Molecular orbitals for octahedral

Fig. 1. Construction of molecular orbitals for octahedral coordination complexes of non w-bonding ligands utilizing metal 3

Fig. 25. Molecular orbitals for octahedral B6 and Co6 clusters based on extended Hiickel calculations (155).

Figure 1.10 Molecular orbitals for octahedral and square-based pyramidal complexes...

Molecular Orbitals for Octahedral Metal Carixmyls and Cyanides.— The coordinate stem adopted for tiie case of full metal valence orbitals are d, ( -h l)s, and ( + l)p. The carbon 2s mid 2pr orbitals will be used for ff-bonding for x-bonding, both the ligand x-bonding (x ) and x-antibonding (x ) molecidar orbitals will be combined urith the d, and p, metal orbitals to form the x-molecular orbital system for the complex. The sin e electron molecular orbitals all are assumed to have the form... 

FIGU RE 17.14 The coordinate system to designate orbitals used in constructing molecular orbitals for an octahedral complex. 

In solids where cation-cation interaction is significant, by can be related to R, where R is the cation-cation separation. In cases where cation-anion-cation interaction is important, by is related to the covalent mixing parameter, X, of the cation-anion orbitals. For octahedrally coordinated cations, as in rocksalt and perovskite structures, the relevant mixing parameters are and in the following molecular wave functions... 

Let us now consider in some detail the molecular orbitals for an octahedral complex containing a first-row transition metal ion. The orbitals that will be used in the bonding scheme are the 3d, 4s, and 4p orbitals of the central atom and the ns and np orbitals of the ligands. The coordinate system that is convenient for the construction of a and n MO s is shown in Figure 8-2. The character table for the Ojj symmetry is given in Table 8-1. 

The energies of the molecular orbitals for an octahedral complex ml6 are shown in Figure 8-15. There are 36 + n electrons to place in the molecular orbitals (6 from each ligand and n from the central atom). As a simple example, we find that the ground state of TiP is... 

There will always be 36 electrons (6 from each ligand) to place in the molecular orbitals for the complex. In addition, the metal may furnish as many as 6 valence electrons for an octahedral metal carbonyl or cyanide complex. The ground state for a d6 metsl hexacarbonyl or hexacyanide is therefore... 

FIGURE 10-5 Molecular Orbitals for an Octahedral Transition Metal Complex. As in Chapter 5, the symmetry labels of the atomic orhitals are capitalized and the labels of the molecular orbitals are in lowercase. (Adapted from R A. Cotton,... 

A complete study of the molecular orbitals for an octahedral complex sue as [Cr(CN)6] or [Co(NH3)6] " " would require linear combinations of all the valence atomic orbitals of the metal and of the ligands. An approximation isl to take the metal valence a.o.s (nine a.o.s for a metal of the first transition series (five 3d orbitals, one 4s and three 4p orbitals)) together with six a.o.s from the ligands, one for each atom directly bonded to the metal atom. Ini general, these six a.o.s are quasi-localized molecular orbitals (see Chapter 8), which point from the ligand to the metal and have essentially non-bonding character ... 

Figure 2.3. Molecular orbitals for an octahedral MLg complex in the orientation given in Scheme 2-2.

Fig. 2 Stone molecular orbitals for the octahedral [BsHg] cluster with a/tt mixing middle). The and V orbitals are given on the left and on the right, respectively...

Fig. 2. Simplified molecular orbital diagram for a low spia octahedral complex, such as [Co(NH3 )g, where A = energy difference a, e, and t may be antisymmetric (subscript ungerade) or centrosymmetric (subscript, gerade) symmetry orbitals. See text.

Figure 19.14 Molecular orbital diagram for an octahedral complex of a first series transition metal (only a interactions are considered in this simplified diagram).

The foregoing discussion indicates that while there are difficulties in the way of a bonding role for 3d orbitals, for certain situations at least it is possible to conceive of ways in which these difficulties may be overcome. However, it is necessary to say that even for hypervalent molecules such as SF6 which seem to require the use of d orbitals, there are molecular orbital treatments not involving the use of d orbitals. In fact, as shown by Bent in an elegant exposition12, the MO model of SF6 involving the use of d orbitals is only one of several possibilities. The octahedral stereochemistry of SF6, traditionally explained in... 

---