Теория поля лигандов и молекулярно-орбитальная теория комплексов переходных металлов.

Molecular orbital theory applied to transition metal complexes
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.

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. 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 a1g, t1u and eg. The metal also has six valence orbitals that span these irreducible representations the s orbital is labeled a1g, a set of three p orbitals is labeled t1u, and the dz2 and dx2−y2 orbitals are labeled eg. The six σ bonding molecular orbitals result from the combinations of ligand SALCs with metal orbitals of the same symmetry.

π bonding in octahedral complexes occurs in two ways: via any ligand p orbitals that are not being used in σ bonding, and via any π or π* molecular orbitals present on the ligand. In the usual analysis, the p orbitals of the metal are used for σ bonding (and have the wrong symmetry to overlap with the ligand p or π or π* orbitals anyway), so the π interactions take place with the appropriate metal d orbitals, i. e. dxy, dxz and dyz. These are the orbitals that are non bonding when only σ bonding takes place. One important π bonding in coordination complexes is metal to ligand π bonding, also called π backbonding. It occurs when the LUMOs (lowest unoccupied molecular orbitals) of the ligand are anti bonding π* orbitals. These orbitals are close in energy to the dxy, dxz and dyz orbitals, with which they combine to form bonding orbitals (i. e. orbitals of lower energy than the aforementioned set of d orbitals). The corresponding anti bonding orbitals are higher in energy than the anti bonding orbitals from σ bonding so, after the new π bonding orbitals are filled with electrons from the metal d orbitals, ΔO has increased and the bond between the ligand and the metal strengthens. The ligands end up with electrons in their π* molecular orbital, so the corresponding π bond within the ligand weakens. The other form of coordination π bonding is ligand to metal bonding. This situation arises when the π symmetry p or π orbitals on the ligands are filled. They combine with the dxy, dxz and dyz orbitals on the metal and donate electrons to the resulting π symmetry bonding orbital between them and the metal. The metal ligand bond is somewhat strengthened by this interaction, but the complementary anti bonding molecular orbital from ligand to metal bonding is not higher in energy than the anti bonding molecular orbital from the σ bonding. It is filled with electrons from the metal d orbitals, however, becoming the HOMO (highest occupied molecular orbital) of the complex. For that reason, ΔO decreases when ligand to metal bonding occurs. The greater stabilization that results from metal to ligand bonding is caused by the donation of negative charge away from the metal ion, towards the ligands. This allows the metal to accept the σ bonds more easily. The combination of ligand to metal σ bonding and metal to ligand
π bonding is a synergic effect, as each enhances the other. As each of the six ligands has two orbitals of π symmetry, there are twelve in total. The symmetry adapted linear combinations of these fall into four triply degenerate irreducible representations, one of which is of t2g symmetry. The dxy, dxz and dyz orbitals on the metal also have this symmetry, and so the π bonds formed between a central metal and six ligands also have it (as these π bonds are just formed by the overlap of two sets of orbitals with t2g symmetry.)