Isotropic and antisymmetric double-exchange, zero-field, Zeeman, and hyperfine splittings in trinuclear valence-delocalized [Cu37+10] clusters

Valence delocalization in the [Cu-3(7+)] trimer is considered in the model of the double-exchange coupling, in which full delocalization corresponds to the migration of the single (d) over capx(2)-y(2) hole and relatively strong isotropic double exchange coupling. Strong double exchange results in the pairing of the individual spins in the delocalized trimer even at room temperature. The model explains the delocalized singlet (1)A(1) ground state in the planar Cu-3(mu(3)-O) core by strong double exchange with positive double-exchange parameter t(0), whereas the delocalized triplet ground state of the [Cu-3(7+)] trimer, which was observed in the Cu-3(mu(3)-S)(2) cluster, may be explained by the double exchange with relatively weak positive t(0): 0 < t 0 < 2J (degenerate E-3 ground state) or negative t(0) (triplet (3)A(2) ground state). An analysis of the splitting of the delocalized degenerate 3E term requires inclusion of the antisymmetric double exchange interaction, which takes into account the spin-orbit coupling in the double-exchange model. The cluster parameter K-Z of the antisymmetric double-exchange coupling is proportional to t(0) and anisotropy of the g factor Delta g(II)[Cu(II)], K-Z << t(0). Antisymmetric double exchange is relatively large in the [Cu-3(7+)] cluster with the d x(2)-y(2) magnetic orbitals lying in the Cu-3 plane [Cu-3(mu(3)-O) core], whereas for the d x(2)-y(2) magnetic orbitals lying in the plane perpendicular to Cu-3, antisymmetric double-exchange coupling is weak [Cu-3(mu(3)-S)(2) cluster]. The antisymmetric double-exchange coupling results in the linear zero-field splitting Delta(K) 2 root 3K(Z) (similar to t(0)) of the delocalized degenerate E-3 term that leads to strong anisotropy of the Zeeman splittings in the external magnetic field and a complex electron paramagnetic resonance (EPR) spectrum. The delocalized model of hyperfine interaction explains the hyperfine structure [10 hyperfine lines with the relative intensities 1:3:6:10:12:12:10:6:3:1 and the interval a/3] of the EPR transitions in the triplet states that was observed in the EPR spectra of the Cu-3(mu(3)-S)(2) cluster.