Antisymmetric double exchange in mixed-valence clusters

Isotropic and Antisymmetric Double-Exchange, Zero-Field, Zeeman, and Hyperfine Splittings in Trinuclear Valence-Delocalized [Cu37+] Clusters

“…For consideration of the splitting of the delocalized degenerate 3 E term, it is necessary to go beyond the framework of the isotropic double-exchange model and include the antisymmetric double-exchange coupling. − This interion coupling in the MV systems is the result of taking into account the spin−orbit coupling (SOC) in the Anderson−Hasegawa 9 isotropic double-exchange model in second-order perturbation theory.…”

“…Antisymmetric double-exchange interaction originates from the combined effect of the SOC admixture of the excited states to the ground state of the Cu(II) ion and ET between the excited and ground states of the neighboring ions. − In the localized clusters [Cu 2 (II)Cu(III)] loc , the local crystal field forms orbitally nondegenerate ground state d x 2 - y 2 = v of the Cu(II) ion. , SOC admixes the excited state d xy = ζ to the ground state d x 2 - y 2 : 58,59 v (± 1 / 2 ) = v 0 (± 1 / 2 ) ± i γ ζ ζ(± 1 / 2 ). In the |α*〉 localization, it corresponds to an admixture of the excited-state cluster to the ground state : Φ α * = + i γ ζ .…”