Heisenberg‐type and double exchange in mixed‐valence clusters

The theory of double exchange is generalized to be applicable for the degenerate states of d‐electrons in crystal fields. A two‐centre three d‐electron system is studied, Coulomb and exchange intercentre interaction and resonance splitting of exchange multiplets are taken into account. A group‐theoretical classification method for resonance‐exchange multiplets in crystal fields is developed. A dependence of the electron transfer parameters on orbital symmetry and the spin of resonant states is found. The energy spectrum of a binuclear cluster is studied. The resonance interactions are assumed to be relatively weak in comparison with intera‐atomic interactions. It is shown that the Heisenberg‐type exchange parameter is redetermined as long as the transfer is taken into account. The results are compared to the conclusions of the Anderson‐Hasegawa theory.