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 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 d-orbitals 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 d-metal complexes
d1:		t2g1: LFSE = -0.4Δo
d2:		t2g2: LFSE = -0.8Δo
d3:		t2g3: LFSE = -1.2Δo
d4:		t2g4: LFSE = -1.6Δo
d4:		t2g3eg1: 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 t_2gⁿ. However, when a 4th electron is added, there are two possible configurations: t_2g⁴ and t_2g³e_g¹. These two configurations differ in LFSE by Δ_o, and so it would be predicted that the t_2g⁴ 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_2g⁴ configuration.

We need to consider the overall stabilization energy, SE, which is the ligand field stabilization energy, LFSE, plus the pairing energy, PE.

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_2g³e_g¹ is known as the weak-field limit, and the second, with configuration t_2g⁴, 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 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-to-e_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.