Abstract
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 indicates that metal–metal through-space interaction is the dominant contributor to antiferromagnetic coupling. At the DFT level a procedure that utilizes pseudopotential substitution is demonstrated that allows evaluation of the direct exchange vs superexchange contributions. A complementary description is obtained with DMRG-SCF calculations that enable state-averaged CASSCF calculations with both metal and bridge orbitals in the active space. A localized orbital subspace analysis supports the DFT conclusions that in contrast to doubly bridged isoelectronic analogues, antiferromagnetic coupling in the chromium dimer arises primarily from direct metal–metal interaction but is significantly enhanced by ligand-mediated superexchange.
Highlights
Dinuclear complexes of open-shell transition metal ions are archetypal systems in the field of molecular magnetism.[1]
The results demonstrate that the magnetic coupling in the Cr(III) dimer can be correctly described by density functional theory (DFT), both qualitatively and quantitatively, provided the broken-symmetry approach is properly applied in combination with spin projection techniques and that the intrusion of irrelevant excited electronic configurations is avoided
In density matrix renormalization group (DMRG)-SCF calculations the orbitals were automatically reordered with the Fiedler algorithm to optimize convergence behavior.[79−82] The number of retained states M in the renormalization step of DMRG calculations was increased until the relative energies of all spin states computed by DMRGSCF were converged to wavenumber accuracy
Summary
Dinuclear complexes of open-shell transition metal ions are archetypal systems in the field of molecular magnetism.[1]. In addition to a long series of successful applications of BSDFT, the density matrix renormalization group (DMRG)[51−54] has recently enabled the first applications of complete active space self-consistent field (CASSCF) and N-electron valence perturbation theory (NEVPT2)[55−58] calculations to dinuclear exchange-coupled transition metal complexes using unprecedent numbers of active electrons and orbitals.[59−61] The use of extended CAS attempts to take explicitly into account excitations that would otherwise have to be treated with a method such as DDCI These recent achievements suggests that the problem of the Cr(III) dimers could be approached with multireference methods using active spaces much larger than the metal-only active space already covered in previous CASSCF studies.[13]. Both methods suggest that superexchange plays an important ancillary role in enhancing the antiferromagnetic coupling
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