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Spin states when describing
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 ...
coordination complex 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 ...
es refers to the potential spin configurations of the central metal's d electrons. For several oxidation states, metals can adopt high-spin and low-spin configurations. The ambiguity only applies to first row metals, because second- and third-row metals are invariably low-spin. These configurations can be understood through the two major models used to describe coordination complexes;
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 ...
and
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 valen ...
(a more advanced version based on
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 molecule ...
).


High-spin vs. low-spin


Octahedral complexes

The Δ splitting of the ''d'' orbitals plays an important role in the electron spin state of a coordination complex. Three factors affect Δ: the period (row in periodic table) of the metal ion, the charge of the metal ion, and the field strength of the complex's ligands as described by the
spectrochemical series A spectrochemical series is a list of ligands ordered by ligand "strength", and a list of metal ions based on oxidation number, group and element. For a metal ion, the ligands modify the difference in energy Δ between the d orbitals, called the l ...
. Only octahedral complexes of first row transition metals adopt high-spin states. In order for low spin splitting to occur, the energy cost of placing an electron into an already singly occupied orbital must be less than the cost of placing the additional electron into an e''g'' orbital at an energy cost of Δ. If the energy required to pair two electrons is greater than the energy cost of placing an electron in an e''g'', Δ, high spin splitting occurs. If the separation between the orbitals is large, then the lower energy orbitals are completely filled before population of the higher orbitals according to the
Aufbau principle The aufbau principle , from the German ''Aufbauprinzip'' (building-up principle), also called the aufbau rule, states that in the ground state of an atom or ion, electrons fill subshells of the lowest available energy, then they fill subshells o ...
. Complexes such as this are called "low-spin" since filling an orbital matches electrons and reduces the total electron spin. If the separation between the orbitals is small enough then it is easier to put electrons into the higher energy orbitals than it is to put two into the same low-energy orbital, because of the repulsion resulting from matching two electrons in the same orbital. So, one electron is put into each of the five ''d'' orbitals before any pairing occurs in accord with
Hund's rule Hund's rule of maximum multiplicity is a rule based on observation of atomic spectra, which is used to predict the ground state of an atom or molecule with one or more open electronic shells. The rule states that for a given electron configuration ...
resulting in what is known as a "high-spin" complex. Complexes such as this are called "high-spin" since populating the upper orbital avoids matches between electrons with opposite spin. The charge of the metal center plays a role in the ligand field and the Δ splitting. The higher the oxidation state of the metal, the stronger the ligand field that is created. In the event that there are two metals with the same d electron configuration, the one with the higher oxidation state is more likely to be low spin than the one with the lower oxidation state; for example, Fe2+ and Co3+ are both d6; however, the higher charge of Co3+ creates a stronger ligand field than Fe2+. All other things being equal, Fe2+ is more likely to be high spin than Co3+. Ligands also affect the magnitude of Δ splitting of the ''d'' orbitals according to their field strength as described by the
spectrochemical series A spectrochemical series is a list of ligands ordered by ligand "strength", and a list of metal ions based on oxidation number, group and element. For a metal ion, the ligands modify the difference in energy Δ between the d orbitals, called the l ...
. Strong-field ligands, such as CN and CO, increase the Δ splitting and are more likely to be low-spin. Weak-field ligands, such as I and Br cause a smaller Δ splitting and are more likely to be high-spin. Some octahedral complexes exhibit
spin crossover Spin crossover (SCO) is a phenomenon that occurs in some metal complexes wherein the spin state of the complex changes due to an external stimulus. The stimuli can include temperature or pressure. Spin crossover is sometimes referred to as spin ...
, where the high and low spin states exist is dynamic equilibrium.


Tetrahedral complexes

The Δ splitting energy for tetrahedral metal complexes (four ligands), Δtet is smaller than that for an octahedral complex. Consequently, tetrahedral complexes are almost always high spin Examples of low spin tetrahedral complexes include Fe(2-norbornyl)4, o(4-norbornyl)4sup>+, and the
nitrosyl complex Sodium nitroprusside, a medicinally significant metal nitrosyl-pentacyanoferrate (Fe-III) compound, used to treat hypertension. Metal nitrosyl complexes are complex (chemistry), complexes that contain nitric oxide, NO, bonded to a transition me ...
Cr(NO)( (N(tms)2)3.


Square planar complexes

Many d8 complexes of the first row metals exist in tetrahedral or square planar geometry. In some cases these geometries exist in measurable equilibria. For example,
dichlorobis(triphenylphosphine)nickel(II) Dichlorobis(triphenylphosphine)nickel(II) refers to a pair of metal phosphine complexes with the formula NiCl2 (C6H5)3sub>2. The compound exists as two isomers, a paramagnetic dark blue solid and a diamagnetic red solid. These complexes function ...
has been crystallized in both tetrahedral and square planar geometries.


Ligand field theory vs crystal field theory

In terms of d-orbital splitting,
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 valen ...
(LFT) 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 ...
(CFT) give similar results. CFT is an older, simpler model that treats ligands as point charges. LFT is more chemical, emphasizes covalent bonding and accommodates pi-bonding explicitly.


High-spin and low-spin systems

In the case of octahedral complexes, the question of high spin vs low spin first arises for d4, since it has more than the 3 electrons to fill the non-bonding d orbitals according to ligand field theory or the stabilized d orbitals according to crystal field splitting. All complexes of second and third row metals are low-spin. ;d4: :Octahedral high-spin: 4 unpaired electrons,
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
, substitutionally labile. Includes Cr2+. Many complexes assigned as Cr(II) are however Cr(III) with reduced ligands.), Mn3+. :Octahedral low-spin: 2 unpaired electrons,
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
, substitutionally inert. Includes Cr2+, Mn3+. ;d5: :Octahedral high-spin: 5 unpaired electrons,
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
, substitutionally labile. Includes Fe3+, Mn2+. Example:
Tris(acetylacetonato)iron(III) Tris(acetylacetonato) iron(III), often abbreviated Fe(acac)3, is a ferric coordination complex featuring acetylacetonate (acac) ligands, making it one of a family of metal acetylacetonates. It is a red air-stable solid that dissolves in nonpolar ...
. :Octahedral low-spin: 1 unpaired electron,
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
, substitutionally inert. Includes Fe3+. Example: e(CN)6sup>3−. ;d6: :Octahedral high-spin: 4 unpaired electrons,
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
, substitutionally labile. Includes Fe2+, Co3+. Examples: e(H2O)6sup>2+, oF6sup>3−. :Octahedral low-spin: no unpaired electrons,
diamagnetic Diamagnetic materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted ...
, substitutionally inert. Includes Fe2+, Co3+, Ni4+. Example: o(NH3)6sup>3+. ;d7: :Octahedral high-spin: 3 unpaired electrons,
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
, substitutionally labile. Includes Co2+, Ni3+. :Octahedral low-spin:1 unpaired electron,
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
, substitutionally labile. Includes Co2+, Ni3+. Example: o(NH3)6sup>2+. ;d8:Octahedral high-spin: 2 unpaired electrons,
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
, substitutionally labile. Includes Ni2+. Example: i(NH3)6sup>2+. :Tetrahedral high-spin: 2 unpaired electrons,
paramagnetic Paramagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, d ...
, substitutionally labile. Includes Ni2+. Example: iCl4sup>2-. :Square planar low-spin: no unpaired electrons,
diamagnetic Diamagnetic materials are repelled by a magnetic field; an applied magnetic field creates an induced magnetic field in them in the opposite direction, causing a repulsive force. In contrast, paramagnetic and ferromagnetic materials are attracted ...
, substitutionally inert. Includes Ni2+. Example: i(CN)4sup>2−.


Ionic radii

The spin state of the complex affects an atom's
ionic radius Ionic radius, ''r''ion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation ...
. For a given d-electron count, high-spin complexes are larger. ;d4 :Octahedral high spin: Cr2+, 64.5 pm. :Octahedral low spin: Mn3+, 58 pm. ;d5: :Octahedral high spin: Fe3+, the ionic radius is 64.5 pm. :Octahedral low spin: Fe3+, the ionic radius is 55 pm. ;d6 :Octahedral high spin: Fe2+, the ionic radius is 78 pm, Co3+ ionic radius 61 pm. :Octahedral low spin: Includes Fe2+ ionic radius 62 pm, Co3+ ionic radius 54.5 pm, Ni4+ ionic radius 48 pm. ;d7 :Octahedral high spin: Co2+ ionic radius 74.5 pm, Ni3+ ionic radius 60 pm. :Octahedral low spin: Co2+ ionic radius 65 pm, Ni3+ionic radius 56 pm. ;d8 :Octahedral high spin: Ni2+ ionic radius 69 pm. :Square planar low-spin: Ni2+ ionic radius 49 pm.


Ligand exchange rates

Generally, the rates of ligand dissociation from low spin complexes are lower than dissociation rates from high spin complexes. In the case of octahedral complexes, electrons in the eg levels are anti-bonding with respect to the metal-ligand bonds. Famous "exchange inert" complexes are octahedral complexes of d3 and low-spin d6 metal ions, illustrated respectfully by Cr3+ and Co3+.


References

{{organometallics Coordination chemistry Electron states