Ligand field theory and pi bonding in complexes
Crystal field theory explains directional d orbital splitting through electrostatic repulsion but omits covalent bonding. Ligand field theory includes orbital overlap and pi bonding to explain why carbon monoxide and cyanide rank above water and halides.
What a learner can do afterwards
- Builds an octahedral orbital diagram from the ligand combinations and identifies where the split appears
- Distinguishes pi donor from pi acceptor ligands and predicts the effect of each on the splitting
- Explains the position of carbon monoxide in the series through back-donation
- States what crystal field theory cannot explain and how the orbital picture repairs it
1 · Read
Crystal field theory treats ligands as negative dots and gets the octahedral splitting pattern right: two orbitals up, three down. But dots cannot donate or accept pi electrons, so the theory has nothing to say about pi bonding. It cannot explain why fluoride sits low in the series and cyanide sits high. Neutral CO sits at the strong end through back-donation, despite having no ligand charge.
Ligand field theory replaces point charges with orbitals while keeping the octahedral splitting pattern. Ligand orbitals combine into symmetry-adapted groups that mix with metal orbitals of the same label. With sigma bonding alone, the metal eg pair mixes with ligand groups and rises as antibonding, while the t2g trio has no sigma partner and stays nonbonding. The gap between t2g and eg is explained through covalent orbital interactions, extending the electrostatic model.
Pi bonding then changes the sigma-only picture. Filled ligand pi orbitals interact with the metal lower set and push it up, which narrows the gap. Empty ligand pi orbitals do the reverse. They accept density back from the metal and pull the lower set down, which widens the gap.
Now the series order makes sense: pi acceptors strong, pure sigma donors in the middle, pi donors weak. Carbon monoxide donates sigma density and then accepts metal density back into its empty pi orbitals. Cyanide, like carbon monoxide, has empty pi orbitals and acts as a pi acceptor. Both widen the gap and sit at the strong end, even though CO is neutral. Water and halides donate pi density and compress the gap, landing at the weak end.
Orbital overlap explains the splitting, and pi donation shrinks the gap while pi acceptance widens it.
Written for this project.
Readings written for this project.
2 · Watch
Take it off screen
Where it sits
Optional connections
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.