High spin and low spin are two potential spin configurations, either of which will be adopted when electrons occupy d-orbitals. High spin (spin-free) refers to configurations that have more unpaired electrons. Conversely, low spin (spin-paired) refers to configurations that have a lesser number of unpaired electrons.
When ligands approach the central metal atom/ion, repulsion is caused between the electrons of ligands and those of the metal d-orbitals. In a spherical field, all the electrons in d-orbitals are equally repelled and are collectively raised in energy. Since the field is not spherical in case of actual geometries, some d-orbitals are raised to energy higher than others.
In octahedral complexes, since six ligands approach on the axes, the orbitals that lie there (eg set containing dx2-y2 and dz2 orbitals) are repelled more and are thus increased in energy. Whereas the other d-orbitals in the t2g set are decreased in energy. This energy difference (from the barycentre) between the sets is known as the ligand field splitting energy and is represented by ΔO for octahedral complexes.
In tetrahedral complexes, four ligands approach in between the axes, and the orbitals dxy, dxz, and dyz comprising the t2 set which occupies that space, are raised in energy. At the same time, the e set is lowered in energy and the resulting splitting is shown by ΔT.
Other geometries such as square planar or tetragonal have their own pattern of splitting of orbitals depending on how the ligands approach the central metal atom/ion.
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Background information:
The filling of electrons takes place on the basis of three principles: The Aufbau principle, Pauli’s exclusion principle, and Hund’s rule.
The Aufbau principle states that lower energy orbitals will be filled first.
Pauli’s exclusion principle claims that no two electrons can have the same values for all four quantum numbers. This implies that if two electrons are present in the same orbital (same principal, azimuthal, and magnetic quantum numbers), their spin quantum number will have different values.
Hund’s rule states that when degenerate orbitals (same energy) are available, an electron would rather occupy an empty orbital than an already half-filled one.
Pairing energy refers to the energy required to put an electron into an already half-filled orbital. It takes into account the repulsion the electron to be added will face from the electron already present in the orbital.
High spin vs. Low spin complexes:
For low-spin complexes, the ligand field splitting energy must be greater than the pairing energy. In this case, greater ligand field splitting will result in more energy being required to put electrons in the higher energy orbitals. So the electrons pair up in the lower energy orbitals.
When the electrons pair up in the lower energy set of d-orbitals, following the Aufbau principle, we have a lesser number of unpaired electrons, and this results in the low-spin (or spin-paired) configuration.
Alternatively, for high spin complexes, the ligand field splitting must be lesser than the pairing energy. With lesser ligand field splitting, lesser energy will be required to put the electron into a higher energy orbital unpaired than to pair it up with an electron already present in the lower energy orbital. So the electrons will remain unpaired and into the next energy orbital.
In this case, more unpaired electrons will be present in the d-orbitals and the configuration would be called high-spin (or spin-free). The electrons will fill up following Hund’s rule of maximum multiplicity.
For octahedral geometry, high spin or low spin configurations can only result for complexes with d-electrons 4 to 7 in number.
For tetrahedral geometry, complexes with 3 to 6 d-electrons will be put into the high-spin or low-spin configuration.
Factors affecting ligand field splitting:
In general, ΔO is about twice as much as ΔT. This is because there are six ligands that approach the central metal ion in octahedral geometry as compared to four in tetrahedral geometry. A greater number of ligands corresponds to greater repulsion and more splitting in turn.
The magnitude of splitting depends on several factors other than geometry which include the oxidation state of the central metal ion, the period of the metal, the nature of the ligand (field strength), and the rule of average environment.
The central metal cation is able to draw ligands closer to itself if it has a higher oxidation state (stronger charge). So the higher the oxidation state of the central metal cation, more will be the ligand field splitting.
Another factor that influences the field splitting energy is the period to which the metal cation belongs. The larger the size of the cation, better will be the orbital overlap and more splitting will take place. This occurs due to less steric hindrance between the ligands. Lesser ligand field splitting is the reason why octahedral complexes of only the first-row transition metals adopt high-spin states.
Nature of the ligands also affects the ligand field splitting as strong-field ligands cause greater splitting as compared to weak-field ligands in the spectrochemical series. The reason being the ability of the ligands to form π-back bonding among others.
The rule of average environment refers to complexes having two or more different types of ligands. In this case, the extent of splitting depends upon the weighted average strength of various ligands.
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Key Takeaway(s)
Low spin states result when the ligand field splitting energy is greater than pairing energy. The electrons tend to pair up forming a diamagnetic or paramagnetic complex.
High spin state results when the pairing energy is greater than ligand field splitting energy. The electrons now remain unpaired in separate orbitals, forming paramagnetic complexes.
Several factors affect the ligand field splitting energy. These include the oxidation state of the central metal ion, the period of the central metal atom/ion, strength of the ligand in the spectrochemical series, and the geometry of the complex.
Concepts Berg
Complexes having a higher number of unpaired electrons are high-spin complexes. High-spin complexes are formed when the ligand field splitting energy is lesser than pairing energy. The electrons fill up the orbitals according to Hund’s rule.
Complexes in which electrons pair up in orbitals and result in a lesser number of unpaired electrons. This occurs when the ligand field splitting energy is greater than the pairing energy. In this case, electrons fill up following the Aufbau principle.
Spin state affects the properties of complexes. High-spin complexes have a greater number of unpaired electrons as compared to Low spin complexes.
Octahedral high-spin complexes are paramagnetic in nature due to the presence of unpaired electrons. On the other hand, octahedral low spin complexes can be paramagnetic or diamagnetic.
The ionic radius of the metal cation also affects the spin state. Octahedral high spin complexes have a larger ionic radius as compared to low spin complexes.
The color of the complexes is also affected by the magnitude of ligand field splitting. High spin complexes with weak field ligands having lesser field splitting will absorb longer wavelengths (less energy).
Although Fe3+ mostly forms high spin complexes, it can form high spin or low spin complexes. It depends on the ligand field splitting. The ligand field splitting can be large or small as it is affected by several factors like the geometry and the field strength of the ligands in the spectrochemical series.
Octahedral complexes are generally low-spin. Octahedral complexes of only the first series of transition metals adopt high-spin states. This is because of lesser ligand field splitting due to smaller size of the cation in the first row of transition elements.
Tetrahedral complexes mainly exist in high spin states due to lesser ligand field splitting resulting from four ligands as compared to 6 in octahedral geometry.
However, there are other factors that influence the spin configuration. These include the nature of ligands and oxidation state of the metal cation.
Strong field ligands in the spectrochemical series will cause more field splitting resulting in low spin complexes and vice versa.
Also, the higher the oxidation state of the metal, closer the ligands will be drawn, and more will be the field splitting. This results in low spin complexes yet again.
Tetrahedral complexes are mostly high spin. First row transition elements mainly form high spin octahedral complexes. Examples of high spin complexes include [Fe(Br)6]3-, [Fe(H2O)6]2+, [CoF6]3−, and [Ni(NH3)]2+.
Transition metal ions, except for the first row, in octahedral geometry, form low spin complexes. Examples of low spin complexes include [Fe(NO2)6]3-, [Fe(CN)6]3-, Fe(2-norbornyl)4, [Co(4-norbornyl)4]+, [Co(NH3)6]3+, and [Ni(Cl)4]2-.
Weak field ligands cause lesser field splitting. This leads to electrons occupying separate orbitals unpaired resulting in high spin complexes. Examples of octahedral weak field ligand complexes include [Fe(Br)6]3-, [Fe(H2O)6]2+, [CoF6]3−, and [Ni(NH3)]2+.
Strong field ligands cause more field splitting. Electrons pair up and fill the lower energy orbitals (t2g set) first in accordance with Aufbau principle. Low spin complexes form. Examples include [Fe(NO2)6]3-, [Fe(CN)6]3-, Fe(2-norbornyl)4, [Co(4-norbornyl)4]+, [Co(NH3)6]3+, and [Ni(Cl)4]2-.
Reference links
- Spin states – Wikipedia
