Six-atom clusters

Table 2. Binding Energy Per Atom Eb, Distance D from Atoms to the Cluster Center, and Average Magnetic Moment Per Atom p for Octahedral Six-Atom Clusters. Data Collected from Zhang et al.107... 

Figures 4.5 and 4.6 show the predicted bond energies per atom (in units of h0 ) for three-, four-, five-, and six-atom clusters as a function of the electron count N for the three different values of the degree of normalized hardness ah = , and (corresponding to = 2, 3, and oo respectively).

Clusters with up to four metal atoms generally obey the 18-electron rule for each metal atom. This is no longer the case for six-atom clusters. For instance, in an octahedral cluster a total of 84 electrons (provided by the metal atoms and the ligands) would be predicted for a stable configuration, counting each edge of the octahedron as a metal-metal bond. The 84-electron count for an octahedral cluster is realized in only one known case, namely [HCufPPhj)] 42, 92), and almost aU other cases, as listed in ref. 20), have 86 electrons. 

The first six-atom cluster, Rh6(CO)i6, was structurally elucidated by Corey, Dahl, and Beck in 1963 today there is an enormous number of them and we can sketch only a few of the main facts. In addition to their intrinsic interest, large clusters, especially the very largest ones, are of importance because they may be expected to show properties verging on those of bulk metals. They provide one approach to answering the question How large does a particle of metal have to be before bulk metal properties begin to appear ... 

The large surface area/volume ratio of nanoparticles means that most of their atoms are on the surface, which allows nanoparticles to react as nearly stoichiometric reagents in chemical reactions, unlike bulk solids. For example, a six-atom cluster in the shape of an octahedron contains 100 percent of its atoms on the surface. If either the CCF or HCF theme is followed, the next smallest close-packed collection of atoms that can be built has a central atom coordinated to six others in one layer, three others in a layer above, and three in a layer beneath. Hence, 12/13 = 92 percent of the atoms in this cluster... 

Unlike [CpMo(CO)2]2 in which unsaturation generates localized metal-metal multiple bonding, here the unsaturation is spread out over the entire six-atom cluster system a conclusion supported by the difference in geometric parameters between the Cr and Re compounds as well as by molecular orbital modeling. Because of the invariant stoichiometry, these observed geometry changes can only be attributed to the change in metal. 

The Six Atom Cluster. For the six atom cluster two different structures are of interest. There is a nearly planar C structure, with one atom above a five-membered ring, and there is the octahedral (Oj ) structure. If all atoms are in the d s state the C structure is preferred and the wavefunction is a closed shell singlet. This does not mean that Ni is non-reactive to since the energy difference to the Oj structure is only 10 Real/mol, and the 0, structure has a triplet ground state with two open shells. Since the exothermicity is most certainly larger than 10 kcal/mol, this structural change is expected to occur during the interaction of with Nig. 

The advent of the first metal carbonyl cluster, Fe3(CO)i2, was also long ago. Here again there was long uncertainty about its structure, resolved only by the work of Dahl in 1966, who was also responsible for clarifying the nature of the analogous Ru3(CO)i2 and Os3(CO)i2. During the same period of time Chini and coworkers prepared the first four-atom metal carbonyl cluster, Co4(CO)i2, whose Rh and Ir analogues were soon to follow, and in 1963 Dahl showed the true formula and structure of the first six-atom cluster compounds of the carbonyl type, Rh6(CO)i6. 

A characteristic reaction of sulfmylimines RNSO is the quantitative addition of R Li reagents to form adducts of the type Li[RNS(R )NR]. ° The structures of these sulfmimidinates are discussed in Section 10.4.4." The reactions of RNSO derivatives with two equivalents of lithium tert-butylamide result in the formation of diazasulfite anions [OSNR(N Bu)] (9.12) (Eq. 9.12)." The dilithium derivatives of these dianions form hexameric thirty-six atom (Lii2Ni206S6) clusters with structures that are dependent on the nature of the R group. 

Similar possibilities arise for 10-atom clusters. Thus, dimerization of the c/oso-CtBj claster l,5-Me2C2B3Et3 (56) by means of K metal then I2 in thf yields the classical adaniantane derivative Me4C4B6Et6 (f) when this is heated to 160° the mdd-tetracaibadecaborane cluster (g) is obtained rapidly and quantitatively. It will be noted that in (f) all four C atoms are 4-coordinate and all six B atoms are 3-coordinate, whereas in (g) the three C atoms in the C3 triangular face are 5-coordinate while the boron atoms are variously 4, 5 or 6 coordinate. 

Agreement is poor for small clusters, but this does not present a fair test—the smallest structure type considered is that derived from a trigonal bipyramid having an S value of 6. However, the predictive power for clusters of four to six atoms, for which the rules perform best, is only moderate. Even in that region, correspondence with the actual... 

Even though qualitative bonding descriptions of metal atom clusters up to six or seven atoms can be derived and in some cases correlated with structural detail, it is clear that most structures observed for higher clusters cannot be treated thus. Nor do the structures observed correlate with those observed for borane derivatives with the same number of vertices. Much of borane chemistry is dominated by the tendency to form structures derived from the icosahedron found in elemental boron. However, elemental transition metals possess either a close-packed or body-centered cubic arrangement. In this connection, one can find the vast majority of metal polyhedra in carbonyl cluster compounds within close-packed geometries, particularly hexagonal close-packing. 

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