The properties of transition-metal complexes can be predicted by the following theories:
        i) Valence-bond model.
        ii) Crystal field theory.
        iii) Ligand-field theory.
However, none of those models can fully explain all the aspects of the chemistry of the transition metals.

As shown in Figure 3141a, in a cubic transition-metal (TM) oxide crystal, the divalent TM ion is in a site that has octahedral O_h symmetry and the d-levels split into threefold degenerate (lower energy) t_2g states and twofold degenerate (higher energy) e_g states that can accommodate six and four electrons, respectively (including spin states). The tetragonal symmetry splits the levels further. The t_2g states split into a singlet, d_xy, and a doublet d_xz and d_yz. The e_g states split into d_3z2_-r2 and d_x2_-y2 levels.

Figure 3141a. Ligand field splitting of d orbitals in an octahedral ligand field.

In some TM cases, the filling of orbitals with electrons may affect the local structure and thus induce geometrical distortion around the TM ion. The Jahn–Teller effect, also called Jahn–Teller distortion, describes this type of distortions. A typical Jahn-Teller ion is Mn³⁺ as shown in Figure 3141b. The ion in the high-spin configuration contains a single electron in the upper e_g state when it is placed in an octahedral LF (ligand field). A tetragonal distortion can lower the energy of the system. The lowering in total energy is due to the lowering of one of the e_g orbitals by lengthening the bond along the z axis. Note that the overall energy of the system is not further lowered by splitting the t_2g state because the center of gravity is retained.