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Mathematical cluster chemistry

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Book cover Structural and Electronic Paradigms in Cluster Chemistry

Part of the book series: Structure and Bonding ((STRUCTURE,volume 87))

Abstract

The application of mathematical methods, such as polyhedral topology, graph theory and group theory, to the study of duster molecules is reviewed. The development of localised orbital and spherical harmonic methods are outlined and there is an introduction to Tensor Surface Harmonic Theory and Group Theory on a Spherical Shell. The inter-relationships between these approaches and their links with simple molecular orbital models, such as Hückel Theory, are detailed and rationalised. The review concludes with case studies which show how some or all of these methodologies have been brought to bear on three problems — deviations from Wade's rules in “non-spherical” borane clusters, the occurrence of approximately non-bonding skeletal molecular orbitals in hydrocarbon clusters; and the prediction of the structures, electronic properties and stabilities of the fullerenes — truly a “mathematical chemist's delight”.

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Authors and Affiliations

  1. School of Chemistry, University of Birmingham, B15 2TT, Edgbaston, Birmingham, UK

    Roy L. Johnston

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  1. Roy L. Johnston
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D. M. P. Mingos

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© 1997 Springer Verlag

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Johnston, R.L. (1997). Mathematical cluster chemistry. In: Mingos, D.M.P. (eds) Structural and Electronic Paradigms in Cluster Chemistry. Structure and Bonding, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0018029

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  • DOI: https://doi.org/10.1007/BFb0018029

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62791-3

  • Online ISBN: 978-3-540-68689-7

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