Model calculations for the study of direct and superexchange interactions

Investigations of the two-atom M²⁺-M²⁺ and the three-atom M²⁺-(F^-)-M²⁺ systems have been made in order to study both direct and superexchange mechanisms. In these model calculations all electrons are treated explicitly within the framework of the unrestricted Hartree-Fock procedure; the Fock matrix is evaluated directly by Monte Carlo integration techniques. The effective exchange parameter J is determined at several internuclear distances, and spin densities are exhibited for the ferromagnetic and anti-ferromagnetic states of the three-atom system. The AF state lies lower in energy beyond a calculated critical bond length. Localization of the uhf eigenfunctions and the significance of the Mott transition for magnetic ordering are discussed.