Model Calculations for the Study of Direct and Superexchange Interactions

Investigations of the two‐atom $M^{\text{2+}}{\mathrm{‐M}}^{\text{2+}}$ and the three‐atom $M^{\text{2+}}{\mathrm{‐(F}}^{-}{\mathrm{)‐M}}^{\text{2+}}$ 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.