Using the unrestricted Hartree-Fock method and supercells containing up to 160 atoms, we calculated the energy level positions in the gap and atomic geometry for the Fe⁴⁺ impurity substituting for a host Ti atom in SrTiO₃. In agreement with experiment, the high-spin (S = 2) state is much lower in energy than the zero-spin state. The energy level positions strongly depend on the asymmetric displacement mode of the six nearest O ions which is a combination of the Jahn-Teller and breathing modes. A considerable covalent bonding between the Fe ion and the four nearest O ions takes place.