Ligand field theory (LFT) describes the bonding in coordination complexes. The term complex in Chemistry is usually used to describe molecules or ensembles formed by the combination of Ligands and metal Ions. ^[1] It represents an application of molecular orbital theory to transition metal complexes. In Chemistry, molecular orbital theory ( MO theory) is a method for determining molecular structure in which Electrons are not assigned to individual A transition metal ion has six hybridized atomic orbitals of equal energy to engage its ligands. An atomic orbital is a Mathematical function that describes the wave-like behavior of an electron in an atom In Chemistry, a ligand is either an Atom, Ion, or Molecule (see also Functional group) that bonds to a central metal generally For first row transition metals, n = 3; for second and third row metals, n = 4 and 5, respectively. The LFT analysis depends on the geometry of the complex, but for explanatory purposes, most analyses focus on octahedral complexes, where six ligands coordinate to the metal. In Chemistry, octahedral molecular geometry describes the shape of compounds where in six atoms or groups of atoms or Ligands are symmetrically arranged around ^[2]

σ-Bonding

The molecular orbitals created by coordination can be seen as resulting from the donation of two electrons by each of six σ-donor ligands to the d-orbitals on the metal. The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J The M acro E xpansion T emplate A ttribute L anguage complements TAL, providing macros which allow the reuse of code across In octahedral complexes, ligands approach along the x-, y- and z-axes, so their σ-symmetry orbitals form bonding and anti-bonding combinations with the d_z² and d_x²−y² orbitals. The d_xy, d_xz and d_yz orbitals remain non-bonding orbitals. Some weak bonding (and anti-bonding) interactions with the s and p orbitals of the metal also occur, to make a total of 6 bonding (and 6 anti-bonding) molecular orbitals.

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). Molecular symmetry in Chemistry describes the Symmetry present in Molecules and the classification of molecules according to their symmetry The irreducible representations that these span are a_1g, t_1u and e_g. In the mathematical field of Representation theory, group representations describe abstract groups in terms of Linear transformations of 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. In the mathematical field of Representation theory, group representations describe abstract groups in terms of Linear transformations of The six σ-bonding molecular orbitals result from the combinations of ligand SALC's with metal orbitals of the same symmetry.

π-bonding

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.

The p-orbitals of the metal are used for σ bonding (and are 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. Symmetry generally conveys two primary meanings The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance such that it reflects beauty or e. d_xy, d_xz and d_yz. 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 of the ligand are anti-bonding π^* orbitals. HOMO and LUMO are Acronyms for highest occupied Molecular orbital and lowest unoccupied Molecular orbital, respectively These orbitals are close in energy to the d_xy, d_xz and d_yz 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, Δ_O 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 d_xy, d_xz and d_yz 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 of the complex. HOMO and LUMO are Acronyms for highest occupied Molecular orbital and lowest unoccupied Molecular orbital, respectively For that reason, Δ_O decreases when ligand-to-metal bonding occurs.

The greater stabilisation 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. Synergy (from the Greek el-Latn syn-ergo, el συνεργός meaning working together is the term used to describe a situation where the final outcome

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 t_2g symmetry. The d_xy, d_xz and d_yz 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 t_2g symmetry. )

High and low spin and the spectrochemical series

The six bonding molecular orbitals that are formed are "filled" with the electrons from the ligands, and electrons from the d-orbitals of the metal ion occupy the non-bonding and, in some cases, anti-bonding MO's. The energy difference between the latter two types of MO's is called Δ_o (o stands for octahedral) and is determined by the nature of the π-interaction between the ligand orbitals with the d-orbitals on the central atom. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός As described above, π-donor ligands lead to a small Δ_O and are called weak- or low-field ligands, whereas π-acceptor ligands lead to a large value of Δ_O and are called strong- or high-field ligands. Ligands that are neither π-donor nor π-acceptor give a value of Δ_O somewhere in-between.

The size of Δ_O determines the electronic structure of the d⁴ - d⁷ ions. In complexes of metals with these d-electron configurations, the non-bonding and anti-bonding molecular orbitals can be filled in two ways: one in which as many electrons as possible are put in the non-bonding orbitals before filling the anti-bonding orbitals, and one in which as many unpaired electrons as possible are put in. The former case is called low-spin, while the latter is called high-spin. A small Δ_O can be overcome by the energetic gain from not pairing the electrons, leading to high-spin. When Δ_O is large, however, the spin-pairing energy becomes negligible by comparison and a low-spin state arises.

The spectrochemical series is an empirically-derived list of ligands ordered by the size of the splitting Δ that they produce. A spectrochemical series is a list of Ligands ordered on ligand strength and a list of metal ions based on oxidation number group and its identity It can be seen that the low-field ligands are all π-donors (such as I^-), the high field ligands are π-acceptors, such as CN^- and CO), and ligands such as H₂O and NH₃, which are neither, are in the middle.

I⁻ < Br⁻ < S²⁻ < SCN⁻ < Cl⁻ < NO₃⁻ < N₃⁻ < F⁻ < OH⁻ < C₂O₄²⁻ < H₂O < NCS⁻ < CH₃CN < py (pyridine) < NH₃ < en (ethylenediamine) < bipy (2,2'-bipyridine) < phen (1,10-phenanthroline) < NO₂⁻ < PPh₃ < CN⁻ < CO

History

Ligand field theory was developed during the 1930s and 1940s as an extension of crystal field theory (CFT). Pyridine is a Chemical compound with the formula C5[[Hydrogen H5]] N. Ethylenediamine (abbreviated as en when a Ligand) is the Organic compound with the formula C2H4(NH22 22'-Bipyridine is a Chemical compound with the formula (C5H4N2 Phenanthroline is a Heterocyclic Organic compound. As a bidentate ligand in Coordination chemistry, commonly abbreviated "phen" it forms The 1930s were described as an abrupt shift to more radical and conservative lifestyles as countries were struggling to find a solution to the Great Depression. The 1940s decade ran from 1940 to 1949 Events and trends The 1940s was a period between the radical 1930s and the conservative 1950s which also leads the period to be Crystal field theory (CFT is a model that describes the Electronic structure of Transition metal compounds all of which can be considered coordination CFT describes certain properties of coordination complexes but is based on a model that emphasizes electrostatic interactions between ligand electrons with the d-electrons on the metal. The term complex in Chemistry is usually used to describe molecules or ensembles formed by the combination of Ligands and metal Ions. CFT does not describe bonding. Ligand Field Theory, in a sense, combined CFT and the then emerging molecular orbital theory. In Chemistry, a molecular orbital (or MO) is a region in which an Electron may be found in a Molecule.

References

1. ^ Schläfer, H. L. ; Gliemann, G. "Basic Principles of Ligand Field Theory" Wiley Interscience: New York; 1969
2. ^ G. L. Miessler and D. A. Tarr “Inorganic Chemistry” 3rd Ed, Pearson/Prentice Hall publisher, ISBN 0-13-035471-6.

See also

• Crystal field theory
• Molecular orbital theory