View source for Spin states (d electrons)

'''Spin states''' when describing [[transition metal]] [[coordination complex]]es refers to the potential spin configurations of the metal centers d electrons. In many molecules these spin states vary between '''high-spin''' and '''low-spin''' configurations. These configurations can be understood through the two major models used to describe coordination complexes; [[ligand field theory]], which is an application of [[molecular orbital theory]] to transition metals, and [[crystal field theory]], which has roots in [[VSEPR theory]].<ref>{{cite book | last = Miessler | first = Gary L. | authorlink = Gary L. Miessler | coauthors = Donald A. Tarr | year = 1998 | title = Inorganic Chemistry (2nd edition)| publisher = Pearson Education, Inc. Pearson Prentice Hall | location = Upper Saddle River, New Jersey | isbn = 0138418918}}</ref>

== High-spin vs Low-spin ==
=== Octahedral complexes ===
[[File:CFT - Low Spin Splitting Diagram 2.png|thumb|right|250px|'''Low-spin''' [Fe(NO<sub>2</sub>)<sub>6</sub>]<sup>3−</sup> crystal field diagram]]

The [[Ligand-field splitting parameter|Δ splitting]] of the [[Atomic orbital|''d''-orbitals]] plays an important role in the electron spin state of a coordination complex. There are three factors that affect the Δ: the period of the metal center, the charge of the metal center, and the field strength of the complex's ligands as described by the [[spectrochemical series]].  

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<sub>''g''</sub> 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<sub>''g''</sub>, 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]]. 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]] 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.  

[[Image:CFT - High Spin Splitting Diagram 2.png|thumb|right|250px|'''High-spin''' [FeBr<sub>6</sub>]<sup>3−</sup> crystal field diagram]]

Within a transition metal [[Group (periodic table)|group]] moving down the series corresponds with in an increase in Δ. The observed result is larger Δ splitting for complexes in octahedral geometries based around transition metal centers of the second or third row, [[Period (periodic table)|periods]] 5 and 6 respectively. This Δ splitting is generally large enough that these complexes do not exist as high-spin state. This is true even when the metal center is coordinated to weak field ligands.  It is only octahedral coordination complexes which are centered around first row transition metals that fluctuate between high and low-spin states.

The charge of the metal center plays a role in the ligand field and the Δ splitting. For example, Fe<sup>2+</sup> and Co<sup>3+</sup> are both d<sup>6</sup>; however, the higher charge of Co<sup>3+</sup> creates a stronger ligand field than Fe<sup>2+</sup>. All other things being equal, Fe<sup>2+</sup> is more likely to be high spin than Co<sup>3+</sup>.  

Ligands also affect the magnitude of Δ splitting of the [[Atomic orbital|''d''-orbitals]] according to their field strength as described by the  [[spectrochemical series]]. Strong-field ligands, such as CN<sup>−</sup> and CO, increase the Δ splitting and are more likely to be low-spin. Weak-field ligands, such as I<sup>−</sup> and Br<sup>−</sup>) cause a smaller Δ splitting and are more likely to be high-spin.

=== Tetrahedral complexes ===

The Δ splitting energy for tetrahedral metal complexes (four ligands), Δ<sub>tet</sub> is smaller than that for an octahedral complex. Therefore, it is rare to have a Δ<sub>tet</sub> large enough to cause electrons to pair before filling high orbitals. Thus, tetrahedral complexes are usually high-spin.

=== Square planar complexes ===

Most spin state transitions are between the same geometry, namely octahedral.  However, in the case of d<sup>8</sup> complexes is a shift in geometry between spin states. There is no possible difference between the high and low-spin states in the d<sup>8</sup> octahedral complexes, however d<sup>8</sup> complexes are able to shift from paramagnetic tetrahedral geometry to a diamagnetic low-spin square planar geometry.

== Ligand field theory vs Crystal field theory==

The rationale for why the spin states exist according to [[ligand field theory]] is essentially the same as the [[crystal field theory]] explanation. However the explanation of why the orbitals split is different accordingly with each model and requires translation.

== High-spin and low-spin systems ==

The first [[d electron count]] (special version of [[electron configuration]]) with the possibility of holding a high spin or low spin state is octahedral d<sup>4</sup> 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. The spin state of the complex also effects an atoms [[ionic radius]].<ref>''Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides'' Shannon R.D. Acta Cryst. A32 751-767 (1976) {{doi|10.1107/S0567739476001551}}</ref> 

;d<sup>4</sup>:Octahedral high-spin: 4 unpaired electrons, [[paramagnetic]], substitutionally labile. Includes Cr<sup>2+</sup> [[ionic radius]] 80 [[picometre|pm]], Mn<sup>3+</sup> [[ionic radius]] 64.5 [[picometre|pm]].
:Octahedral low-spin: 2 unpaired electrons, [[paramagnetic]], substitutionally inert. Includes Cr<sup>2+</sup> [[ionic radius]] 73 [[picometre|pm]], Mn<sup>3+</sup> [[ionic radius]] 58 [[picometre|pm]].

;d<sup>5</sup>:Octahedral high-spin: 5 unpaired electrons, [[paramagnetic]], substitutionally labile. Includes Fe<sup>3+</sup> [[ionic radius]] 55 [[picometre|pm]].
:Octahedral low-spin: 1 unpaired electron, [[paramagnetic]], substitutionally inert. Includes Fe<sup>3+</sup> [[ionic radius]] 64.5 [[picometre|pm]].

;d<sup>6</sup>:Octahedral high-spin: 4 unpaired electrons, [[paramagnetic]], substitutionally labile. Includes Fe<sup>2+</sup> [[ionic radius]] 78 [[picometre|pm]], Co<sup>3+</sup> [[ionic radius]] 61 [[picometre|pm]].
:Octahedral low-spin: no unpaired electrons, [[diamagnetic]], substitutionally inert. Includes Fe<sup>2+</sup> [[ionic radius]] 62 [[picometre|pm]], Co<sup>3+</sup> [[ionic radius]] 54.5 [[picometre|pm]], Ni<sup>4+</sup> [[ionic radius]] 48 [[picometre|pm]].

;d<sup>7</sup>:Octahedral high-spin: 3 unpaired electrons, [[paramagnetic]], substitutionally labile. Includes Co<sup>2+</sup> [[ionic radius]] 74.5 [[picometre|pm]], Ni<sup>3+</sup> [[ionic radius]] 60 [[picometre|pm]].
:Octahedral low-spin:1 unpaired electron, [[paramagnetic]], substitutionally labile. Includes Co<sup>2+</sup> [[ionic radius]] 65 [[picometre|pm]], Ni<sup>3+</sup> [[ionic radius]] 56 [[picometre|pm]].

;d<sup>8</sup>:Octahedral high-spin: 2 unpaired electrons, [[paramagnetic]], substitutionally labile. Includes Ni<sup>2+</sup> [[ionic radius]] 69 [[picometre|pm]]. 
:Square planar low-spin: no unpaired electrons, [[diamagnetic]], substitutionally inert. Includes Ni<sup>2+</sup> [[ionic radius]] 49 [[picometre|pm]].

== References ==
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[[Category:Inorganic chemistry]][[Category:coordination chemistry]]
[[Category:2Fix]]