When a metal is subjected to the perturbation of an octahedral
field, the energies of the d-orbitals split into two groups, the
lower energy t2g, at -0.4Δo,
and the higher energy eg, at 0.6Δo,
where Δo is the ligand field
When electrons are put into these orbitals, the orbitals which
become occupied depend on the value of Δo.
When there are x electrons in the t2g orbitals, and
y electrons in the eg orbitals, the total energy of
the electrons relative to the average energy of the electrons
is known as the Ligand Field Stabilization
LFSE = (-0.4x + 0.6y)ΔDo
The LFSE therefore depends on the number of electrons
in the d-orbitals of the metal, x+y, the value of Δo,
and the distribution of electrons between the t2g
and eg levels.
When calculating the electronic configuration
of a transition metal complex, we should note that the electrons
always occupy the lowest energy configuration.
Configurations of d-metal complexes
LFSE = -0.4Δo
LFSE = -0.8Δo
LFSE = -1.2Δo
LFSE = -1.6Δo
LFSE = -0.6Δo
As we can see, when the number of d-electrons
is 0, 1, 2, or 3, there is no trouble assigning an electronic
configuration, it being t2gn. However,
when a 4th electron is added, there are two possible configurations:
t2g4 and t2g3eg1.
These two configurations differ in LFSE by Δo,
and so it would be predicted that the t2g4
configuration would be lower in energy. However, this configuration
involves the pairing of electrons in one of the t2g
orbitals, and the extra repulsion associated with paired electrons,
with energy P, in the same orbital acts to destabilize the t2g4
We need to consider the overall stabilization
energy, SE, which is the ligand field stabilization energy,
LFSE, plus the pairing energy, PE.
stabilization energy of a d4 complex
||SE = LFSE + PE =
-1.6Δo + P
||SE = LFSE + PE
= -0.6Δo + 0
The configuration adopted therefore depends upon
the relative magnitude of the splitting parameter, Δo,
and the pairing energy, P. If Δo<P,
then the upper eg orbital is occupied to minimize
the pairing energy, whereas if Δo>P,
the lower t2g orbital is occupied to maximize the
LFSE. P does not change, for a given element, and so the configuration
is determined by the value of Δo.
The first situation, with configuration t2g3eg1
is known as the weak-field limit,
and the second, with configuration t2g4,
is known as the strong-field limit.
If we consider the MO diagrams for the two d4
complexes, we see that in the weak-field limit, all the electron
spins are parallel, and the overall electron spin is 2 In the
strong-field limit, two of the electrons are paired, and hence
have antiparallel spins, so the overall electron spin is 1.
When there is a choice of possible electronic configurations,
the configuration with the lowest number of parallel electron
spins is known as the low-spin configuration,
and it corresponds to the strong field, and the configuration
with the highest number of parallel electron spins is known
at the high-spin configuration,
and it corresponds to the weak-field limit.
Similar arguments can be constructed for d5,
d6, and d7 complexes, but for d8,
d9, and d10, there is again only one possible
Ligand field transitions
occur when an electron is excited from an orbital with one energy
to an orbital with another energy. One example is the t2g-to-eg
transition from which the LFSE, Δo,
may be calculated. These will sometimes involve a change in
the electron spin, and hence have an effect on the magnetic
properties if the complex: the magnetic
properties of the complex are determined by the number
of unpaired electrons.