Superexchange interaction and symmetry properties of electron orbitals

The relation between the symmetry of electron orbitals and superexchange interaction is discussed. It is shown that the sign of the superexchange interaction is closely connected with the cation orbital state, when the cation is subject to the crystalline field arising from octahedrally or tetrahedrally surrounding anions. In some cases, the sign of the superexchange interaction is definitely determined from the symmetry relations. The cases in which each cation is subject to an octahedral cubic field and the lines connecting the interacting cations to the intervening anion make an angle of either 180° or 90° are discussed in particular. Our discussion of the 180° case is applicable to crystals of the perovskite type and NaCl type and that of the 90° case to anhydrous chlorides. In the case where each cation is subject to a tetrahedral cubic field, there is a definite relation between the symmetry of the cation electron orbitals and superexchange interaction, if only the s-orbital of anion participates in the superexchange interaction. TiH2 is an example of this case. The interaction between nearest-neighbor cations in the crystal of the NaCl type is also discussed.