Distances in Clusters

Whereas the main object of this survey is to explore how the shapes of various substances reflect the number of electron pairs holding them together, it is worth considering also how their sizes can be rationalized using the electron-counting approach already outlined (203). 

In a oloso-cluster species such as a borane anion B H , in which the n skeletal atoms are held together by (n -h 1) bond pairs, the interatomic distances—the edge lengths of the B polyhedron—can be rationalized if one regards the skeletal atoms as held together by a network of 

The average edge bond order for a particular closo species can be calculated by dividing the total number of skeletal bond pairs ( 4- 1) by the number of edges, which, for exclusively triangular-faced poly-hedra with n vertices, is (3 — 6). This leads directly to the formal boron-boron bond order for those borane anions (ITU) and 

Skeletal (Polyhedron-Edge) Bond Orders for Anions BnHn  

Bond orders calculated on this basis for the various types of two-center link in anions BgHg (100), BgHg (99), and BjoHio (57) are 

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In cluster hydrides, the resonance for bridging hydrides tends to lie further upfield (— 15 to — 25 p.p.m.) than those for terminal M—H groups (0 to —15 p.p.m.), but exceptions exist.103 Nematic phase NMR has been used to determine M—H distances in cluster hydrides.110... 

Most of the Nb—Nb distances in clusters containing discrete Nb6Oi2 units fall within a narrow range of 2.79-2.89 A. 

Linkage distance In clustering, the distance between two points amalgamated into one cluster, usually expressed as the Euclidean distance. 

Various partitions, resulted from the different combinations of clustering parameters. The estimation of the number of classes and the selection of optimum clustering is based on separability criteria such as the one defined by the ratio of the minimum between clusters distance to the maximum of the average within-class distances. In that case the higher the criterion value the more separable the clustering. By plotting the criterion value vs. the number of classes and/or the algorithm parameters, the partitions which maximise the criterion value is identified and the number of classes is estimated. 

Boron-boron distances in the cluster increase with increasing coordination number (as expected). Average B-B distances are 5-coordinate B 170pm, 6-coordinate B 177pm, 7-coordinate B 186pm. 

The initial results on the [NaA ] clusters have been extended to the heterocyclic ring species [XAls] (X = Si, Ge, Sn, Pb) bearing a single charge and as a result are not prone to dissociation of an electron like the [Al4] or [Ga4H2] anions [69]. A planar four-membered ring structure is in all cases the most stable structural isomer with Al—Al distances in the range 2.57-2.61 A. 

X-ray absorption spectroscopy has been performed on the isolated Rieske protein from bovine heart mitochondrial bc complex 69) as well as on the Rieske-type cluster in Burkholderia cepacia phthalate dioxygenase (PDO) (72). The analysis performed by Powers et al. 69) was significantly hampered by the fact that the presence of two histidine ligands was not fully recognized therefore, only the results obtained with the dioxygenase where the mononuclear iron has been depleted will be considered here. Table VII gives a comparison of the distances obtained from the fit of the EXAFS spectra assuming an idealized Rieske model and of the distances in the crystal structures... 

Fe-S and Fe-Fe distances in [2Fe-2S], [3Fe-4S], and [4Fe-4S] clusters are all very similar 2.3 and 2.7 A, respectively. In the [6Fe-6S] prismane model cluster, however, there is an additional Fe-Fe distance at 3.7 A (Fig. 2). If a [6Fe-6S] cluster were present in the Fepr protein, then this longer Fe-Fe distance should he visible with extended X-ray absorption fine structure (EXAFS). As a consequence, EXAFS studies were carried out at the CCLRC Synchrotron Radiation facility in Daresbury, UK. The two Fepr proteins (those of D. vulgaris and D. desulfuricans), as well as a synthetic [6Fe-6S] cluster, were subjected to an EXAFS study. Low-temperature EXAFS... 

The copper-copper interatomic distance in rhodium-copper clusters is substantially longer than in metallic copper (2.62-2.63A vs. 2.556A) and closer to the value (2.64A) obtained for the rhodium-... 

Recently we reported EXAFS results on bimetallic clusters of iridium and rhodium, supported on silica and on alumina (15). The components of this system both possess the fee structure in Efie metallic state, as do the components of the platinum-iridium system. The nearest neighbor interatomic distances in metallic iridium and rhodium are not very different (2.714A vs. 2.690A). From the results of the EXAFS measurements, we concluded that the interatomic distances corresponding to the various atomic pairs (i.e., iridium-iridium, rhodium-rhodium, and iridium-rhodium) in the clusters supported on either silica or alumina were equal within experimental error. Since the Interatomic distances of the pure metals differ by only 0.024A, the conclusion is not surprising. 

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