Complex bond orbitals

Hoffman s extended Huckel theory, EHT (Hoffman, 1963), includes all bonding orbitals in the secular matrix rather than just all n bonding orbitals. This inclusion increases the complexity of the calculations so that they are not practical without a computer. The basis set is a linear combination that includes only valence orbitals... 

There is always a transformation between symmetry-adapted and localized orbitals that can be quite complex. A simple example would be for the bonding orbitals of the water molecule. As shown in Figure 14.1, localized orbitals can... 

The interaction between the three cr localized orbitals is slightly more complex. As we have just shown, it is proper to start by combining orbitals of same energy (the crCIf2 pair), and then to interact the new combinations with the remaining orbitals. The procedure is simple here because, by symmetry, only the in-phase combination of the crCH2 group orbitals mixes with the acc bond orbital (see Fig. 17). The reader will notice that the acc orbital has been placed,... 

For elements adjacent to the noble gases the principal orbitals used in bond formation are those formed by hybridisation of the s and p orbitals. For the transition elements there are nine stable orbitals to be taken into consideration, which in general are hybrids of five d orbitals, one s orbital, and three p orbitals. An especially important set of six bond orbitals, directed toward the comers of a regular octahedron, are the d2sps orbitals, which are involved in most of the Werner octahedral complexes formed by the transition elements. 

The stability of sexivalent chromium, in the chromate ion and related ions, can also be understood. The chromic complexes, involving tervalent chromium, make use of d2sp3 bond orbitals, the three remaining outer electrons of the chromium atom being in three of the 3d orbitals, with parallel spins. The resonance energy of these three atomic electrons in a quartet state helps to stabilise the chromic compounds. However, if all of the nine outer orbitals of the chromium atom were available for bond formation, stable compounds might also be expected... 

Two other, closely related, consequences flow from our central proposition. If the d orbitals are little mixed into the bonding orbitals, then, by the same token, the bond orbitals are little mixed into the d. The d electrons are to be seen as being housed in an essentially discrete - we say uncoupled - subset of d orbitals. We shall see in Chapter 4 how this correlates directly with the weakness of the spectral d-d bands. It also follows that, regardless of coordination number or geometry, the separation of the d electrons implies that the configuration is a significant property of Werner-type complexes. Contrast this emphasis on the d" configuration in transition-metal chemistry to the usual position adopted in, say, carbon chemistry where sp, sp and sp hybrids form more useful bases. Put another way, while the 2s... 

Bonding orbitals in a metal complex may be thought of as molecular orhitals built from appropriate metal and ligand functions. In the case of an M-L o bond orbital, i/ , for example, we write... 

Among the compounds that form complexes with silver and other metals are benzene (represented as in 9) and cyclooctatetraene. When the metal involved has a coordination number >1, more than one donor molecule participates. In many cases, this extra electron density comes from CO groups, which in these eomplexes are called carbonyl groups. Thus, benzene-chromium tricarbonyl (10) is a stable compound. Three arrows are shown, since all three aromatic bonding orbitals contribute some electron density to the metal. Metallocenes (p. 53) may be considered a special case of this type of complex, although the bonding in metallocenes is much stronger. 

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