Can anisotropic exchange be reliably calculated using density functional methods? a case study on trinuclear Mn^III-M^III-Mn ^III (M=Fe, Ru, and Os) cyanometalate single-molecule magnets

Density functional studies have been performed on a set of trinuclear single-molecule magnets (SMMs) of general formula [{Mn₂(5-Br salen)₂(MeOH)₂}M(CN)₆](NEt₄) (M=Fe^III (1), Ru^III (2) and Os^III (3); 5-Brsalen=N,N′-ethylenebis(5-bromosalicylidene)iminato anion). We have computed the orbital-dependent exchange interaction for all three complexes for the first time using DFT and complete active space self-consistent field (CASSCF) methods. DFT calculations yield the anisotropic exchange as J _ξξ=3.5 cm^-1 for 1; J_ξξ=12.1 cm ^-1, J_ζζ=-6.9 cm^-1 and J _ηη=-14 cm^-1 for 2; and J_ξξ=23.7 cm^-1 and J_ζζ=-11.1 cm^-1 for 3. The computed values are in agreement with the experimental report, and this suggests that the established methodology can be used to compute the anisotropic exchange in larger clusters. Our calculations reiterate the fact that the exchange is described by a three-axis anisotropic exchange for complexes 2 and 3 as evidenced by the experiments. A stronger exchange coupling as we move down the periodic table from 3d to 5d is reproduced by our calculations, and the origin of this enhancement in the exchange interaction has been probed by using molecular orbital analysis. The electronic origin of different types of exchange observed in this series is found to be related to the energy difference between possible degenerate pairs and the nature of orbital interactions. By computing the exchange interaction, the single-ion anisotropy of Mn^III and zero-field splitting of the S=9/2 ground state of complexes 1-3 using CASSCF and/or DFT methods, we have attempted to shed light on the issue of anisotropic exchange and the barrier height for the magnetisation reversal in SMMs. Comprehensive magneto-structural correlations have been developed to offer clues on how to further enhance the barrier height in this class of SMMs. Singles club: The role of anisotropic exchange in trinuclear single-molecule magnets (SMMs) has been explored using DFT calculations and ab initio studies (see figure).