Complexes with no metal–ligand π-bonding

   We illustrate the application of MO theory to d-block metal complexes first by considering an octahedral complex such as [Co)NH₃(₆]³⁺‏ in which metal–ligand π-bonding is dominant.  In the construction of an M energy level diagram for such a complex, many approximations are made and the result is only qualitatively accurate. Even so, the results are useful to an understanding of metal–ligand bonding. For a first row metal, the valence shell atomic orbitals are 3d, 4s and 4p. Under Oh symmetry, the s orbital has a_1g symmetry, the p orbitals are degenerate with t_1u symmetry, and the d orbitals split into two sets with eg (d_z² and d_x²_-y² orbitals) and t_2g (d_xy, d_yz and d_xz orbitals) symmetries, respectively (Figure 1.1). Each ligand, L, provides one orbital and derivation of the ligand group orbitals for the O_h L₆ fragment is analogous to those for the F₆ fragment in SF₆. These LGOs have a1g, t_1u and e_g symmetries (Figure 1.1).

Fig. 1.1 Metal atomic orbitals s, p_x, p_y, p_z, d_x² _{_y}² , d_z² matched by symmetry with ligand group orbitals for an octahedral(Oh)complex with only π-bonding.

   Symmetry matching between metal orbitals and LGOs allows the construction of the MO diagram shown in Figure 1.2.  Combinations of the metal and ligand orbitals generate six bonding and six antibonding molecular orbitals. The metal d_xy, d_yz and d_xz atomic orbitals have t_2g symmetry and are non-bonding (Figure 1.2).

Fig. 1.2 An approximate MO diagram for the formation of [ML₆]^n‏+ (where M is a first row metal) using the ligand group orbital approach; the orbitals are shown pictorially in Figure 1.1. The bonding only involves M^_L π-interactions.

    The overlap between the ligand and metal s and p orbitals is greater than that involving the metal d orbitals, and so the a_1g and t_1u MOs are stabilized to a greater extent than the eg MOs. In an octahedral complex with no π-bonding, the energy difference between the t_2g and e_g^* levels corresponds to Δ_oct in crystal field theory (Figure 1.2).   Having constructed the MO diagram in Figure 1.2, we are able to describe the bonding in a range of octahedral σ- bonded complexes. For example:

• in low-spin [Co(NH₃)₆]³⁺, 18 electrons (six from Co³⁺ and two from each ligand) occupy the a_1g, t_1u, e_g and t_2g MOs;
• in high-spin [CoF₆]^3-, 18 electrons are available, 12 occupy the a_1g, t_1u and e_g MOs, four the t_2g level, and two the e_g^* level.

    Whether a complex is high- or low-spin depends upon the energy separation of the t_2g and e_g^* levels. Notionally, in a σ-bonded octahedral complex, the 12 electrons supplied by the ligands are considered to occupy the a_1g, t_1u and e_g orbitals. Occupancy of the t_2g and e_g^* levels corresponds to the number of valence electrons of the metal ion, just as in crystal field theory. The molecular orbital model of bonding in octahedral complexes gives much the same results as crystal field theory. It is when we move to complexes with M^_L π-bonding that distinctions between the models emerge.