Abstract :
The spin-coupling model of zero-field splitting (ZFS) of tetrameric mixed-valent and monovalent clusters is developed. The 〈|ŝi0(2)|〉 matrix elements of the individual ZFS tensor operator of the second rank were calculated for tetramers of the general type in the representation of the total and intermediate spins. The spin-dependent correlations between ZFS parameters DS of the cluster states S and Di of individual ions si were obtained for [4Fe–4S]+ centers of native systems and synthetic model compounds with the high-spin Sgr=3/2 ground state. It was shown that the single-particle spin parameters fi=〈|ŝiz2−si(si+1)/3|〉/〈|Ŝz2−S(S+1)/3|〉 of the [Fe3(II)Fe(III)] center essentially depend on the total, intermediate and local spins and on the exchange parameters. In the spin schemes with fixed intermediate spins, the correlation between the cluster total spin ZFS parameters, DS, and the individual ZFS parameters, Di, are determined by the total, intermediate and individual spins. Anisotropic cluster ZFS parameters DS strongly depend on isotropic Heisenberg exchange and double exchange inter-ion interactions due to exchange mixing of the states with different intermediate spins. It was shown that the cluster ZFS parameters DS, for the states with S=3/2, change their values and sign under the variation of the Heisenberg exchange and double exchange parameters during the cluster deformation. The single-particle ZFS parameters Di and the exchange effects determine the observed strong positive (DS=1.5–6 cm−1) and negative (DS=−1.7 to −5 cm−1) cluster ZFS splittings of the ground Sgr=3/2 states of the [4Fe–4S]+ clusters. Positive (negative) cluster ZFS parameters DS correspond to negative (positive) individual ZFS parameters D1−3 [Fe(II)]. The theory explains the observation of small negative effective hyperfine constants Ai for the Sgr=3/2 clusters with positive and negative cluster ZFS parameters DS. The correlations between the individual and cluster ZFS parameters were obtained for mixed-valent high-spin [4Fe–4S]+ clusters with Sgr=5/2, 7/2 and monovalent [4Fe–4S]0 cluster with Sgr=4.
