Topic

# Cluster (physics)

About: Cluster (physics) is a(n) research topic. Over the lifetime, 27759 publication(s) have been published within this topic receiving 664003 citation(s).

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Abstract: During experiments aimed at understanding the mechanisms by which long-chain carbon molecules are formed in interstellar space and circumstellar shells1, graphite has been vaporized by laser irradiation, producing a remarkably stable cluster consisting of 60 carbon atoms. Concerning the question of what kind of 60-carbon atom structure might give rise to a superstable species, we suggest a truncated icosahedron, a polygon with 60 vertices and 32 faces, 12 of which are pentagonal and 20 hexagonal. This object is commonly encountered as the football shown in Fig. 1. The C60 molecule which results when a carbon atom is placed at each vertex of this structure has all valences satisfied by two single bonds and one double bond, has many resonance structures, and appears to be aromatic. Before 1985, it was generally accepted that elemental carbon exists in two forms, or allotropes: diamond and graphite. Then, Kroto et al. identified the signature of a new, stable form of carbon that consisted of clusters of 60 atoms. They called this third allotrope of carbon 'buckminsterfullerene', and proposed that it consisted of polyhedral molecules in which the atoms were arrayed at the vertices of a truncated icosahedron. In 1990, the synthesis of large quantities of C60 [see Nature 347, 354–358 (1990)] confirmed this hypothesis.

12,456 citations

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Abstract: An algorithm is presented for carrying out decomposition of electronic charge density into atomic contributions. As suggested by Bader [R. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, New York, 1990], space is divided up into atomic regions where the dividing surfaces are at a minimum in the charge density, i.e. the gradient of the charge density is zero along the surface normal. Instead of explicitly finding and representing the dividing surfaces, which is a challenging task, our algorithm assigns each point on a regular (x,y,z) grid to one of the regions by following a steepest ascent path on the grid. The computational work required to analyze a given charge density grid is approximately 50 arithmetic operations per grid point. The work scales linearly with the number of grid points and is essentially independent of the number of atoms in the system. The algorithm is robust and insensitive to the topology of molecular bonding. In addition to two test problems involving a water molecule and NaCl crystal, the algorithm has been used to estimate the electrical activity of a cluster of boron atoms in a silicon crystal. The highly stable three-atom boron cluster, B3I is found to have a charge of ! 1.5 e, which suggests approximately 50% reduction in electrical activity as compared with three substitutional boron atoms.

5,741 citations

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TL;DR: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster which can be used to infer the appropriateness of data partitions.

Abstract: A measure is presented which indicates the similarity of clusters which are assumed to have a data density which is a decreasing function of distance from a vector characteristic of the cluster. The measure can be used to infer the appropriateness of data partitions and can therefore be used to compare relative appropriateness of various divisions of the data. The measure does not depend on either the number of clusters analyzed nor the method of partitioning of the data and can be used to guide a cluster seeking algorithm.

5,640 citations

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Abstract: We present a molecular dynamics computer simulation method for calculating equilibrium constants for the formation of physical clusters of molecules. The method is based on Hill’s formal theory of physical clusters. In the method, a molecular dynamics calculation is used to calculate the average potential energy of a cluster of molecules as a function of temperature, and the equilibrium constants are calculated from the integral of the energy with respect to reciprocal temperature. The method is illustrated by calculations of the equilibrium constants for the formation of clusters of two to five water molecules that interact with each other by an intermolecular potential devised by Watts. The method is compared with other procedures for calculating the thermodynamic properties of clusters.

2,940 citations