Magnetostructural relations from a combined ab initio and ligand field analysis for the nonintuitive zero-field splitting in Mn(III) complexes.

The zero-field splitting (ZFS) of a model monometallic Mn(III) complex is theoretically studied as function of a systematic symmetry lowering. First, we treat the octahedral case for which the standard S.D.S model Hamiltonian cannot be applied due to a zero-field splitting in the absence of anisotropy induced by the spin-orbit coupling between the two spatial components of the (5)E(g) state at second-order of perturbation. Next, the symmetry is lowered to D(4h) and D(2h) and the anisotropic spin Hamiltonian is extracted using effective Hamiltonian theory. A simple relation is derived between the ratio E//D/ and the applied rhombic and axial distortions. Moreover, it is shown that close to O(h) symmetry, the orbital mixing due to spin-orbit coupling can be accurately described with Stevens fourth-order operators. The calculated tendencies are interpreted within a refined Racah plus ligand field model and it is shown that the ZFS parameters in Mn(III) complexes follow special rules that are nonintuitive compared to other d(n) configurations. Finally, some angular distortions are applied to study their effect on the anisotropy.