How Many Networks Can Be Made from Four-Coordinate Atoms?

Müller, Ulrich

doi:10.1002/(sici)1521-3773(20000204)39:3<502::aid-anie502>3.0.co;2-n

Angewandte Chemie International Edition

2000

DOI: 10.1002/(sici)1521-3773(20000204)39:3<502::aid-anie502>3.0.co;2-n

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How Many Networks Can Be Made from Four-Coordinate Atoms?

Ulrich Müller¹

Abstract: In how many ways can three‐dimensional space be divided into tiles such that four edges meet at every vertex? A procedure to calculate the number of possibilities was recently presented by the mathematician A. Dress. Some of the tilings correspond to the structures of zeolites and other networks.

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Cited by 14 publications

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Strukturübergänge in Clustern

Hartke

2002

Angew. Chem.

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Lagert man an einen Cluster aus einzelnen Teilchen weitere Teilchen an, so bleibt die energetisch günstigste Grundstruktur weder erhalten noch ändert sie sich kontinuierlich. Stattdessen findet man Größenbereiche mit jeweils einem stark dominierenden Bauprinzip und vergleichsweise schmale Grenzen zwischen diesen Bereichen. Die Struktur des Festkörpers wird in der Regel erst nach mehreren Strukturübergängen bei relativ großen Clustern erreicht. Für das Auftreten dieser Strukturübergänge scheint es keine Rolle zu spielen, ob die Teilchen Atome oder Moleküle sind und ob der Cluster homogen oder heterogen ist. Offenbar handelt es sich um ein kollektives Vielteilchenphänomen, das in rein reduktionistischer Sicht zwar prinzipiell berechnet, aber nicht einfach verstanden werden kann. Weil die tatsächliche Berechnung bei hinreichender Genauigkeit derzeit noch am viel zu hohen Rechenaufwand scheitert – auch beim Einsatz unkonventioneller evolutionärer Algorithmen zur globalen Geometrieoptimierung –, wären einfachere Strukturregeln sehr wertvoll. Denn bei diesen Strukturübergängen geht es nicht nur um die akademische Frage nach dem Zusammenhang zwischen Potentialenergiefläche und Clusterstruktur, sondern auch um wichtige Vorgänge in der Natur und in der technischen Chemie, vom Wachstum von Kristallkeimen bis zur Nanotechnologie. Hier wird eine exemplarische Übersicht über die Untersuchung von Strukturübergängen bei Clustern gegeben – von einfachen Modellsystemen, bei denen erste qualitative Erklärungsversuche bereits Erfolge zeigen, bis zu realistischeren, komplexen Systemen, die sich unserem Verständnis noch weitestgehend entziehen.

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Strukturübergänge in Clustern

Hartke

2002

Angew. Chem.

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Structural Transitions in Clusters

Hartke¹

2002

Angew. Chem. Int. Ed.

130

109

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If one adds more particles to a cluster, the energetically optimal structure is neither preserved nor does it change in a continuous fashion. Instead, one finds several cluster size regions where one structural principle dominates almost without exception, and rather narrow boundary regions in‐between. The structure of the solid is usually reached only at relatively large sizes, after more than one structural transition. The occurrence of this general phenomenon of size‐dependent structural transitions does not seem to depend on the nature of the particles, it is found for atomic, molecular, homogeneous, and heterogeneous clusters alike. Clearly, it is a collective many‐body phenomenon which can in principle be calculated but not understood in a fully reductionistic manner. Actual calculations with sufficient accuracy are not feasible today, because of the enormous computational expense, even when unconventional evolutionary algorithms are employed for global geometry optimization. Therefore, simple rules for cluster structures are highly desirable. In fact, we are dealing here not just with the academic quest for linkages between cluster structure and features of the potential energy surface, but structural transitions in clusters are also of immediate relevance for many natural and industrial processes, ranging from crystal growth all the way to nanotechnology. This article provides an exemplary overview of research on this topic, from simple model systems where first qualitative explanations start to be successful, up to more realistic complex systems which are still beyond our understanding.

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ChemInform Abstract: How Many Networks Can Be Made from Four‐Coordinate Atoms?

Muêller

2000

ChemInform

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How Many Networks Can Be Made from Four-Coordinate Atoms?

Cited by 14 publications

References 4 publications

Strukturübergänge in Clustern

Strukturübergänge in Clustern

Structural Transitions in Clusters

ChemInform Abstract: How Many Networks Can Be Made from Four‐Coordinate Atoms?

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