Ligand and Crystal Field theories are used to describe the nature
of the bonding in transition metal complexes. Crystal
Field Theory is based upon the effect of a perturbation
of the d-orbitals consisting of electronic interaction between
the metal cation nucleus and the negatively charged electrons
of the ligands: the metal-ligand interactions are electrostatic
only. Ligand Field Theory treats
the metal-ligand interaction as a covalent
bonding interaction, and depends upon considering the overlap
between the d-orbitals on the metals and the ligand donor orbitals.
Crystal Field Theory
Let us consider an octahedral
arrangement of ligands around the central metal ion. For the octahedral
field generated, the ligands are considered to be point charges
sited on the cartesian axes, and the effect these point charges
have on the valence orbitals of the metal ion is calculated.
The s-orbital of the
metal is spherically symmetric, and so the result of its interaction
with the ligand field is that its energy is raised: the increased
repulsion between the negative point charges representing the
ligands and the negative charge of the electrons in the s-orbital
mean that the s-orbital electrons lie at higher energy.
Similarly, the metal p-orbitals
lie along the cartesian axes, and so point directly towards the
point charges, and this means that the p-orbitals all have the
same degree of interaction with the ligands, and so they remain
degenerate, but the extra repulsion between the p-orbital electrons
and the point charges of the ligands means that the p-orbitals
are raised in energy.
|Crystal field around the
||Crystal Field around the
The main effect the introduction of the ligands
has on the orbitals of the metal ion is on the d-orbitals.
The symmetry of the d-orbitals means that they fall into two
categories when the ligand field is introduced. Some of the
orbitals point directly towards the ligands, and some point
between the ligands.
|d-orbitals which point towards the ligands
|d-orbitals which point between the ligands
and d(z2) orbitals have
lobes which point directly towards the point charges of the
ligands, and so the have a greater electrostatic repulsion.
The d(xy), d(xz),
and d(yz) orbitals have lobes which
point between the charges, and so have a lesser electrostatic
Therefore, the d-orbitals are no longer degenerate,
due to their different electrostatic repulsion with the ligands,
and they split into two groups which have different energies.
Group theory can be used to show that the d(x2-y2)
and d(z2) orbitals belong to the eg
symmetry group in the octahedral field, and the d(xy), d(xz),
and d(yz) orbitals belong to the t2g
diagram for the metal orbitals in the octahedral Crystal
||The metal s- and p-orbitals increase in
energy, and the d-orbitals split into two groups in the
octahedral field. The difference in energy between the
two sets is the ligand field splitting
The energy difference between the two sets of
orbitals from the d-orbitals in the crystal field is known as
the ligand field splitting parameter,
Δo, where the o
refers to the fact that it is an octahedral
field. Conservation of energy states that the energies
of the t2g orbitals lie at -0.4Δo
and the eg orbitals lie at +0.6Δo,
so the total energy is [3x(-0.4Δo)]+[2x(+0.6Δo)]