
When a metal is subjected to the perturbation of an octahedral
field, the energies of the dorbitals split into two groups, the
lower energy t_{2g}, at 0.4Δ_{o},
and the higher energy e_{g}, at 0.6Δ_{o},
where Δ_{o} is the ligand field
splitting parameter.
When electrons are put into these orbitals, the orbitals which
become occupied depend on the value of Δ_{o}.
When there are x electrons in the t_{2g} orbitals, and
y electrons in the e_{g} orbitals, the total energy of
the electrons relative to the average energy of the electrons
is known as the Ligand Field Stabilization
Energy (LFSE):
LFSE = (0.4x + 0.6y)ΔDo
The LFSE therefore depends on the number of electrons
in the dorbitals of the metal, x+y, the value of Δ_{o},
and the distribution of electrons between the t_{2g}
and e_{g} levels.
When calculating the electronic configuration
of a transition metal complex, we should note that the electrons
always occupy the lowest energy configuration.
Electronic
Configurations of dmetal complexes 
d^{1}: 

t_{2g}^{1}:
LFSE = 0.4Δ_{o} 
d^{2}: 

t_{2g}^{2}:
LFSE = 0.8Δ_{o} 
d^{3}: 

t_{2g}^{3}:
LFSE = 1.2Δ_{o} 
d^{4}: 

t_{2g}^{4}:
LFSE = 1.6Δ_{o} 
d^{4}: 

t_{2g}^{3}e_{g}^{1}:
LFSE = 0.6Δ_{o} 
As we can see, when the number of delectrons
is 0, 1, 2, or 3, there is no trouble assigning an electronic
configuration, it being t_{2g}^{n}. However,
when a 4th electron is added, there are two possible configurations:
t_{2g}^{4} and t_{2g}^{3}e_{g}^{1}.
These two configurations differ in LFSE by Δ_{o},
and so it would be predicted that the t_{2g}^{4}
configuration would be lower in energy. However, this configuration
involves the pairing of electrons in one of the t_{2g}
orbitals, and the extra repulsion associated with paired electrons,
with energy P, in the same orbital acts to destabilize the t_{2g}^{4}
configuration.
We need to consider the overall stabilization
energy, SE, which is the ligand field stabilization energy,
LFSE, plus the pairing energy, PE.
Overall
stabilization energy of a d^{4} complex 
t_{2g}^{4}: 
SE = LFSE + PE =
1.6Δ_{o} + P 
t_{2g}^{3}e_{g}^{1}: 
SE = LFSE + PE
= 0.6Δ_{o} + 0
= 1.6Δ_{o}
+ Δ_{o} 
The configuration adopted therefore depends upon
the relative magnitude of the splitting parameter, Δ_{o},
and the pairing energy, P. If Δ_{o}<P,
then the upper e_{g} orbital is occupied to minimize
the pairing energy, whereas if Δ_{o}>P,
the lower t_{2g} 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 Δ_{o}.
The first situation, with configuration t_{2g}^{3}e_{g}^{1}
is known as the weakfield limit,
and the second, with configuration t_{2g}^{4},
is known as the strongfield limit.
If we consider the MO diagrams for the two d^{4}
complexes, we see that in the weakfield limit, all the electron
spins are parallel, and the overall electron spin is 2 In the
strongfield 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 lowspin configuration,
and it corresponds to the strong field, and the configuration
with the highest number of parallel electron spins is known
at the highspin configuration,
and it corresponds to the weakfield limit.
Similar arguments can be constructed for d^{5},
d^{6}, and d^{7} complexes, but for d^{8},
d^{9}, and d^{10}, there is again only one possible
configuration.
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 t_{2g}toe_{g}
transition from which the LFSE, Δ_{o},
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.

