Magnetic exchange of trinuclear spin frustration system: CASPT2 and density functional theory study on hydroxo-bridged chromium complex [Cr3(NH3)10(OH)4]·Br5

The Effect of Geometry, Spin, and Orbital Optimization in Achieving Accurate, Correlated Results for Iron-Sulfur Cubanes

Iron-sulfur clusters comprise an important functional motif in the catalytic centers of biological systems, capable of enabling important chemical transformations at ambient conditions. This remarkable capability derives from a notoriously complex electronic structure that is characterized by a high density of states that is sensitive to geometric changes. The spectral sensitivity to subtle geometric changes has received little attention from correlated, large active space calculations, owing partly to the exceptional computational complexity for treating these large and correlated systems accurately. To provide insight into this aspect, we report the first Complete Active Space Self Consistent Field (CASSCF) calculations for different geometries of the [Fe(II/III)₄S₄(SMe)₄]^-2 clusters using two complementary, correlated solvers: spin-pure Adaptive Sampling Configuration Interaction (ASCI) and Density Matrix Renormalization Group (DMRG). We find that the previously established picture of a double-exchange driven magnetic structure, with minute energy gaps (<1 mHa) between consecutive spin states, has a weak dependence on the underlying geometry. However, the spin gap between the singlet and the spin state 2S + 1 = 19, corresponding to a maximal number of Fe-d electrons being unpaired and of parallel spin, is strongly geometry dependent, changing by a factor of 3 upon slight deformations that are still within biologically relevant parameters. The CASSCF orbital optimization procedure, using active spaces as large as 86 electrons in 52 orbitals, was found to reduce this gap compared to typical mean-field orbital approaches. Our results show the need for performing large active space calculations to unveil the challenging electronic structure of these complex catalytic centers and should serve as accurate starting points for fully correlated treatments upon inclusion of dynamical correlation outside the active space.

Subsystem density-functional theory for interacting open-shell systems: spin densities and magnetic exchange couplings

We investigate the possibility of describing interacting open-shell systems in high-spin and broken-symmetry (BS) states with subsystem density-functional theory (sDFT). This subsystem method typically starts from the electronic-structure results obtained for individual systems, for which the spin states can be individually defined. Through the confining effect of the embedding potential and/or the use of monomer basis sets, these individual spin states can be preserved in sDFT calculations. This offers the possibility of easy convergence to broken-symmetry states with arbitrary local spin patterns. We show that the resulting spin densities are in very good agreement with successfully converged broken-symmetry Kohn-Sham density-functional theory (KS-DFT) calculations. Yet sDFT can even cure those BS cases where KS-DFT suffers from convergence problems or convergence to undesired spin states. In contrast to KS-DFT, the sDFT-results only show a mild exchange-correlation functional dependence. We also show that magnetic coupling constants from sDFT are not satisfactory with standard approximations for the non-additive kinetic energy. When this component is evaluated "exactly", i.e. based on potential reconstruction, however, the magnetic coupling constants derived from spin-state energy differences are greatly improved. Hence, the interacting radicals studied here represent cases where even (semi-)local approximations for the non-additive kinetic-energy potential work well, while the parent energy functionals do not yield satisfactory results for spin-state energy differences.

A perfect triangular dysprosium single-molecule magnet with virtually antiparallel Ising-like anisotropy

A perfect triangular Dy₃ single-molecule magnet was reported. Each Dy(iii) magnetic axis is oriented almost normal to the plane of Dy₃, and the intramolecular magnetic dipole interaction gives rise to a virtually antiparallel Ising-like ground state.

Metal-ion induced ferromagnetic polarization in a mixed-spin system

Three new 3d-3d heterometallic complexes, [CuM^II(hmb)₆(OH)]ClO₄·H₂O (M = Zn (1), Ni (2) and Co (3)) (Hhmb = 2-hydroxy-3-methoxy-benzaldehyde), have been synthesized. Structural analysis reveals that the three complexes are isostructural. Three Cu^II ions are in a perfect trigonal geometrical frustration and form a tetrahedral frustrated system with the introduced fourth ion Zn^II/Ni^II/Co^II. Magnetic studies indicate the antiferromagnetic coupling between metal ions in all 1, 2 and 3. Due to the geometrical frustration, spin-frustrated magnetism is also a typical feature of 1-3 and the magnetostructural correlation is far more complicated than their structures. The detailed magnetic investigation found that the ground state spin of 2 cannot be simply determined by the antiferromagnetically linear arrangement of spins, because the strong antiferromagnetic coupling between Cu^II and Ni^II ions quenches the spin frustration and ferromagnetically polarizes the spins of the [Cu] unit. Contrarily, the antiferromagnetic coupling between Cu^II and Co^II ions is not strong enough in 3, so there is no similar behaviour compared to 2.

Quantitative prediction and interpretation of spin energy gaps in polyradicals: the virtual magnetic balance

Open-shell organic molecules possessing more than two unpaired electrons and sufficient stability at room temperature are very unusual, but some of them were recently synthesized and promise a number of fascinating applications.

A unified view of the theoretical description of magnetic coupling in molecular chemistry and solid state physics

The magnetic interactions in organic diradicals, dinuclear inorganic complexes and ionic solids are presented from a unified point of view. Effective Hamiltonian theory is revised to show that, for a given system, it permits the definition of a general, unbiased, spin model Hamiltonian. Mapping procedures are described which in most cases permit one to extract the relevant magnetic coupling constants from ab initio calculations of the energies of the pertinent electronic states. Density functional theory calculations within the broken symmetry approach are critically revised showing the contradictions of this procedure when applied to molecules and solids without the guidelines of the appropriate mapping. These concepts are illustrated by describing the application of state-of-the-art methods of electronic structure calculations to a series of representative molecular and solid state systems.