Ligand field theory

Ligand field theory (LFT) describes the bonding, orbital arrangement, and other characteristics of coordination complexes. It represents an application of molecular orbital theory to transition metal complexes. A transition metal ion has nine valence atomic orbitals - consisting of five nd, one (n+1)s, and three (n+1)p orbitals. These orbitals have the appropriate energy to form bonding interactions with ligands. The LFT analysis is highly dependent on the geometry of the complex, but most explanations begin by describing octahedral complexes, where six ligands coordinate with the metal. Other complexes can be described with reference to crystal field theory. Inverted ligand field theory (ILFT) elaborates on LFT by breaking assumptions made about relative metal and ligand orbital energies.

History

Ligand field theory resulted from combining the principles laid out in molecular orbital theory and crystal field theory, which describe the loss of degeneracy of metal d orbitals in transition metal complexes. John Stanley Griffith and Leslie Orgel championed ligand field theory as a more accurate description of such complexes, although the theory originated in the 1930s with the work on magnetism by John Hasbrouck Van Vleck. Griffith and Orgel used the electrostatic principles established in crystal field theory to describe transition metal ions in solution and used molecular orbital theory to explain the differences in metal-ligand interactions, thereby explaining such observations as crystal field stabilization and visible spectra of transition metal complexes. In their paper, they proposed that the chief cause of color differences in transition metal complexes in solution is the incomplete d orbital subshells.

[[Image:LFTi(III).png|center|thumb|400px|Ligand-Field scheme summarizing σ-bonding in the octahedral complex [Ti(H₂O)₆]³⁺.]]

In molecular symmetry terms, the six lone-pair orbitals from the ligands (one from each ligand) form six symmetry-adapted linear combinations (SALCs) of orbitals, also sometimes called ligand group orbitals (LGOs). The irreducible representations that these span are a_1g, t_1u and e_g. The metal also has six valence orbitals that span these irreducible representations - the s orbital is labeled a_1g, a set of three p-orbitals is labeled t_1u, and the d_z² and d_{x²−y²} orbitals are labeled e_g. The six σ-bonding molecular orbitals result from the combinations of ligand SALCs with metal orbitals of the same symmetry.