Mean coordination numbers and the non-metal–metal transition in clusters

The mean first-nearest-neighbour coordination number text-decoration:overlineN1 of atoms in a cluster is an important parameter characteristic of cluster size and geometry. For metal clusters and catalysts, its value is directly measurable by EXAFS spectroscopy. Literature expressions for text-decoration:overlineN1 in clusters are not accurate; ideal values have previously had to be worked out numerically by counting atomic site types. New, rigorous analytical formulae for text-decoration:overlineN1 as a function of cluster edge length have now been derived for icosahedral and cuboctahedral geometries. For clusters of the same size, text-decoration:overlineN1(icos) always exceeds text-decoration:overlineN1(cuboct), by a factor which is greatest for small clusters. The value of text-decoration:overlineN1 has recently been proposed to play an important role in the non-metal–metal transition of mercury and other metal-atom clusters; it follows that an icosahedral cluster might be ‘more metallic’ than a cuboctahedral one with the same number of atoms, a consequence which should readily be testable experimentally. The use of the text-decoration:overlineN1 parameter also gives new insight into cluster growth mechanisms.