Intra-cluster bonding

In contrast to chloride compounds, niobium oxides have a VEC of 14 electrons, due to an overall anti-bonding character of the a2u state, caused by a stronger Nb-O anti-bonding contribution. In some cases, the VEC cannot be determined unambiguously due to the uncertainty in the electron distribution between the clusters and additional niobium atoms present in the majority of the structures. The 14-electron compounds exhibit semiconducting properties and weak temperature-independent paramagnetism. Unlike niobium chlorides, the oxides do not exhibit a correlation between the electronic configuration and intra-cluster bond distances. 

There are 12 outward-pointing radial hybrids and 13 bonding molecular orbitals for intra-cluster bonding. Therefore, the boron icosahedron within a structure is two-electron-deficient 36 - (12 +13 x 2) = -2. This can be well understood by considering (B12H12)-2, for example. It should be noted that the formation of the boron cluster is extremely "economic" in terms of electrons, since conventional pair bonding would require 60 electrons, rather than 26. 

Regular connectivities of [R (Z)]X 2X cluster units, examples and electron counts n for intra-cluster bonding... 

M60 octahedra (see Fig. 4.28). The solid-state structure results from the packing of such groups. The inter-cluster distances are similar to those found in the metals. According to Simon, these compounds could be described as ([Rb902]5+, 5e ) and ([Csh03]5+, 5e ) with the five electrons donated to a conduction band, both inter-and intra-cluster metal-metal bonding, in agreement with the metallic conductivity of these compounds. 

There are several prerequisites which have to be fulfilled for the one electron ECP approach to be applicable. In the case of metal clusters the atomic configuration must be known, i.e. one must safely be able to assume a dns2 or a drL+1s1 configurations on the atoms in the cluster. The d orbitals should not form covalent bonds neither within the cluster nor between the cluster and the adsorbate. Ferromagnetic metals and copper are likely to have these properties. For other metals this is not so clear. Indications are that e.g. the ground state of the Pts cluster is low spin with developed covalent intra cluster d-d bonds[22]. 

Fig. 33. Perspective views from the top-layer side (Panel a) and from the bottom-layer side (Panel b) of the representative, nearly-stoichiometric surface cluster V360 98- The geometric structure of the V205 (010)- surface cluster (see Fig. 26) involves the SINDOl optimized intra-layer bond lengths [28] and the crystallographic values of the bond angles and the inter-layer V-O bond length. The surface layer views of alternative perpendicular adsorptions of toluene on the bridging oxygen 0(2) from the top layer side (c) and from the bottom layer side (d), and two alternative parallel adsorptions (Panels e, f) on the bottom layer. In Panel d the same adsorbate-substrate separation as in Figs. 7a, 9 and 25e has been adopted, while in the remaining panels this separation has been increased by 1 A relative to those shown in Fig. 25...

On the other hand, there are 8 electrons for intra-cluster covalent bonding when one counts as (4x2)-i-(l x6)- (6xl) = 8. Sulfide-chloride derivatives, [R4N]S3Cl3 of this structure type may be obtained with the trivalent lanthanides R=La-Nd, Gd (Lissner and Schleid 1994). Again, these may be understood with the ionic or the covalent view, according to, for example, [(La3+)4(N3-)](S2-)3(Cr)3 vs. (4x3)-f(1 x5)-(3x2)-(3x 1) = 8. 

These constrained MD methods rely on efficient solutions to the rigid-body EOM and on the use of atomistic, simplified atomistic (i.e., no intra-cluster valence or non-bond interactions) or coarse-grain force fields, discussed next. 

The three hexanuclear clusters are mixed valency complexes of two M(III) and four M(IV) centers, and the average oxidation state of the metal is +3.67. The number of cluster valence electrons is 14, which agrees with seven M—M bonds. Relatively short M-M distances for the intra- and intertriangles suggest that the clusters can be viewed as dimers of triangular clusters. Extension of the triangle condensation would lead to higher polymers. 

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