# 7.1.1: Tetrahedral and Octahedral Geometries

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Until this point, we have focused on one of the most common cases for metal complexes, the 6-coordinate octahedral ligand field geometry. Now, we will examine other geometries, with a focus on 4-coordinate ligand fields. Almost everything you have already learned about octahedrons can be applied to 4-coordinate metal complexes (effects of metal and ligands on \(\Delta\)); the main difference is the splitting pattern of d-orbitals is different in each 4-coordinate complex than it was in the octahedral cases. Also, the magnitudes of splitting are different in important ways.

Since CFT is simpler than LFT, let's use CFT to describe and derive these "new-to-you" splitting patterns. Now is a good time to go back and recall how CFT was used to derive the splitting of d-orbitals in an octahedral field so that you can use that as a launching pad for deriving the tetrahedron (harder) and square planar geometries:

## LFSE and SE for Other Geometries

Just like in the case of octahedral metal complexes, we can apply CFT (or LFT) to calculate LFSE and SE of 4-coordinate (or any-coordinate) metal complexes. Once again, in terms of the d orbital splitting diagram, the results are similar to what we see from molecular orbital theory. For tetrahedral geometry, which is the most common geometry when the coordination number is four, we get a set of two high-lying orbitals and three lower ones.

The overall splitting is expressed as Δ_{t}; the t stands for tetrahedral. However, sometimes it is useful to compare different geometries. In crystal field theory, it can be shown that the amount of splitting in a tetrahedral field is much smaller than in an octahedral field. In general, Δ_{t} = 4/9 Δ_{o}.

## Which geometries are most likely?

** We wouldn't usually use crystal field theory to decide whether a metal is more likely to adopt a tetrahedral or an octahedral geometry**. In most cases, the outcome is more strongly dependent on factors other than the d orbital energies. For example, maybe a complex would be too crowded with six ligands, so it only binds four; it becomes tetrahedral rather than octahedral. Or maybe a metal does not have enough electrons in its valence shell, so it binds a couple more ligands; it becomes octahedral rather than tetrahedral.

However, this comparison between Δ_{o} and Δ_{t} does help to explain why tetrahedral complexes are much more likely than octahedral complexes to adopt high-spin configurations. The splitting is smaller in tetrahedral geometry, so pairing energy is more likely to become the deciding factor there than it is in octahedral cases.

Crystal field theory has also been used to determine the splitting between the orbitals in a square planar geometry. That is a much more complicated case, because there are four different levels. Once again, the energy levels are often expressed in terms of Δ_{o}.

We could use a calculation of stabilisation energy to predict whether a particular complex is likely to adopt a tetrahedral or a square planar geometry. Both geometries are possible, so it would be useful to be able to predict which geometry occurs in which case. However, just as in the case of comparing octahedral and tetrahedral gemoetries, there is another factor that is often more important.

That factor is steric crowding. In a tetrahedron, all the ligands are 109^{o} from each other. In a square planar geometry, the ligands are only 90^{o} away from each other. Tetrahedral geometry is always less crowded than square planar, so that factor always provides a bias toward tetrahedral geometry. As a result, we might expect square planar geometry to occur only when sterics is heavily outweighed by ligand field stabilisation energy.