Magnetic exchange coupling in Cu dimers studied with modern multireference methods and broken-symmetry coupled cluster theory

Synthesis and Properties of Ba6Fe2Te3S7, with an Fe Dimer in a Magnetic Singlet State

A new quaternary sulfide telluride, Ba6Fe2Te3S7, was synthesized by a solid-state reaction, and its crystal structure is novel. X-ray diffraction data on powder and single crystals reveal an orthorhombic lattice with a = 9.7543(3) Å, b = 18.2766(6) Å, and c = 12.0549(4) Å, and the noncentrosymmetric space group Cmc21 (No. 36). The properties of the compound were studied by magnetic susceptibility investigations, specific heat measurements, Mössbauer spectroscopy, and density functional theory calculations. Assuming Ba2+ and, as verified by the Mössbauer spectra, Fe3+, the charge balance requires the presence of a polytelluride, suggested to be a straight-chain [Te34-] polyanion. Further, the crystal structure contains [Fe2S7]8- dimers of two vertex-sharing tetrahedra, with a nearly linear Fe-S-Fe atom arrangement. The dimer exhibits antiferromagnetic coupling, with a coupling constant J = -10.5 meV (H = -2JS1S2) and S = 5/2, resulting in a spin singlet ground state. The interdimer magnetic interaction is so weak that the magnetic dimers can be treated as individuals.

Predicting Magnetic Coupling and Spin-Polarization Energy in Triangulene Analogues

Triangulene and its analogue metal-free magnetic systems have garnered increasing attention since their discovery. Predicting the magnetic coupling and spin-polarization energy with quantitative accuracy is beyond the predictive power of today's density functional theory (DFT) due to their intrinsic multireference character. Herein, we create a benchmark dataset of 25 magnetic systems with nonlocal spin densities, including the triangulene monomer, dimer, and their analogues. We calculate the magnetic coupling (J) and spin-polarization energy (ΔE_spin) of these systems using complete active space self-consistent field (CASSCF) and coupled-cluster methods as high-quality reference values. This reference data is then used to benchmark 22 DFT functionals commonly used in material science. Our results show that, while some functionals consistently correctly predict the qualitative character of the ground state, achieving quantitative accuracy with small relative errors is currently not feasible. PBE0, M06-2X, and MN15 are predicting the correct electronic ground state for all systems investigated here and also have the lowest mean absolute error for predicting both ΔE_spin (0.34, 0.32, and 0.31 eV) and J (11.74, 12.66, and 10.64 meV). They may therefore also serve as starting points for higher-level methods such as the GW or the random phase approximation. As other functionals fail for the prediction of the ground state, they cannot be recommended for metal-free magnetic systems.

Revisiting magnetic exchange couplings in heterodinuclear complexes through the decomposition method in KS-DFT

Providing tools to understand the physical mechanisms governing magnetic properties in transition metal-based compounds is still of great interest. Here, the magnetic exchange coupling in a series of heterodinuclear complexes is investigated by means of the decomposition method. This work presents the first application of the decomposition method to systems where magnetic centres may bear more than one unpaired electron. By decomposing the coupling into three physical contributions (direct exchange, kinetic exchange, and spin polarisation), we provide numerical arguments to confirm or infirm the rationalisation allowed by the conceptual analysis of the magnetic d orbitals. We also take advantage of the recently proposed generalisation of the method [David et al., J. Chem. Theory Comput., 2023, 19, 157] to get more insights into the underlying mechanisms by disentangling the coupling between centres into its electron-electron interactions.

Magneto-structural maps and bridged-ligand effect for dichloro-bridged dinuclear copper(ii) complexes: a theoretical perspective

Theoretical understanding of magneto-structural correlations in dichloro-bridged dicopper(ii) complexes can guide the design of magnetic materials having broad-scale applications. However, previous reports suggest these correlations are complicated and unclear. To clarify possible correlations, magnetic coupling constants (J _calc) of variants of a representative {Cu-(μ-Cl)₂-Cu} complex A were calculated through BS-DFT. The variation of the Cu-(μ-Cl)-Cu angle (α), Cu⋯Cu distance (R ₀), and Cu-Cl-Cu-Cl dihedral angle (τ) followed by structural optimization and calculation of the magnetic coupling constant (J _calc) revealed several trends. J _calc increased linearly with R ₀ and τ, and initially increased and then decreased with α. Further, bridging ligand effects on J _calc for dicopper(ii) complexes were evaluated through BS-DFT; the results revealed that J _calc increased with increasing ligand field strength (I^- < Br^- < Cl^- < N₃ ^- < F^-). Furthermore, a linear relationship was found between the spin density of the bridging ligand and J _calc.

Magneto-Structural Correlations in a Mixed Porphyrin(Cu2+ )/Trityl Spin System: Magnitude, Sign, and Distribution of the Exchange Coupling Constant

Tetrathiatriarylmethyl radicals (TAM or trityl) are receiving increasing attention in various fields of magnetic resonance such as imaging, dynamic nuclear polarization, spin labeling, and, more recently, molecular magnetism and quantum information technology. Here, a trityl radical attached via a phenyl bridge to a copper(II)tetraphenylporphyrin was synthesized, and its magnetic properties studied by multi-frequency continuous-wave electron paramagnetic resonance (EPR) spectroscopy and magnetic measurements. EPR revealed that the electron spin-spin coupling constant J between the trityl and Cu²⁺ spin centers is ferromagnetic with a magnitude of -2.3 GHz (-0.077 cm^-1 , + J S → 1 S → 2 ${+J{\vec{S}}_{1}{\vec{S}}_{2}}$ convention) and a distribution width of 1.2 GHz (0.040 cm^-1 ). With the help of density functional theory (DFT) calculations, the obtained ferromagnetic exchange coupling, which is unusual for para-substituted phenyl-bridged biradicals, could be related to the almost perpendicular orientation of the phenyl linker with respect to the porphyrin and trityl ring planes in the energy minimum, while the J distribution was rationalized by the temperature weighted rotation of the phenyl bridge about the molecular axis connecting both spin centers. This study exemplifies the importance of molecular dynamics for the homogeneity (or heterogeneity) of the magnetic properties of trityl-based systems.

Cooperativity-Driven Reactivity of a Dinuclear Copper Dimethylglyoxime Complex

In this report, we present the dinuclear copper(II) dimethylglyoxime (H₂ dmg) complex [Cu₂ (H₂ dmg)(Hdmg)(dmg)]⁺ (1), which, in contrast to its mononuclear analogue [Cu(Hdmg)₂ ] (2), is subject to a cooperativity-driven hydrolysis. The combined Lewis acidity of both copper centers increases the electrophilicity of the carbon atom in the bridging μ₂ -O-N=C-group of H₂ dmg and thus, facilitates the nucleophilic attack of H₂ O. This hydrolysis yields butane-2,3-dione monoxime (3) and NH₂ OH that, depending on the solvent, is then either oxidized or reduced. In ethanol, NH₂ OH is reduced to NH₄ ⁺ , yielding acetaldehyde as the oxidation product. In contrast, in CH₃ CN, NH₂ OH is oxidized by Cu^II to form N₂ O and [Cu(CH₃ CN)₄ ]⁺ . Herein are presented the combined synthetic, theoretical, spectroscopic and spectrometric methods that indicate and establish the reaction pathway of this solvent-dependent reaction.

Ab initio molecular dynamics free energy study of enhanced copper (II) dimerization on mineral surfaces

Understanding the adsorption of isolated metal cations from water on to mineral surfaces is critical for toxic waste retention and cleanup in the environment. Heterogeneous nucleation of metal oxyhydroxides and other minerals on material surfaces is key to crystal growth and dissolution. The link connecting these two areas, namely cation dimerization and polymerization, is far less understood. In this work we apply ab initio molecular dynamics calculations to examine the coordination structure of hydroxide-bridged Cu(II) dimers, and the free energy changes associated with Cu(II) dimerization on silica surfaces. The dimer dissociation pathway involves sequential breaking of two Cu2+-OH- bonds, yielding three local minima in the free energy profiles associated with 0-2 OH- bridges between the metal cations, and requires the design of a (to our knowledge) novel reaction coordinate for the simulations. Cu(II) adsorbed on silica surfaces are found to exhibit stronger tendency towards dimerization than when residing in water. Cluster-plus-implicit-solvent methods yield incorrect trends if OH- hydration is not correctly depicted. The predicted free energy landscapes are consistent with fast equilibrium times (seconds) among adsorbed structures, and favor Cu2+ dimer formation on silica surfaces over monomer adsorption.