Meeting the Challenge of Magnetic Coupling in a Triply-Bridged ChromiumDimer: Complementary Broken-Symmetry Density Functional Theory andMultireference Density Matrix Renormalization Group Perspectives

摘要

Face-sharing octahedral dinuclear Cr(III) compounds with d³–d³ electronic configurations represent nontrivial examples of electronic complexity, posing particular challenges for theoretical and computational studies. A tris-hydroxy-bridged Cr(III)–Cr(III) system has proven to be a richly rewarding target for studies of magnetism and electron paramagnetic resonance spectroscopy. It was also reported to be a peculiarly difficult system to treat with density functional theory (DFT). In this work the magnetic coupling problem for this dimer is approached with broken-symmetry (BS)-DFT and multireference calculations that utilize the density matrix renormalization group (DMRG) to handle full-valence active spaces. BS-DFT is shown to recover the correct ordering and energy spacing of Heisenberg spin states if used in conjunction with appropriate spin projection procedures, albeit with pronounced functional sensitivity. The contrasting conclusions of previous studies are traced to incorrect inclusion of electronically excited configurations. Analysis of the direct and differential overlap of corresponding orbital pairs from the BS-DFT solution indicatesthat metal–metal through-space interaction is the dominantcontributor to antiferromagnetic coupling. At the DFT level a procedurethat utilizes pseudopotential substitution is demonstrated that allowsevaluation of the direct exchange vs superexchange contributions.A complementary description is obtained with DMRG-SCF calculationsthat enable state-averaged CASSCF calculations with both metal andbridge orbitals in the active space. A localized orbital subspaceanalysis supports the DFT conclusions that in contrast to doubly bridgedisoelectronic analogues, antiferromagnetic coupling in the chromiumdimer arises primarily from direct metal–metal interactionbut is significantly enhanced by ligand-mediated superexchange.