Cluster vertex connectivity

The simultaneous function of a transition metal atom as a lone-pair acceptor and as a cluster vertex atom is realized in [(77 -Ge9)Cu(ry -Geg)] (Fig. 5j), in which the two [Geg]" units are connected in an r/ - and an r/" -fashion to the same Cu ion. Transition metal bridges between Geg clusters are also found in various other coordination modes in [Ge9(/i -Au)3Geg] (Fig. 5k), three bridging Au atoms each are coordinated by two Ge atoms of two different Geg units in an almost linear way and entertain aurophUic interactions within the resulting triangle of Au" " ions two [GegR3] anions are coordinated via their triangular face to ( M = Zn, Cd,... 

The polyhedral shapes pertinent to this class of clusters are the deltahedra shown in Figure 2.7. Deltahedra are polyhedra containing exclusively triangular faces. The vertex connectivities are shown on the drawings. Those for n = 4 (not shown), 6 and 12 have uniform connectivities of three, four and five hence, the cluster atom centers lie on a sphere. The others with less uniform connectivities are less spherical in shape if all edge lengths are equal. As it is a three-connect cluster, the tetrahedron... 

We begin with an obvious question. Given that a metal atom can accommodate larger coordination numbers than main-group atoms, why cannot clusters containing vertex connectivities greater than three be accommodated with two-center-two-electron bonding plus application of the 18-electron rule Consider an octahedral... 

This approach is perhaps best illustrated by a simple example. Consider a deltahedral cluster where the vertex connectivity is greater than three, for example, BeHe ". One... 

Figure 3 Isomeric possibilities for structures for E Mx-n, n = (x — 1) — l,x = 4-6. Only the geometry of highest total vertex connectivity (usually denoted as closo but note the ambiguity for x = 4) and that of next highest (usually denoted as nido) are shown for economy of space. Likewise, only the binary E and M clusters are enumerated. Clearly, many more structures are possible if more open structures are allowed or more than one type of main group or transition metal element is used in the compound...

Figure 8 Schematic vertex assignment (a) and the most symmetric form of the sab net (b) found in MOF-CJ3 and UCT-1. Note that vertices are chosen where there are no atoms in the center of the Zn-cluster (six connected, blue) and in the middle of the benzene rings (three connected, red). .

Each vertex of a buckyball cluster is attached by three H-bonds, and hence must have net donor (2D1A) or acceptor (1D2A) character that seems to preclude significant cooperativity. However, by suitably pairing each donor and acceptor monomer, one may produce connected dimers that are each of effective 3D3A pseudo-closed-CT character. Such cooperative dimer units may then be joined in proton-ordered fashion to form closed polyhedra that retain a high degree of cooperative stabilization. 

For triangular clusters, for instance, this means 18 or 48 electrons. A classic example may be the Os3 triangular group in the carbonyl compound Os3(CO)12 in which 4 CO are connected to each Os (to each triangle vertex). Each Os atom contributes 8 valence electrons whereas the CO group acts as a 2-electron donor so ... 

The structures and skeletal bond valences of Oss(CO)i6 and B5H52- are similar as a pair, as are also Fe5C(CO)is and B5H9. But the bonding types in the boranes and the metal clusters are not the same. Since every B atom in a polyhedral borane has three AO s for bonding of the BM skeleton, any vertex more than three-connected must involve multicenter bonds. In the transition-metal skeleton, the Mm atoms form either 2c-2e single bonds or 3c-2e multicenter bonds. 

MOLCONN-Z EduSoft, LC www.eslc.vabiotech.com/molconn/ Molecular connectivity, molecular connectivity difference, and kappa shape indices, E-state indices, atom-type and group-type E-state indices, topological equivalence classification of atoms, other topological indices, counts of subgraphs paths, rings, clusters, etc. vertex eccentricities... 

Figure 1. Sketch of an icelike cluster around a selected water molecule. In this structure, a molecule from a sublayer (dotted lines) of one layer (delimited with full lines) is connected via hydrogen bonds with three molecules of the other sublayer of the same layer (only two bonds are drawn in the picture it should be noted that the molecules drawn are not in the same plane) and with one water molecule from an adjacent layer. The first four neighbors are located at the vertexes of a tetrahedron. The projection of the position of the water molecules from one layer in the plane of the surface (denoted in the text as xy) is a hexagonal network. Each icelike cluster involves 26 molecules around the selected molecule (marked) they are located in three water layers a central and the two adjacent ones.

The overall structure of the supercluster has the following topology (Figure 6) where each vertex represents one of the two central Mo atoms (one inside the other relative to the sphere) in the linking (Mo)Mo5 groups holding the water H-bonded connecting clusters. 

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