Ligand Field & Molecular Orbital Theory — formula sheet

Ligand field theory: the molecular-orbital treatment of a coordination compound, in which the crystal-field parameters (Δ_o, the Racah parameters) are retained as empirical quantities but are reinterpreted as consequences of metal–ligand orbital overlap rather than of electrostatic repulsion. It is CFT with covalency allowed back in.

Symmetry-adapted linear combination (SALC): a sum of ligand orbitals, with signs and coefficients chosen so that the combination transforms as one irreducible representation of the molecular point group — and therefore has the same symmetry as some particular metal orbital, or as none.

Δ_o, in the MO picture: the energy gap between the non-bonding t_2g set and the σ-antibonding e_g* set. It is large when the metal–ligand σ overlap is large, because strong overlap pushes e_g* high; it has nothing directly to do with the ligand’s charge.

π-donor (π-base) ligand: a ligand carrying filled orbitals of π symmetry with respect to the M–L axis, lying below the metal d orbitals in energy. It donates π density to the metal, raises t_2g, and decreases Δ_o.π-acceptor (π-acid) ligand: a ligand carrying empty orbitals of π symmetry, lying above the metal d orbitals. It accepts π density from the metal, lowers t_2g, and increases Δ_o.

Synergic bonding (the Dewar–Chatt–Duncanson picture): a metal–ligand bond with two components that reinforce each other — σ donation from a filled ligand orbital into an empty metal orbital, and π back-donation from a filled metal d orbital into an empty ligand π* orbital. Each component increases the driving force for the other, so the total bond is stronger than either alone would suggest.

Nephelauxetic effect: the reduction of the interelectron repulsion parameter B when a free metal ion is placed in a complex. The name is Greek for ‘cloud-expanding’: the d electrons repel each other less because the orbitals holding them have expanded, spreading onto the ligands. It is a direct measure of the covalency of the metal–ligand bond.

Innocent ligand (Jørgensen): a ligand that allows the oxidation state of the central atom to be defined unambiguously.Non-innocent ligand: one that does not — because it possesses two or more accessible redox forms of comparable energy, so the distribution of electrons between metal and ligand is genuinely ambiguous. The ambiguity is physical, not a failure of bookkeeping.

The 18-electron rule, in MO terms: an octahedral complex has nine molecular orbitals that can be filled without occupying a strongly antibonding level — the six M–L σ-bonding MOs and the three t_2g orbitals. Nine orbitals hold eighteen electrons. The tenth orbital, e_g*, is M–L antibonding, so filling it is resisted whenever Δ_o is large.