Introduction to Crystal Field Theory

In a free metal ion (this is hypothetical because it does not actually exist!), the five d orbitals are degenerate. When this ion is surrounded by ligands, there is a net stabilisation due to electrostatic attraction between the positive TM ion and the negatively charged ligands, but there also exists an electron- electron repulsion between the outer shell electrons of the metal and the ligands. This repulsion varies in size for each d orbital depending on whether it is pointing directly to a ligand or not. This leads to the degeneracy of the d orbitals, hence the term "Crystal Field Splitting". For more information look at the crystal field splitting diagrams for an octahedral field or a tetrahedral field or a square planar field.

It should be noted that a few assumptions are made in this theory which are not exactly true. Firstly, the TM is assumed to be a positively charged ion, and ligands are negatively charged ions (but the TM can be neutral, cationic or anionic and the ligand can be neutral as well as negatively charged). It follows from this assumption that the electrostatic attraction between the TM and ligands form the ionic bonds (but we know that the bonding is actually coordinate).

An important concept to appreciate is whether the electron chooses high spin or low spin. Basically if the splitting of the d orbitals is large, low spin is preferred (i.e electrons would prefer to pair); but small splitting favours high spin (electrons would rather occupy orbitals singly). The size of splitting is affected by several factors:

Oxidation State of Metal
TM Series of Metal
Strength of Ligand

What`s the Use of Crystal Field Theory?

CFT Predicts Magnetic Behaviour of Complexes

Determines whether a compound is paramagnetic (contains unpaired electrons) or diamagnetic (has no unpaired electrons).

CFT Explains why Compounds are Coloured

This is due to excitation of an electron from a more stabilised d orbital to a higher energy orbital. This difference in energy corresponds to the energy of visible light, which results in the regions of the visible spectrum which are not absorbed to be seen by the eye.

CFT Accounts for Extra Thermodynamic Stability of TM Compounds

For example hydration energies are generally larger than expected, implying added stability which is due to Crystal Field Stabilisation Energy. CFSE is the added stability with respect to the average increase in energy of the free metal ions due to the repulsion between the negatively charged ligands and the outer shell electrons of the TM ion. Since electrons are assigned to the lowest energy d orbital available, this will usually result in net stabilisation, unless all the d orbitals are half-filled or fully occupied.

For fuller explanations, look at:

Splitting Diagram for Octahedral Complex

Splitting Diagram for Tetrahedral Complex

Splitting Diagram for Square Planar Complex

Diamagnetism or Paramagnetism

High Spin vs Low Spin

Before we can assign electrons to orbitals in order to predict the magnetic behaviour of a compound , we must first decide whether the electron chooses high spin or low spin. High spin favours the maximum number of unpaired electrons (upe`s). Low Spin favours the minimun number of upe`s (i.e prefers pairing). For example when the fourth electron is loaded onto an octahedral structure, it may be paired up in the lower level ,t_2g, illustrating low spin, or it can occupy singly in the higher level, e_g, (high spin).

This choice is affected by two factors:

The size of splitting
The Pairing Energy (energy needed to overcome repulsions between 2 electrons in an orbital)

If the size of splitting is larger than pairing energy, low spin is preferred, if vice versa, then high spin is preferred. Firstly let us consider the pairing energy. The pairing energy decreases as the d orbital gets larger. Therefore going from the First TM Series to the Second, pairing energy decreases which implies that low spin is favoured.

The size of splitting is more complicated because it is affected by three other factors:

Oxidation State of Metal

As the positive charge on the metal increases the negatively charged ligands are drawn closer towards the metal. This increases the electron-electron repulsion between the metal and the ligand therefore splitting is larger so for high oxidation states, low spin is preferred.

Compound Size of Splitting e^- configuration Spin Number of upe`s
[Fe(NH ₃)₆] ²⁺ Splitting < Pairing energy d⁶ High Spin 4 upe`s

[Co(NH₃)₆]³⁺ Splitting > Pairing energy d⁶ Low Spin 0 upe`s

This explains why two different compounds with the same d-electron configuration can result in one being diamagnetic and the other paramagnetic.

TM Series of Metal

Compound	Size of Splitting	e^- configuration	Spin	Number of upe`s
[Fe(NH ₃)₆] ²⁺	Splitting < Pairing energy	d⁶	High Spin	4 upe`s
[Co(NH₃)₆]³⁺	Splitting > Pairing energy	d⁶	Low Spin	0 upe`s

As the size of the d orbitals increase, the repulsive interaction between the metal electrons and the ligand electrons will also increase, which causes splitting to be large. This implies that low spin is preferred in going from the first to the second to the third transition series.

Strength of Ligand: Weak Field or Strong Field

Different ligands have different abilities to cause splitting. Ligands which cause small splitting are called weak field ligands and those causing large splitting are known as strong field ligands.
The Spectrochemical Series is a list showing increasing Crystal Field Strength:
I ^- < Br ^- < SCN ^- < F ^- < OH ^- < H ₂O < NCS ^- < NH ₃ ~ py < en < bipy < phen < NO ₂^- < PR ₃ < CN ^- ~ CO ~ C ₂H ₄
Strong field ligands result in Low Spin, e.g. CN-
Weak field ligands reult in High Spin e.g. H₂O

Click here to see illustrations of high spin vs low spin .

Tutorial Questions

Return to Bristol University Homepage