Spin states (d electrons)

Spin states when describing transition metal coordination complexes refers to the potential spin configurations of the metal center's d electrons. In many 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.^[1]

High-spin vs Low-spin

Octahedral complexes

Low-spin [Fe(NO₂)₆]³⁻ crystal field diagram

The Δ splitting of the 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 (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.

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. 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.

High-spin [FeBr₆]³⁻ crystal field diagram

Within a transition metal group moving down the series corresponds with 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, 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, 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. 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.

Tetrahedral complexes

The Δ splitting energy for tetrahedral metal complexes (four ligands), Δ_tet is smaller than that for an octahedral complex. Therefore, it is rare to have a Δ_tet large enough to cause electrons to pair before filling high orbitals. Thus, tetrahedral complexes are usually high spin. "There are no known ligands powerful enough to produce the strong-field case in a tetrahedral complex" (Transition metals and Coordination Chemistry:The Crystal field Model by Steven S. Zumdahl. Chemical Principles)

Square planar complexes

Most spin-state transitions are between the same geometry, namely octahedral. However, in the case of d⁸ complexes is a shift in geometry between spin states. There is no possible difference between the high and low-spin states in the d⁸ octahedral complexes. However, d⁸ 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 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. The spin state of the complex also affects an atom's ionic radius.^[2]

d⁴

Octahedral high-spin: 4 unpaired electrons, paramagnetic, substitutionally labile. Includes Cr²⁺ ionic radius 80 pm, Mn³⁺ ionic radius 64.5 pm.

Octahedral low-spin: 2 unpaired electrons, paramagnetic, substitutionally inert. Includes Cr²⁺ ionic radius 73 pm, Mn³⁺ ionic radius 58 pm.

d⁵

Octahedral high-spin: 5 unpaired electrons, paramagnetic, substitutionally labile. Includes Fe³⁺ ionic radius 64.5 pm.

Octahedral low-spin: 1 unpaired electron, paramagnetic, substitutionally inert. Includes Fe³⁺ ionic radius 55 pm.

d⁶

Octahedral high-spin: 4 unpaired electrons, paramagnetic, substitutionally labile. Includes Fe²⁺ ionic radius 78 pm, Co³⁺ ionic radius 61 pm.

Octahedral low-spin: no unpaired electrons, diamagnetic, substitutionally inert. Includes Fe²⁺ ionic radius 62 pm, Co³⁺ ionic radius 54.5 pm, Ni⁴⁺ ionic radius 48 pm.

d⁷

Octahedral high-spin: 3 unpaired electrons, paramagnetic, substitutionally labile. Includes Co²⁺ ionic radius 74.5 pm, Ni³⁺ ionic radius 60 pm.

Octahedral low-spin:1 unpaired electron, paramagnetic, substitutionally labile. Includes Co²⁺ ionic radius 65 pm, Ni³⁺ ionic radius 56 pm.

d⁸

Octahedral high-spin: 2 unpaired electrons, paramagnetic, substitutionally labile. Includes Ni²⁺ ionic radius 69 pm.

Square planar low-spin: no unpaired electrons, diamagnetic, substitutionally inert. Includes Ni²⁺ ionic radius 49 pm.

References

1. Miessler, Gary L.; Donald A. Tarr (1998). Inorganic Chemistry (2nd edition). Upper Saddle River, New Jersey: Pearson Education, Inc. Pearson Prentice Hall. ISBN 0-13-841891-8.
2. Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides Shannon R.D. Acta Crystallogr. A32 751-767 (1976) doi:10.1107/S0567739476001551