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Ligand field theory (LFT) describes the bonding, orbital arrangement, and other characteristics of
coordination complexes A coordination complex consists of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of bound molecules or ions, that are in turn known as ''ligands'' or complexing agents. Many ...
. It represents an application of
molecular orbital theory In chemistry, molecular orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century. In molecular orbital theory, electrons in a molec ...
to
transition metal In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. They are the elements that can ...
complexes. A transition metal ion has nine valence
atomic orbital In atomic theory and quantum mechanics, an atomic orbital is a function describing the location and wave-like behavior of an electron in an atom. This function can be used to calculate the probability of finding any electron of an atom in any sp ...
s - consisting of five ''n''d, one (''n''+1)s, and three (''n''+1)p orbitals. These orbitals are of appropriate energy to form bonding interaction with ligands. The LFT analysis is highly dependent on the geometry of the complex, but most explanations begin by describing
octahedral In geometry, an octahedron (plural: octahedra, octahedrons) is a polyhedron with eight faces. The term is most commonly used to refer to the regular octahedron, a Platonic solid composed of eight equilateral triangles, four of which meet at ea ...
complexes, where six ligands coordinate to the metal. Other complexes can be described by reference to crystal field theory.G. L. Miessler and D. A. Tarr "Inorganic Chemistry" 3rd Ed, Pearson/Prentice Hall publisher, .


History

Ligand field theory resulted from combining the principles laid out in molecular orbital theory and
crystal field theory Crystal field theory (CFT) describes the breaking of degeneracies of electron orbital states, usually ''d'' or ''f'' orbitals, due to a static electric field produced by a surrounding charge distribution (anion neighbors). This theory has been used ...
, which describes the loss of degeneracy of metal d orbitals in transition metal complexes. John Stanley Griffith and
Leslie Orgel Leslie Eleazer Orgel FRS (12 January 1927 – 27 October 2007) was a British chemist. He is known for his theories on the origin of life. Biography Leslie Orgel was born in London, England, on . He received his Bachelor of Arts degree in chemi ...
Griffith, J.S. and L.E. Orgel
"Ligand Field Theory".
''Q. Rev. Chem. Soc.'' 1957, 11, 381-393
championed ligand field theory as a more accurate description of such complexes, although the theory originated in the 1930s with the work on magnetism of 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. That is, the unoccupied d orbitals of transition metals participate in bonding, which influences the colors they absorb in solution. In ligand field theory, the various d orbitals are affected differently when surrounded by a field of neighboring ligands and are raised or lowered in energy based on the strength of their interaction with the ligands.


Bonding


σ-bonding (sigma bonding)

In an octahedral complex, 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 A metal (from Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electricity and heat relatively well. Metals are typica ...
. 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''''z''2 and ''d''''x''2−''y''2 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 In
molecular symmetry Molecular symmetry in chemistry describes the symmetry present in molecules and the classification of these molecules according to their symmetry. Molecular symmetry is a fundamental concept in chemistry, as it can be used to predict or explain ...
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 ''d''''z''2 and ''d''''x''2−''y''2 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 (pi 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. 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. ''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 (lowest unoccupied molecular orbitals) of the ligand are anti-bonding π* orbitals. 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, 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 ''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 (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 Synergy is an interaction or cooperation giving rise to a whole that is greater than the simple sum of its parts. The term ''synergy'' comes from the Attic Greek word συνεργία ' from ', , meaning "working together". History In Christia ...
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 ''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 ''t2g'' 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 MOs. The energy difference between the latter two types of MOs is called ΔO (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. As described above, π-donor ligands lead to a small ΔO and are called weak- or low-field ligands, whereas π-acceptor ligands lead to a large value of ΔO and are called strong- or high-field ligands. Ligands that are neither π-donor nor π-acceptor give a value of ΔO somewhere in-between. The size of ΔO determines the electronic structure of the ''d''4 - ''d''7 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 ΔO can be overcome by the energetic gain from not pairing the electrons, leading to high-spin. When ΔO 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. 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 Ethylenediamine (abbreviated as en when a ligand) is the organic compound with the formula C2H4(NH2)2. This colorless liquid with an ammonia-like odor is a basic amine. It is a widely used building block in chemical synthesis, with approximately 5 ...
) < bipy (
2,2'-bipyridine The comma is a punctuation mark that appears in several variants in different languages. It has the same shape as an apostrophe or single closing quotation mark () in many typefaces, but it differs from them in being placed on the baseline ...
) < phen (1,10-
phenanthroline 1,10-Phenanthroline (phen) is a heterocyclic organic compound. It is a white solid that is soluble in organic solvents. The 1,10 refer to the location of the nitrogen atoms that replace CH's in the hydrocarbon called phenanthrene. Abbreviate ...
) < NO2 < PPh3 < CN < CO


See also

*
Crystal field theory Crystal field theory (CFT) describes the breaking of degeneracies of electron orbital states, usually ''d'' or ''f'' orbitals, due to a static electric field produced by a surrounding charge distribution (anion neighbors). This theory has been used ...
*
Ligand dependent pathway There are two types of pathway for substitution of ligands in a complex. The ligand dependent pathway is the one whereby the chemical properties of the ligand affect the rate of substitution. Alternatively, there is the ligand independent pathwa ...
*
Molecular orbital theory In chemistry, molecular orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century. In molecular orbital theory, electrons in a molec ...
*
Nephelauxetic effect The nephelauxetic effect is a term used in the inorganic chemistry of transition metals. It refers to a decrease in the Racah interelectronic repulsion parameter, given the symbol ''B'', that occurs when a transition-metal free ion forms a comple ...


References


External links


Crystal-field Theory, Tight-binding Method, and Jahn-Teller Effect
in E. Pavarini, E. Koch, F. Anders, and M. Jarrell (eds.): Correlated Electrons: From Models to Materials, Jülich 2012, {{Organometallics Chemical bonding Inorganic chemistry