Framework bonding orbitals

How can carbon, with only four valence orbitals, form bonds to more than four surrounding transition metal atoms Ru CCCOfiy, with a central core of Of, symmetry, is a useful example. The 2s orbital of carbon has A symmetry and the 2p orbitals have T]u symmetry in the Of, point group. The octahedral Rus core has framework bonding orbitals of the same symmetry as in described earlier in this chapter (see Figure... 

Seven orbital combinations (n + 1) lead to bonding interactions within the B6 core these are shown in Figure 13-10. Constructive overlap of all six hybrid orbitals at the center of the octahedron yields one framework bonding orbital, labeled /l,.17 Additional bonding interactions are of two types overlap of two sp hybrid orbitals with parallel p orbitals on four boron atoms (three such interactions, symmetry label and overlap of p orbitals on four boron atoms within the same plane (three interactions, symmetry label t2 )- The remaining orbitals form antibonding molecular orbitals or are nonbonding. A summary follows. 

The valence theory (4) includes both types of three-center bonds shown as well as normal two-center, B—B and B—H, bonds. For example, one resonance stmcture of pentaborane(9) is given in projection in Figure 6. An octet of electrons about each boron atom is attained only if three-center bonds are used in addition to two-center bonds. In many cases involving boron hydrides the valence stmcture can be deduced. First, the total number of orbitals and valence electrons available for bonding are determined. Next, the B—H and B—H—B bonds are accounted for. Finally, the remaining orbitals and valence electrons are used in framework bonding. Alternative placements of hydrogen atoms require different valence stmctures. 

Symmetry of orbitals on the B6 octahedron, (a) Six outward-pointing (sp) orbitals used for a bonding to 6 H. (b) Six inward-pointing (sp) orbitals used to form the fi framework bonding molecular orbital, (c) ComponenLS for one of the fiM framework bonding molecular orbitals — the other two molecular orbitals are in the yz and zr planes, (d) (Components ftM one of the t2 framework bonding molecular orbitals — the other two molecular orbitals are in the yz and x planes. 

Hiickel s calculations on planar conjugated systems were extensively exploited, and I refer you once again to Streitwieser s classic book. Molecular Orbital Theory for Organic Chemists. What few calculations that had been done at that time on the (T framework had used the method of linear combination of bond orbitals. 

Some 50 years have now passed since the publication of a series of papers bearing the title The Nature of the Chemical Bond. 1 7 These papers have provided chemists, physicists, biologists, and mineralogists with the conceptual framework, based on simple valence bond theory and the theory of hybrid bond orbitals, required to investigate a myriad of problems involving the nature of the bonding exhibited in molecules and solids. The ideas contained in these papers were subsequently elaborated on in The Nature of the Chemical Bond which is probably the most often-cited book in the scientific literature.9... 

In the bond framework in Figure 10-18. all the bonds form from end-on overlap of orbitals directed toward each other. As illustrated by the three examples in Figure 10-20. this type of overlap gives high electron density distributed symmetrically along the intemuclear axis. A bond of this type is called a sigma (cr) bond, and a bonding orbital that describes a cr bond is a (7 orbital. 

Each carbon atom has a steric number of 2, indicating that acetylene is a linear molecule and that sp hybrid orbitals can be used to construct the bonding orbital framework. Figure 10-24a shows the a bonding system of acetylene. 

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