{"history":[],"article":{"id":"6a9c6524-051a-4208-9bff-b4effd36d5b4","title":"Crystal field theory","slug":"crystal-field-theory","content":":::summary\n:::\n\n# \nIn [molecular physics](https://bliptext.com/articles/molecular-physics), **crystal field theory** (**CFT**) describes the breaking of [degeneracies](https://bliptext.com/articles/degenerate-energy-levels) of electron orbital states, usually d or f orbitals, due to a static electric field produced by a surrounding charge distribution (anion neighbors).\nThis theory has been used to describe various spectroscopies of [transition metal](https://bliptext.com/articles/transition-metal) [coordination complexes](https://bliptext.com/articles/complex-chemistry), in particular optical spectra (colors).\nCFT successfully accounts for some [magnetic](https://bliptext.com/articles/magnetic) properties, [colors](https://bliptext.com/articles/color-of-chemicals), [hydration](https://bliptext.com/articles/hydration-reaction) [enthalpies](https://bliptext.com/articles/enthalpy), and [spinel](https://bliptext.com/articles/spinel) structures of transition metal complexes, but it does not attempt to describe bonding.\nCFT was developed by physicists [Hans Bethe](https://bliptext.com/articles/hans-bethe) and [John Hasbrouck van Vleck](https://bliptext.com/articles/john-hasbrouck-van-vleck) in the 1930s.\nCFT was subsequently combined with [molecular orbital theory](https://bliptext.com/articles/molecular-orbital-theory) to form the more realistic and complex [ligand field theory](https://bliptext.com/articles/ligand-field-theory) (LFT), which delivers insight into the process of [chemical bonding](https://bliptext.com/articles/chemical-bonding) in transition metal complexes.\nCFT can be complicated further by breaking assumptions made of relative metal and ligand orbital energies, requiring the use of [inverted ligand field theory](https://bliptext.com/articles/inverted-ligand-field-theory) (ILFT) to better describe bonding.\n\n# Overview\nAccording to crystal field theory, the interaction between a transition metal and [ligands](https://bliptext.com/articles/ligand) arises from the attraction between the positively charged metal cation and the negative charge on the non-bonding electrons of the ligand.\nThe theory is developed by considering energy changes of the five [degenerate](https://bliptext.com/articles/degenerate-orbital) d-orbitals upon being surrounded by an array of point charges consisting of the ligands.\nAs a ligand approaches the metal ion, the electrons from the ligand will be closer to some of the d-orbitals and farther away from others, causing a loss of degeneracy.\nThe electrons in the d-orbitals and those in the ligand repel each other due to repulsion between like charges.\nThus the d-electrons closer to the ligands will have a higher energy than those further away which results in the d-orbitals splitting in energy.\nThis splitting is affected by the following factors:\nThe most common type of complex is [octahedral](https://bliptext.com/articles/octahedral-molecular-geometry), in which six ligands form the vertices of an octahedron around the metal ion.\nIn octahedral symmetry the d-orbitals split into two sets with an energy difference, **Δoct** (the [crystal-field splitting parameter](https://bliptext.com/articles/crystal-field-splitting-parameter), also commonly denoted by 10Dq for ten times the \"differential of quanta\" ) where the dxy, dxz and dyz orbitals will be lower in energy than the dz2 and dx2-y2, which will have higher energy, because the former group is farther from the ligands than the latter and therefore experiences less repulsion.\nThe three lower-energy orbitals are collectively referred to as **t2g**, and the two higher-energy orbitals as **eg**.\nThese labels are based on the theory of [molecular symmetry](https://bliptext.com/articles/molecular-symmetry): they are the names of [irreducible representations](https://bliptext.com/articles/irreducible-representation) of the [octahedral point group](https://bliptext.com/articles/octahedral-symmetry), Oh.(see the [Oh character table](https://bliptext.com/articles/list-of-character-tables-for-chemically-important-3d-point-groups)) Typical orbital energy diagrams are given below in the section High-spin and low-spin.\nTetrahedral complexes are the second most common type; here four ligands form a tetrahedron around the metal ion.\nIn a tetrahedral crystal field splitting, the d-orbitals again split into two groups, with an energy difference of **Δtet**.\nThe lower energy orbitals will be dz2 and dx2-y2, and the higher energy orbitals will be dxy, dxz and dyz - opposite to the octahedral case.\nFurthermore, since the ligand electrons in tetrahedral symmetry are not oriented directly towards the d-orbitals, the energy splitting will be lower than in the octahedral case.\n[Square planar](https://bliptext.com/articles/square-planar-molecular-geometry) and other complex geometries can also be described by CFT.\nThe size of the gap Δ between the two or more sets of orbitals depends on several factors, including the ligands and geometry of the complex.\nSome ligands always produce a small value of Δ, while others always give a large splitting.\nThe reasons behind this can be explained by [ligand field theory](https://bliptext.com/articles/ligand-field-theory).\nThe [spectrochemical series](https://bliptext.com/articles/spectrochemical-series) is an empirically-derived list of ligands ordered by the size of the splitting Δ that they produce (small Δ to large Δ; see also [this table](https://bliptext.com/articles/ligand)):\n[I](https://bliptext.com/articles/iodide)− < [Br](https://bliptext.com/articles/bromide)− < [S](https://bliptext.com/articles/sulfide)2− < [S](https://bliptext.com/articles/sulfide)[CN](https://bliptext.com/articles/cyanide)− ([S](https://bliptext.com/articles/sulfide)–bonded) < [Cl](https://bliptext.com/articles/chloride)− < [NO3](https://bliptext.com/articles/nitrate)− < [N3](https://bliptext.com/articles/azide)− < [F](https://bliptext.com/articles/fluoride)− < [OH](https://bliptext.com/articles/hydroxide)− < [C2O4](https://bliptext.com/articles/oxalate)2− < [H2O](https://bliptext.com/articles/water-molecule) < NC[S](https://bliptext.com/articles/sulfide)− (N–bonded) < [CH3CN](https://bliptext.com/articles/acetonitrile) < [py](https://bliptext.com/articles/pyridine) < [NH3](https://bliptext.com/articles/ammonia) < [en](https://bliptext.com/articles/ethylenediamine) < 2,2'-bi[py](https://bliptext.com/articles/pyridine)ridine < ph[en](https://bliptext.com/articles/ethylenediamine) < [NO2](https://bliptext.com/articles/nitrite)− < [PPh3](https://bliptext.com/articles/triphenylphosphine) < [CN](https://bliptext.com/articles/cyanide)− < [CO](https://bliptext.com/articles/carbon-monoxide).\nIt is useful to note that the ligands producing the most splitting are those that can engage in metal to ligand [back-bonding](https://bliptext.com/articles/pi-backbonding).\nThe oxidation state of the metal also contributes to the size of Δ between the high and low energy levels.\nAs the oxidation state increases for a given metal, the magnitude of Δ increases.\nA V3+ complex will have a larger Δ than a V2+ complex for a given set of ligands, as the difference in charge density allows the ligands to be closer to a V3+ ion than to a V2+ ion.\nThe smaller distance between the ligand and the metal ion results in a larger Δ, because the ligand and metal electrons are closer together and therefore repel more.\n\n## High-spin and low-spin\nLigands which cause a large splitting Δ of the d-orbitals are referred to as strong-field ligands, such as CN− and CO from the [spectrochemical series](https://bliptext.com/articles/spectrochemical-series).\nIn complexes with these ligands, it is unfavourable to put electrons into the high energy orbitals.\nTherefore, the lower energy orbitals are completely filled before population of the upper sets starts according to the [Aufbau principle](https://bliptext.com/articles/aufbau-principle).\nComplexes such as this are called \"low spin\".\nFor example, NO2− is a strong-field ligand and produces a large Δ.\nThe octahedral ion [Fe(NO2)6]3−, which has 5 d-electrons, would have the octahedral splitting diagram shown at right with all five electrons in the t2g level.\nThis low spin state therefore does not follow [Hund's rule](https://bliptext.com/articles/hund-s-rule).\nConversely, ligands (like I− and Br−) which cause a small splitting Δ of the d-orbitals are referred to as weak-field ligands.\nIn this case, it is easier to put electrons into the higher energy set of orbitals than it is to put two into the same low-energy orbital, because two electrons in the same orbital repel each other.\nSo, one electron is put into each of the five d-orbitals in accord with Hund's rule, and \"high spin\" complexes are formed before any pairing occurs.\nFor example, Br− is a weak-field ligand and produces a small Δoct.\nSo, the ion [FeBr6]3−, again with five d-electrons, would have an octahedral splitting diagram where all five orbitals are singly occupied.\nIn 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 eg orbital at an energy cost of Δ.\nAs noted above, eg refers to the\ndz2 and dx2-y2 which are higher in energy than the t2g in octahedral complexes.\nIf the energy required to pair two electrons is greater than Δ, the energy cost of placing an electron in an eg, high spin splitting occurs.\nThe crystal field splitting energy for tetrahedral metal complexes (four ligands) is referred to as Δtet, and is roughly equal to 4/9Δoct (for the same metal and same ligands).\nTherefore, the energy required to pair two electrons is typically higher than the energy required for placing electrons in the higher energy orbitals.\nThus, tetrahedral complexes are usually high-spin.\nThe use of these splitting diagrams can aid in the prediction of magnetic properties of co-ordination compounds.\nA compound that has unpaired electrons in its splitting diagram will be paramagnetic and will be attracted by magnetic fields, while a compound that lacks unpaired electrons in its splitting diagram will be diamagnetic and will be weakly repelled by a magnetic field.\n# [Low Spin [Fe(NO2)6]3− crystal field diagram | upload.wikimedia.org/wikipedia/commons/2/26/CFT-Low///Spin///Splitting///Diagram-Vector.svg]\n# [High Spin [FeBr6]3− crystal field diagram | upload.wikimedia.org/wikipedia/commons/3/31/CFT-High///Spin///Splitting///Diagram-Vector.svg]\n\n# Stabilization energy\nThe crystal field stabilization energy (CFSE) is the stability that results from placing a transition metal ion in the crystal field generated by a set of ligands.\nIt arises due to the fact that when the d-orbitals are split in a ligand field (as described above), some of them become lower in energy than before with respect to a spherical field known as the barycenter in which all five d-orbitals are degenerate.\nFor example, in an octahedral case, the t2g set becomes lower in energy than the orbitals in the barycenter.\nAs a result of this, if there are any electrons occupying these orbitals, the metal ion is more stable in the ligand field relative to the barycenter by an amount known as the CFSE.\nConversely, the eg orbitals (in the octahedral case) are higher in energy than in the barycenter, so putting electrons in these reduces the amount of CFSE.\nIf the splitting of the d-orbitals in an octahedral field is Δoct, the three t2g orbitals are stabilized relative to the barycenter by 2/5 Δoct, and the eg orbitals are destabilized by 3/5 Δoct.\nAs examples, consider the two d5 configurations shown further up the page.\nThe low-spin (top) example has five electrons in the t2g orbitals, so the total CFSE is 5 x 2/5 Δoct = 2Δoct.\nIn the high-spin (lower) example, the CFSE is (3 x 2/5 Δoct) - (2 x 3/5 Δoct) = 0 - in this case, the stabilization generated by the electrons in the lower orbitals is canceled out by the destabilizing effect of the electrons in the upper orbitals.\n# [Octahedral crystal field stabilization energy. Degenerate atomic d-orbitals of a free metal ion (left), destabilization of d-orbitals within a spherical negative electric field (center), and loss of degeneracy relative to the spherical field when ligands are treated as point charges in an octahedral geometry. | upload.wikimedia.org/wikipedia/commons/0/00/Octahedral///cfse.svg]\n\n## Optical properties\nThe optical properties (details of absorption and emission spectra) of many [coordination complexes](https://bliptext.com/articles/coordination-complex) can be explained by Crystal Field Theory.\nOften, however, the deeper colors of metal complexes arise from more intense [charge-transfer excitations](https://bliptext.com/articles/charge-transfer-complex).\n\n# Geometries and splitting diagrams","current_revision":null,"created_by":"kACnuQmH5k9Nr5VNVEpVeg7XpvUmMctD","created_at":"2025-01-25T21:15:43.635Z","updated_at":"2025-01-25T21:15:43.635Z","search_vector":"'crystal':1 'field':2 'theori':3","search_content":" \n \n\n# \nIn [molecular physics](https://bliptext.com/articles/molecular-physics), **crystal field theory** (**CFT**) describes the breaking of [degeneracies](https://bliptext.com/articles/degenerate-energy-levels) of electron orbital states, usually d or f orbitals, due to a static electric field produced by a surrounding charge distribution (anion neighbors).\nThis theory has been used to describe various spectroscopies of [transition metal](https://bliptext.com/articles/transition-metal) [coordination complexes](https://bliptext.com/articles/complex-chemistry), in particular optical spectra (colors).\nCFT successfully accounts for some [magnetic](https://bliptext.com/articles/magnetic) properties, [colors](https://bliptext.com/articles/color-of-chemicals), [hydration](https://bliptext.com/articles/hydration-reaction) [enthalpies](https://bliptext.com/articles/enthalpy), and [spinel](https://bliptext.com/articles/spinel) structures of transition metal complexes, but it does not attempt to describe bonding.\nCFT was developed by physicists [Hans Bethe](https://bliptext.com/articles/hans-bethe) and [John Hasbrouck van Vleck](https://bliptext.com/articles/john-hasbrouck-van-vleck) in the 1930s.\nCFT was subsequently combined with [molecular orbital theory](https://bliptext.com/articles/molecular-orbital-theory) to form the more realistic and complex [ligand field theory](https://bliptext.com/articles/ligand-field-theory) (LFT), which delivers insight into the process of [chemical bonding](https://bliptext.com/articles/chemical-bonding) in transition metal complexes.\nCFT can be complicated further by breaking assumptions made of relative metal and ligand orbital energies, requiring the use of [inverted ligand field theory](https://bliptext.com/articles/inverted-ligand-field-theory) (ILFT) to better describe bonding.\n\n# Overview\nAccording to crystal field theory, the interaction between a transition metal and [ligands](https://bliptext.com/articles/ligand) arises from the attraction between the positively charged metal cation and the negative charge on the non-bonding electrons of the ligand.\nThe theory is developed by considering energy changes of the five [degenerate](https://bliptext.com/articles/degenerate-orbital) d-orbitals upon being surrounded by an array of point charges consisting of the ligands.\nAs a ligand approaches the metal ion, the electrons from the ligand will be closer to some of the d-orbitals and farther away from others, causing a loss of degeneracy.\nThe electrons in the d-orbitals and those in the ligand repel each other due to repulsion between like charges.\nThus the d-electrons closer to the ligands will have a higher energy than those further away which results in the d-orbitals splitting in energy.\nThis splitting is affected by the following factors:\nThe most common type of complex is [octahedral](https://bliptext.com/articles/octahedral-molecular-geometry), in which six ligands form the vertices of an octahedron around the metal ion.\nIn octahedral symmetry the d-orbitals split into two sets with an energy difference, **Δoct** (the [crystal-field splitting parameter](https://bliptext.com/articles/crystal-field-splitting-parameter), also commonly denoted by 10Dq for ten times the \"differential of quanta\" ) where the dxy, dxz and dyz orbitals will be lower in energy than the dz2 and dx2-y2, which will have higher energy, because the former group is farther from the ligands than the latter and therefore experiences less repulsion.\nThe three lower-energy orbitals are collectively referred to as **t2g**, and the two higher-energy orbitals as **eg**.\nThese labels are based on the theory of [molecular symmetry](https://bliptext.com/articles/molecular-symmetry): they are the names of [irreducible representations](https://bliptext.com/articles/irreducible-representation) of the [octahedral point group](https://bliptext.com/articles/octahedral-symmetry), Oh.(see the [Oh character table](https://bliptext.com/articles/list-of-character-tables-for-chemically-important-3d-point-groups)) Typical orbital energy diagrams are given below in the section High-spin and low-spin.\nTetrahedral complexes are the second most common type; here four ligands form a tetrahedron around the metal ion.\nIn a tetrahedral crystal field splitting, the d-orbitals again split into two groups, with an energy difference of **Δtet**.\nThe lower energy orbitals will be dz2 and dx2-y2, and the higher energy orbitals will be dxy, dxz and dyz - opposite to the octahedral case.\nFurthermore, since the ligand electrons in tetrahedral symmetry are not oriented directly towards the d-orbitals, the energy splitting will be lower than in the octahedral case.\n[Square planar](https://bliptext.com/articles/square-planar-molecular-geometry) and other complex geometries can also be described by CFT.\nThe size of the gap Δ between the two or more sets of orbitals depends on several factors, including the ligands and geometry of the complex.\nSome ligands always produce a small value of Δ, while others always give a large splitting.\nThe reasons behind this can be explained by [ligand field theory](https://bliptext.com/articles/ligand-field-theory).\nThe [spectrochemical series](https://bliptext.com/articles/spectrochemical-series) is an empirically-derived list of ligands ordered by the size of the splitting Δ that they produce (small Δ to large Δ; see also [this table](https://bliptext.com/articles/ligand)):\n[I](https://bliptext.com/articles/iodide)− < [Br](https://bliptext.com/articles/bromide)− < [S](https://bliptext.com/articles/sulfide)2− < [S](https://bliptext.com/articles/sulfide)[CN](https://bliptext.com/articles/cyanide)− ([S](https://bliptext.com/articles/sulfide)–bonded) < [Cl](https://bliptext.com/articles/chloride)− < [NO3](https://bliptext.com/articles/nitrate)− < [N3](https://bliptext.com/articles/azide)− < [F](https://bliptext.com/articles/fluoride)− < [OH](https://bliptext.com/articles/hydroxide)− < [C2O4](https://bliptext.com/articles/oxalate)2− < [H2O](https://bliptext.com/articles/water-molecule) < NC[S](https://bliptext.com/articles/sulfide)− (N–bonded) < [CH3[CN](https://bliptext.com/articles/cyanide)](https://bliptext.com/articles/acetonitrile) < [py](https://bliptext.com/articles/pyridine) < [NH3](https://bliptext.com/articles/ammonia) < [en](https://bliptext.com/articles/ethylenediamine) < 2,2'-bi[py](https://bliptext.com/articles/pyridine)ridine < ph[en](https://bliptext.com/articles/ethylenediamine) < [NO2](https://bliptext.com/articles/nitrite)− < [PPh3](https://bliptext.com/articles/triphenylphosphine) < [CN](https://bliptext.com/articles/cyanide)− < [CO](https://bliptext.com/articles/carbon-monoxide).\nIt is useful to note that the ligands producing the most splitting are those that can engage in metal to ligand [back-bonding](https://bliptext.com/articles/pi-backbonding).\nThe oxidation state of the metal also contributes to the size of Δ between the high and low energy levels.\nAs the oxidation state increases for a given metal, the magnitude of Δ increases.\nA V3+ complex will have a larger Δ than a V2+ complex for a given set of ligands, as the difference in charge density allows the ligands to be closer to a V3+ ion than to a V2+ ion.\nThe smaller distance between the ligand and the metal ion results in a larger Δ, because the ligand and metal electrons are closer together and therefore repel more.\n\n## High-spin and low-spin\nLigands which cause a large splitting Δ of the d-orbitals are referred to as strong-field ligands, such as CN− and CO from the [spectrochemical series](https://bliptext.com/articles/spectrochemical-series).\nIn complexes with these ligands, it is unfavourable to put electrons into the high energy orbitals.\nTherefore, the lower energy orbitals are completely filled before population of the upper sets starts according to the [Aufbau principle](https://bliptext.com/articles/aufbau-principle).\nComplexes such as this are called \"low spin\".\nFor example, NO2− is a strong-field ligand and produces a large Δ.\nThe octahedral ion [Fe(NO2)6]3−, which has 5 d-electrons, would have the octahedral splitting diagram shown at right with all five electrons in the t2g level.\nThis low spin state therefore does not follow [Hund's rule](https://bliptext.com/articles/hund-s-rule).\nConversely, ligands (like I− and Br−) which cause a small splitting Δ of the d-orbitals are referred to as weak-field ligands.\nIn this case, it is easier to put electrons into the higher energy set of orbitals than it is to put two into the same low-energy orbital, because two electrons in the same orbital repel each other.\nSo, one electron is put into each of the five d-orbitals in accord with Hund's rule, and \"high spin\" complexes are formed before any pairing occurs.\nFor example, Br− is a weak-field ligand and produces a small Δoct.\nSo, the ion [FeBr6]3−, again with five d-electrons, would have an octahedral splitting diagram where all five orbitals are singly occupied.\nIn 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 eg orbital at an energy cost of Δ.\nAs noted above, eg refers to the\ndz2 and dx2-y2 which are higher in energy than the t2g in octahedral complexes.\nIf the energy required to pair two electrons is greater than Δ, the energy cost of placing an electron in an eg, high spin splitting occurs.\nThe crystal field splitting energy for tetrahedral metal complexes (four ligands) is referred to as Δtet, and is roughly equal to 4/9Δoct (for the same metal and same ligands).\nTherefore, the energy required to pair two electrons is typically higher than the energy required for placing electrons in the higher energy orbitals.\nThus, tetrahedral complexes are usually high-spin.\nThe use of these splitting diagrams can aid in the prediction of magnetic properties of co-ordination compounds.\nA compound that has unpaired electrons in its splitting diagram will be paramagnetic and will be attracted by magnetic fields, while a compound that lacks unpaired electrons in its splitting diagram will be diamagnetic and will be weakly repelled by a magnetic field.\n# [Low Spin [Fe(NO2)6]3− crystal field diagram | upload.wikimedia.org/wikipedia/commons/2/26/CFT-Low///Spin///Splitting///Diagram-Vector.svg]\n# [High Spin [FeBr6]3− crystal field diagram | upload.wikimedia.org/wikipedia/commons/3/31/CFT-High///Spin///Splitting///Diagram-Vector.svg]\n\n# Stabilization energy\nThe crystal field stabilization energy (CFSE) is the stability that results from placing a transition metal ion in the crystal field generated by a set of ligands.\nIt arises due to the fact that when the d-orbitals are split in a ligand field (as described above), some of them become lower in energy than before with respect to a spherical field known as the barycenter in which all five d-orbitals are degenerate.\nFor example, in an octahedral case, the t2g set becomes lower in energy than the orbitals in the barycenter.\nAs a result of this, if there are any electrons occupying these orbitals, the metal ion is more stable in the ligand field relative to the barycenter by an amount known as the CFSE.\nConversely, the eg orbitals (in the octahedral case) are higher in energy than in the barycenter, so putting electrons in these reduces the amount of CFSE.\nIf the splitting of the d-orbitals in an octahedral field is Δoct, the three t2g orbitals are stabilized relative to the barycenter by 2/5 Δoct, and the eg orbitals are destabilized by 3/5 Δoct.\nAs examples, consider the two d5 configurations shown further up the page.\nThe low-spin (top) example has five electrons in the t2g orbitals, so the total CFSE is 5 x 2/5 Δoct = 2Δoct.\nIn the high-spin (lower) example, the CFSE is (3 x 2/5 Δoct) - (2 x 3/5 Δoct) = 0 - in this case, the stabilization generated by the electrons in the lower orbitals is canceled out by the destabilizing effect of the electrons in the upper orbitals.\n# [Octahedral crystal field stabilization energy. Degenerate atomic d-orbitals of a free metal ion (left), destabilization of d-orbitals within a spherical negative electric field (center), and loss of degeneracy relative to the spherical field when ligands are treated as point charges in an octahedral geometry. | upload.wikimedia.org/wikipedia/commons/0/00/Octahedral///cfse.svg]\n\n## Optical properties\nThe optical properties (details of absorption and emission spectra) of many [coordination complexes](https://bliptext.com/articles/coordination-complex) can be explained by Crystal Field Theory.\nOften, however, the deeper colors of metal complexes arise from more intense [charge-transfer excitations](https://bliptext.com/articles/charge-transfer-complex).\n\n# Geometries and splitting diagrams","revisionCount":0},"hasMore":false,"nextCursor":null}

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