weights corresponding to the precision of open cluster data is described. Using these weights, some properties of open clusters can be studied more accurately than was possible earlier. It is clear that there are three types of objects: unbound clusters, bound clusters in the thin disk, and older bound clusters. Galactic gradients of metallicity, longevity, and linear diameter are studied. Distributions at right angles to the galactic plane are discussed in the light of the different cluster types. The clumping of clusters in complexes is studied. An estimate of the selection effects influencing the present material of open cluster data is made in order to evaluate the role played by open clusters in the history of the galactic disk. 58 references.

Journal ArticleDOI
TL;DR: In this article, the photofragmentation of hydrated electron clusters (H2O)−n, 15≤n≤40, are excited at 1064 nm (1.165 eV).
Abstract: Photofragmentation is found to be surprisingly efficient when hydrated electron clusters (H2O)−n, 15≤n≤40, are excited at 1064 nm (1.165 eV). The decay probability into ionic channels rises sharply from zero in the size range 15≤n≤20 before leveling off at a value of 0.56±0.10. The propensity of smaller clusters to detach an electron rather than fragment is correlated with the peculiar shape of the cluster ion distribution obtained by dissociative attachment of low energy electrons onto neutral water clusters, where the ionic clusters are only observed in abundance for n≥11.

Journal ArticleDOI
TL;DR: In this article, the absolute cross sections for all ionic products formed in reactions of B+1−13 with oxygen have been measured under single collision conditions, at collision energies from 0.25 to 10 eV.
Abstract: Absolute cross sections for all ionic products formed in reactions of B+1–13 with oxygen have been measured under single collision conditions, at collision energies from 0.25 to 10 eV. Three main reaction mechanisms appear to be important: oxidative fragmentation, collision induced dissociation, and boron atom abstraction. The dominant oxidation process are exoergic for all cluster sizes, but appear to have bottlenecks or activation barriers for the larger cluster ions. Clusters smaller than B+6 have similar chemistry, then there is a sharp transition in chemistry for clusters larger than B+6 . Correlations are explored between cluster reactivity and cluster stability, and the oxidation chemistry is compared to the similar results found for aluminum cluster ion oxidation.

Journal ArticleDOI
TL;DR: In this paper, the ground state of two-dimensional CuO 2 superconductors was studied to identify the pairing mechanism of holes, and it was shown that a doped hole on oxygen couples strongly with two neighboring Cu spins, which in turn causes a large magnetic distortion in the surrounding Cu spin system.
Abstract: The strongly correlated two-dimensional CuO 2 model is studied to identify the pairing mechanism of holes. Detailed studies of the ground state of clusters up to 30 atoms (10 Cu and 20 O atoms) reveal a binding of two holes doped on oxygen sites for particular values of parameters, which appear relevant to high- T c superconductors. The wave function for the ground state shows that a doped hole on oxygen couples strongly with two neighboring Cu spins, which in turn causes a large magnetic distortion in the surrounding Cu spin system. The interaction between two holes becomes attractive through a constructive interference of the magnetic distortions.