The mean first-nearest-neighbour coordination number /5, 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 Kl 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 /5, as a function of cluster edge length have now been derived for icosahedral and cuboctahedral geometries. For clusters of the s a m e size, fil(icos) always exceeds N,(cuboct), by a factor which is greatest for small clusters. The value of /5, has recently been proposed to play an important role in t h e 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 s a m e number of atoms, a consequence which should readily be testable experimentally. The use of the m1 parameter also gives new insight into cluster growth mechanisms.The mean nearest-neighbour coordination number N of atoms in a cluster is an important parameter characteristic of cluster size and shape. It has been proposed that in metalatom clusters, N, is not just a geometrical parameter but correlates more directly than the cluster nuclearity with the degree of metallic character. This has been considered for the d-band width,'p2 the cohesive energy,3p5 the binding energies of core and valence electrons6 and the ionisation ~o t e n t i a l . ~. ~The transition from van der Waals to metallic bonding in mercury clusters has recently been discussed in detail. Good correlation between experimental cluster ionisation potentials

The structure and bonding of a series of gold clusters and gold nanomaterials stabilized by ligands or confined within nanoporous alumina have been investigated using EXAFS, XANES, and WAXS. Two gold clusters stabilized by two different ligands, Au55(PPh3)12Cl6 and Au55(T8 -OSS−SH)12Cl6, were confirmed to be of face-centered cubic structure type with metal−metal distances of 2.785 and 2.794 Å, respectively, shorter than in bulk gold. Colloidal gold of 180 Å diameter stabilized by sulfonated phosphine ligands had structural and electronic properties very similar to those of bulk gold but smaller Debye−Waller factors. The cluster Au55(PPh3)12Cl6 adsorbed into nanoporous alumina membrane was found to retain its integrity inside the membrane but with slightly longer Au−Au bonds due to some aggregation. The same cluster thermally transformed into colloidal gold within the alumina membrane was found to be almost identical structurally and electronically to the bulk. Gold nanowires electrochemically grown within the nanoporous alumina were found to be composed on average of 120 Å diameter crystallites. These have the same structure as the bulk, but with smaller Debye−Waller factors, indicating either a better crystallinity or that the gold atoms are more tightly held than in the bulk. The difference of area method L3 − kL2 was used to quantify the d orbital occupancy. The two ligand-stabilized Au55 clusters both had a smaller value (2.7) than the bulk material (4.1). The nanomaterials inside the membrane also showed smaller L3 − kL2 values. The geometrical and electronic structures of these gold materials show a very clear pattern of buildup as the number of gold atoms increases from Au55 clusters through Au colloids and nanowires to the bulk metal.

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E x a c t A n a l y t i c a l F o r m u l a e for M e a n C o o r d i n a t i o n N u m b e r s in ClustersH a n s -G e r h a r d Fritsche 1 ~z R o b e r t E. Benfield ~ 1Fakult~t ffir Chemic, Friedrich-Schiller UniversitY.t, Am SteigeI 3, A b s t r a c t .Rigorous analytical formulae for mean nearest-neighbour coordination numbers in clusters as a function of cluster size have been derived for a range of geometries: the tetrahedron, octahedron, cuboctahedron, icosahedron and bcc rhombic dodecahedron. Formulae for outer-neighbour coordination numbers are also reported, including a complete analysis of interatomic distances and mean coordination numbers in icosahedra. The formulae will find application in studies of electronic structure and interpretation of EXAFS data.