On the importance of the biquadratic terms in exchange coupled systems: A post-HF investigation

Tale of Three Molecular Nitrides: Mononuclear Vanadium (V) and (IV) Nitrides As Well As a Mixed-Valence Trivanadium Nitride Having a V3N4 Double-Diamond Core

Transmetallation of [VCl₃(THF)₃] and [TlTp^tBu,Me] afforded [(Tp^tBu,Me)VCl₂] (1, Tp^tBu,Me = hydro-tris(3-tert-butyl-5-methylpyrazol-1-yl)borate), which was reduced with KC₈ to form a C_3v symmetric V^II complex, [(Tp^tBu,Me)VCl] (2). Complex 1 has a high-spin (S = 1) ground state and displays rhombic high-frequency and -field electron paramagnetic resonance (HFEPR) spectra, while complex 2 has an S = 3/2 ⁴A₂ ground state observable by conventional EPR spectroscopy. Complex 1 reacts with NaN₃ to form the V^V nitride-azide complex [(Tp^tBu,Me)V≡N(N₃)] (3). A likely V^III azide intermediate en route to 3, [(Tp^tBu,Me)VCl(N₃)] (4), was isolated by reacting 1 with N₃SiMe₃. Complex 4 is thermally stable but reacts with NaN₃ to form 3, implying a bis-azide intermediate, [(Tp^tBu,Me)V(N₃)₂] (A), leading to 3. Reduction of 3 with KC₈ furnishes a trinuclear and mixed-valent nitride, [{(Tp^tBu,Me)V}₂(μ₄-VN₄)] (5), conforming to a Robin-Day class I description. Complex 5 features a central vanadium ion supported only by bridging nitride ligands. Contrary to 1, complex 2 reacts with NaN₃ to produce an azide-bridged dimer, [{(Tp^tBu,Me)V}₂(1,3-μ₂-N₃)₂] (6), with two antiferromagnetically coupled high-spin V^II ions. Complex 5 could be independently produced along with [(κ₂-Tp^tBu,Me)₂V] upon photolysis of 6 in arene solvents. The putative {V^IV≡N} intermediate, [(Tp^tBu,Me)V≡N] (B), was intercepted by photolyzing 6 in a coordinating solvent, such as tetrahydrofuran (THF), yielding [(Tp^tBu,Me)V≡N(THF)] (B-THF). In arene solvents, B-THF expels THF to afford 5 and [(κ₂-Tp^tBu,Me)₂V]. A more stable adduct (B-OPPh₃) was prepared by reacting B-THF with OPPh₃. These adducts of B are the first neutral and mononuclear V^IV nitride complexes to be isolated.

Magnetic Anisotropy in a Cubane-like Ni4 Complex: An Ab Initio Perspective

Magnetic anisotropy, in the absence of an external magnetic field, relates to the degeneracy lift of energy levels. In the standard case of transition metal complexes, this property is usually modeled by an anisotropic spin Hamiltonian and one speaks of "zero-field splitting" (ZFS) of spin states. While the case of mononuclear complexes has been extensively described by means of ab initio quantum mechanical calculations, the literature on polynuclear complexes studied with these methodologies is rather scarce. In this work, advanced multiconfigurational wave function theory methods are applied to compute the ZFS of the ground S = 4 state of an actual tetranickel(II) complex, displaying a magnet behavior below 0.5 K. First, the isotropic couplings are computed in the absence of the spin-orbit coupling operator, in the full complex and also in clusters with only two active nickel(II) centers, confirming the occurrence of weak ferromagnetic couplings in this system. Second, the single-site magnetic anisotropies are computed on a cluster bearing only one active nickel(II) site, showing that the single-site anisotropy axes are not oriented in an optimal fashion for generating a large uniaxial molecular anisotropy. Furthermore, the possibility for involving only a few local orbital excited states in the calculation is assessed, actually opening the way for a consistent and manageable treatment of the ZFS of the ground S = 4 state. Third, multiconfigurational calculations are performed on the full complex, confirming the weak uniaxial anisotropy occurring for this state and also, interestingly, revealing a significant contribution of the lowest-lying orbitally excited S = 3 states. Overall, by comparison with the experiment, the reported results question the common habit of using only one structure, in particular derived from a crystallography experiment, to compute magnetic anisotropy parameters.

Exchange Coupling Interactions from the Density Matrix Renormalization Group and N-Electron Valence Perturbation Theory: Application to a Biomimetic Mixed-Valence Manganese Complex

The accurate description of magnetic level energetics in oligonuclear exchange-coupled transition-metal complexes remains a formidable challenge for quantum chemistry. The density matrix renormalization group (DMRG) brings such systems for the first time easily within reach of multireference wave function methods by enabling the use of unprecedentedly large active spaces. But does this guarantee systematic improvement in predictive ability and, if so, under which conditions? We identify operational parameters in the use of DMRG using as a test system an experimentally characterized mixed-valence bis-μ-oxo/μ-acetato Mn(III,IV) dimer, a model for the oxygen-evolving complex of photosystem II. A complete active space of all metal 3d and bridge 2p orbitals proved to be the smallest meaningful starting point; this is readily accessible with DMRG and greatly improves on the unrealistic metal-only configuration interaction or complete active space self-consistent field (CASSCF) values. Orbital optimization is critical for stabilizing the antiferromagnetic state, while a state-averaged approach over all spin states involved is required to avoid artificial deviations from isotropic behavior that are associated with state-specific calculations. Selective inclusion of localized orbital subspaces enables probing the relative contributions of different ligands and distinct superexchange pathways. Overall, however, full-valence DMRG-CASSCF calculations fall short of providing a quantitative description of the exchange coupling owing to insufficient recovery of dynamic correlation. Quantitatively accurate results can be achieved through a DMRG implementation of second order N-electron valence perturbation theory (NEVPT2) in conjunction with a full-valence metal and ligand active space. Perspectives for future applications of DMRG-CASSCF/NEVPT2 to exchange coupling in oligonuclear clusters are discussed.