Molecular orbitals for octahedral complexes

The six ligand donor orbitals collectively form a reducible representation E in the point group. This representation can be reduced by the method described in Section 4-4-2 applied to the character table in Table 10-4. This results in r - Aig + Tiu + Eg, shown in the last rows of the table. 

Bonding interaction between two ligand orbitals and metal d 2 orbital 

Bonding interaction between four ligand orbitals and metal if i 2 orbital 

As in Chapter 5, we will first consider group orbitals on ligands based on Oh symmetry, and then consider how these group orbitals can interact with orbitals of matching symmetry on the central atom, in this case a transition metal. We will consider sigma interactions first. The character table for Oh symmetry is provided in Table 10.4. 

The basis for a reducible representation is a set of six donor orbitals on the ligands as, for example, o--donor orbitals on six NH3 ligands. Using this set as a basis—or equivalently 

Pi bonding interaction between four ligand orbitals 

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

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 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... 

Fig. 4.4 Molecular orbital diagram for octahedral complexes (cr-interaction only)...

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

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... 

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,... 

It is extremely common for coordination compounds also to exhibit strong charge-transfer absorptions, typically in the ultraviolet and/or visible portions of the spectrum. These absorptions may be much more intense than d-d transitions (which for octahedral complexes usually have e values of 20 L moF cm or less) molar absorp-tivities of 50,000 L mole cm or greater are not uncommon for these bands. Such absorption bands involve the transfer of electrons from molecular orbitals that are primarily ligand in character to orbitals that are primarily metal in character (or vice versa). For example, consider an octahedral d complex with cr-donor ligands. The ligand electron pairs are stabilized, as shown in Figure 11-15. 

Figure 1. Molecular orbital (ligand field) diagram for octahedral complex (schematic)...

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 ... 

A molecular orbital theory for octahedral / complexes is described. It is pointed out that the neglect of covalent bonding in the analysis of optical data for the actinide complexes is not justified, and that its inclusion leads to orbital reductions which are considerably greater than have usually been assumed. 

On the basis of this molecular orbital treatment it is a fairly simple matter to make approximate predictions as to the composition of the various levels. Following Figgis (5) we may classify the metal or ligand contribution to a given molecular orbital as large (80%), moderate (50%), or small (20%), and the usual situation for octahedral complexes is shown in Table 1 (ii). Thus the highest Isdng orbitals, 2 hg and 2 eg are dominantly metal in character, and the occupation of these levels... 

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

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