This journal is c The Royal Society of Chemistry 2013 Chem. Commun., 2013, 49, 3615--3616 3615 Cite this: Chem. Commun., 2013, 49, 3615 The significance and impact of Wade’s rules Alan J. Welch* The emergence of a set of simple yet powerful electron counting rules following a classic paper by Wade published in 1971 in J. Chem. Soc. D has transformed the way chemists think about the structures of clusters with delocalised skeletal bonding. In 1971 a landmark paper in cluster chemistry ‘‘The Structural Significance of the Number of Skeletal Bonding Electron-pairs in Carboranes, the Higher Boranes and Borane Anions, and Various Transition-metal Carbonyl Cluster Compounds’’ was published in J. Chem. Soc. D, 1 the forerunner of Chemical Communications. The principles outlined in this communication were to become known as Wade’s rules and they provide a straightforward and eloquent rationalisation of the shapes of ‘‘electron-deficient’’† cluster compounds in terms of the number of skeletal electron pairs (SEPs) these molecules possess. The communication focused on boranes, carboranes and other heteroboranes, low- valent transition-metal clusters whose structures could not be explained by 2c–2e bonding, carbido transition-metal clusters and mixed transition-metal–main group element clusters. Shortly after Wade’s initial communication, Mingos extended the principle of counting SEPs to electron-precise and electron- rich clusters, provided a generalised method of calculating the SE contribution of a wide variety of transition-metal fragments including recognising that it was not necessary to know whether CO ligands were terminal or bridging, and introduced the principle that excess electrons resulted in bond breaking. 2 Thereafter the rules became popularly known as the Wade– Mingos rules or, more formally, the Polyhedral Skeletal Electron Pair theory. In whatever form they are known the greatest impact of ‘‘the rules’’ has been in providing a simple and elegant explanation of the shapes of ‘‘electron-deficient’’ clusters, since prior to them the main approach to the structures of the boranes and related species was Lipscomb’s topological model involving styx numbers and rules, 3 which was somewhat limited in applicability. The stimulus for Wade’s paper was the earlier recognition by Williams 4 that the structures of open boranes and carboranes were not (as had been previously assumed) simply fragments of an icosahedron. Rather, once they were arranged into three families (closo, nido and arachno) it was clear that, structurally, a nido (n 1)-vertex polyhedron and an arachno (n 2)-vertex polyhedron were fragments of the appropriate parent closo n-vertex polyhedron, the structures of these parent polyhedra being exemplified by dianionic borates [B n H n ] 2 and by the carboranes C 2 B (n 2) H n . The usual representa- tion of these structural relationships is that popularised by Rudolph 5 and reproduced in Fig. 1. Wade’s outstanding contribution was to recognise why these structural patterns existed, i.e. that closo n-vertex, nido (n 1)-vertex and arachno (n 2)-vertex polyhedra all shared the same number (n + 1) of skeletal bonding molecular orbitals and hence SEPs. Alternatively, expressing the rules in their more usual form, a closo cluster has (n + 1), a nido cluster has (n + 2) and an arachno cluster has (n + 3) SEPs where n is simply the number of cluster vertices. These empirical rules work because they are underpinned by the results of molecular orbital analyses 6 and more generally by Tensor Surface Harmonic Theory. 7 Skeletal electron counting rules are now very much part of the fabric of modern cluster chemistry and are routinely taught in all undergraduate inorganic chemistry courses. For those active in cluster research they provide an immediate and very clear starting point from which to think about and describe cluster structures. The impact of the rules on the research community is clearly evidenced by a current total citation count Institute of Chemical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK. E-mail: [email protected] Received 4th January 2013, Accepted 13th March 2013 DOI: 10.1039/c3cc00069a www.rsc.org/chemcomm † This term, which originates from the fact that such clusters contain more connections between adjacent, covalently-bonded, atoms than skeletal electron pairs, should be used cautiously. Whilst the fragments of which such clusters are composed are electron deficient, e.g. {BH} has 3 valence orbitals but only 2 valence electrons, in terms of molecular orbitals the clusters themselves are not, e.g. in [B 12 H 12 ] 2 all of the skeletal bonding molecular orbitals, and non of the antibonding molecular orbitals, are occupied. A more suitable descriptor of the nature of the clusters that Wade’s rules rationalise might therefore be ‘‘clusters with delocalised skeletal bonding’’ (we thank a referee for this suggestion). ChemComm VIEWPOINT Published on 14 March 2013. Downloaded by Durham University Careers Centre on 20/03/2014 14:08:54. 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