Characterizing Potential Surface Topographies through the Distribution of Saddles and Minima

Cox, Graham A.; Berry, R. Stephen; Johnston, Roy L.

doi:10.1021/jp0630572

Cited by 10 publications

(6 citation statements)

References 25 publications

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“…Of these structures, only 7e has been proposed elsewhere , as feasible. In fact, although structure 7a has been proposed as the GM for other binary compounds, e.g., zinc sulfide, silver iodide, and magnesium oxide, we have not found it reported by others for zinc oxide. The other structures that have already been reported as metastable include 7c and 7f (as 7h and 7f by Wang et al) and 7i (as 7b by both Maxtxain et al and Wang et al).…”

Section: Resultscontrasting

confidence: 85%

“…The ease of locating a metastable structure (local minimum) depends on the relative width of the basin within which it sits compared to its neighbors, the relative width of the superbasin containing neighboring local minima that are connected by barriers below a defined height or the basin on the relaxed landscape, and the relative width of the supersuper basin etc. Others − have employed a technique for such analyses, where the landscape is drawn so that it resembles the roots of a tree, a disconnectivity graph, and from which one can see whether the landscape is likely to funnel the EA toward a local minimum or the GM. These analyses need the knowledge of the barrier heights between the local minima and are therefore beyond our present study.…”

Section: Resultsmentioning

confidence: 99%

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Structures of Zinc Oxide Nanoclusters: As Found by Revolutionary Algorithm Techniques

et al. 2008

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We report the stable and low energy metastable structures of zinc oxide clusters, (ZnO) n , n ) 1-32, found using an evolutionary algorithm with polarizable shell interatomic potentials. This study comprises the first systematic search for nanoparticulate structures for this compound above n ) 18 and includes a comparison with other recent studies. As a function of n, global minimum and low energy metastable clusters evolve from rings (up to ca. 0.8 nm in diameter) to perfect closed bubbles (up to ca. 1.2 nm in diameter in the range reported), which are the structures that only contain tetragonal and hexagonal faces and all ions have a coordination number of three. The transition between the two structural families is blurred, with key structures that are also (i) open bubbles, which contain octagonal or larger faces, and (ii) bubbles that have handles, or two-dimensional ring fragments attached. A new nomenclature to describe these structures is defined. We find a greater stability of tetrahedral and trigonal coordinations compared to tetragonal for ZnO clusters in the range considered. Of the predicted global minimum clusters, spheroid cages n ) 12, 16, and 28, with symmetry point groups T h , T d and T, and barrels, which are a common motif, exhibit a relatively high stability. Bulklike wurtzite, or multilayered clusters, as well as the simple cuboid and related rock salt configurations are not found to be thermodynamically stable in the size range considered.

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Section: Resultscontrasting

confidence: 85%

Section: Resultsmentioning

confidence: 99%

Structures of Zinc Oxide Nanoclusters: As Found by Revolutionary Algorithm Techniques

et al. 2008

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“…Yagi et al demonstrated through in situ experiments that such shape changes could occur, later confirmed by Iijima and Ichihashi . While there were initially some questions as to the role of electron-beam heating or core excitations in the experiments, a more general explanation by Ajayan et al − indicated that the activation energy for transformations between structures was relatively modest, similar to the energy landscape model for much smaller clusters developed by Berry and co-workers. − Ajayan et al also speculated that there should be a size–temperature phase diagram for nanoparticles.…”

Section: Introductionmentioning

confidence: 89%

Kinetic and Thermodynamic Modified Wulff Constructions for Twinned Nanoparticles

2013

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Wulff constructions are a powerful tool to predict the shape of nanoparticles, which strongly influences their performance in catalysis, sensing, and surface-enhanced spectroscopies. Previous Wulff models focused on energy minimization and included contributions from the surface energy, interface energy, twin boundaries, and segregation-induced bulk energy changes. However, a large number of shapes cannot be understood by such thermodynamic approaches, in particular many of the twinned late transition metal (Ag, Au, Pt, Pd, etc.) particles of interest in catalysis and plasmonics. A review of the modified Wulff (i.e., twinned) construction is presented here, followed by the development of a modified kinetic Wulff model, which, by including kinetic parameters, explains the emergence of commonly observed shapes such as bitetrahedra, truncated bitetrahedra, thin triangular platelets, perfect decahedra, and decahedral rods.

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“…Evolutionary Computation Volume 20, Number 4 For the 13-atom Morse cluster, a thorough characterization of the landscape topography in function of a single parameter ρ of the Morse pair potential can be found in Cox et al (2006). Putative ground states of Morse clusters for N ≤ 80 and different ρ values are reported in the Cambridge Cluster Database (Wales et al, 2009).…”

Section: Discussionmentioning

confidence: 99%

Energy Landscapes of Atomic Clusters as Black Box Optimization Benchmarks

Müller

Sbalzarini

2012

Evolutionary Computation

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We present the energy minimization of atomic clusters as a promising problem class for continuous black box optimization benchmarks. Finding the arrangement of atoms that minimizes a given potential energy is a specific instance of the more general class of geometry optimization or packing problems, which are generally NP-complete. Atomic clusters are a well-studied subject in physics and chemistry. From the large set of available cluster optimization problems, we propose two specific instances: Cohn-Kumar clusters and Lennard-Jones clusters. The potential energies of these clusters are governed by distance-dependent pairwise interaction potentials. The resulting collection of landscapes is composed of smooth and rugged single-funnel topologies, as well as tunable double-funnel topologies. In addition, all problems possess a feature that is not covered by the synthetic functions in current black box optimization test suites: isospectral symmetry. This property implies that any atomic arrangement is uniquely defined by the pairwise distance spectrum, rather than the absolute atomic positions. We hence suggest that the presented problem instances should be included in black box optimization benchmark suites.

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Characterizing Potential Surface Topographies through the Distribution of Saddles and Minima

Cited by 10 publications

References 25 publications

Structures of Zinc Oxide Nanoclusters: As Found by Revolutionary Algorithm Techniques

Structures of Zinc Oxide Nanoclusters: As Found by Revolutionary Algorithm Techniques

Kinetic and Thermodynamic Modified Wulff Constructions for Twinned Nanoparticles

Energy Landscapes of Atomic Clusters as Black Box Optimization Benchmarks

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