Cooperative Magnetism in Crystalline N-Aryl-Substituted Verdazyl Radicals: First-Principles Predictions and Experimental Results

Electronic and Magnetic Interactions in 6-Oxoverdazyl Diradicals: Connection through N(1) vs C(3) Revisited

Four isomeric di-6-oxoverdazyl diradicals connected at their N(1) or C(3) positions with either 1,3- or 1,4-phenylene linkers were obtained and characterized by spectroscopic, electrochemical, magnetic, and structural methods. These results were compared to those for the corresponding 6-oxoverdazyl monoradicals. UV-vis spectroscopy demonstrated that only the N(1)-connected para-through-benzene diradical has a distinct spectrum with significant bathochromic and hypsochromic shifts relative to the remaining species. Electrochemical analysis revealed two one-electron reduction processes in all diradiacals, while only the N(1)-connected para-through-benzene diradical exhibits two one-electron oxidation processes separated by 0.10 V. Variable temperature EPR measurements in polystyrene solid solutions gave negative mean exchange interaction energies J for all diradicals, suggesting the dominance of conformers with significant intramolecular antiferromagnetic interactions for the meta-through-benzene isomers. DFT calculations predict a small preference for the triplet state with the ΔES-T of about 0.25 kcal mol-1 for both meta-through-benzene connected diradicals.

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.

X-ray Absorption Near-Edge Structure Spectroscopy of a Stable 6-Oxoverdazyl Radical and Its Diamagnetic Precursor

The electronic structure of 1,3,5-triphenyl-6-oxoverdazyl, a heteroatom-rich stable organic radical, and its diamagnetic 1,3,5-triphenyl-6-oxotetrazane precursor are probed using X-ray absorption near-edge structure (XANES) spectroscopy. The N K-edge XANES spectra of the 6-oxoverdazyl radical contain strong N 1s → π* resonances for each set of equivalent nitrogen atoms. The fact that these resonances are absent from the analogous spectra of the 6-oxotetrazane, whereas the O K-edge and C K-edge XANES spectra of both species are very similar, demonstrates that the unpaired electron of the radical is localized primarily on the N atoms of the 6-oxoverdazyl heterocycle. The O K-edge XANES spectra of both species contain strong O 1s → π* (C═O) peaks, but the peak of the radical is red-shifted by 0.5 eV relative to that of the 6-oxotetrazane, which indicates that the C═O bond in the radical is part of a larger π-conjugated system. The proposed interpretations of the XANES spectra are aided by density-functional calculations.

Ferro- or antiferromagnetism? Heisenberg chains in the crystal structures of verdazyl radicals

In this study, we address the question of the origin of ferromagnetic or antiferromagnetic interactions in alkynyl-substituted 1,5-diphenyl-6-oxo verdazyl radicals. While a TMS-alkynyl derivative (3) shows antiferromagnetic ordering at low temperatures, the corresponding deprotected alkynyl verdazyl (4) shows ferromagnetic interactions. For both compounds, magnetic Heisenberg chains are characteristic, which were studied systematically by means of X-ray crystallography and quantum chemical calculations. Ferromagnetic interactions are rarely found in such radicals. Therefore, uncovering such structure-property relationships is of crucial importance in order to understand and design promising ferromagnetic networks. Using this knowledge, we were able to design and crystallize diyne derivatives showing comparable solid state characteristics and therefore antiferro- and ferromagnetic Heisenberg chain structures. We show that the understanding of such property-structure relationships is adequate for the design of organic-magnetic materials with defined cooperative effects within the class of verdazyl radicals.

Towards reliable references for electron paramagnetic resonance parameters based on quantum chemistry: the case of verdazyl radicals

We present an efficient and accurate computational procedure to calculate properties measurable by EPR spectroscopy. We simulate a molecular dynamics (MD) trajectory by employing the quantum mechanically derived force field (QMDFF) [S. Grimme, J. Chem. Theory Comput., 2014, 10, 4497] and sample the trajectory at different time steps. For each snapshot EPR properties are calculated with a hybrid density functional theory (DFT) method. EPR spectra are simulated based on the averaged results. We applied the strategy to a number of previously published and novel verdazyl radicals, for which we recorded EPR spectra. The resulting simulated spectra are compatible with experiment already before employing an additional fitting step, in contrast to those from single point electronic-structure calculations. After the refinement, the experimental data are excellently reproduced, and the fitted EPR parameters do not deviate much from the calculated ones. This provides confidence in ascribing a direct physical meaning to the refined data in terms of experimental EPR parameters rather than merely considering them as mathematical fit parameters. We also find that couplings to hydrogen nuclei have a significant influence on the spectra of verdazyl radicals.

Syntheses, spectroscopy, and crystal structures of 3-(4-bromo-phen-yl)-1,5-di-phenyl-formazan and the 3-(4-bromo-phen-yl)-1,5-di-phenyl-verdazyl radical and the crystal structure of the by-product 5-anilino-3-(4-bromo-phen-yl)-1-phenyl-1H-1,2,4-triazole

The title compounds, C19H15BrN4, C20H16BrN4 and C20H15BrN4, are nitro-gen-rich organic compounds that are related by their synthesis. The verdazyl radical, in which stacking leads to anti-ferromagnetic inter-actions, was reported previously [Iwase et al. (2013 ▸). Phys. Rev. B, 88, 184431]. For this compound, improved structural data and spectroscopic data are presented. The other two compounds have been crystallized for the first time and form stacks of dimers, roughly along the a-axis direction of the crystal. The formazan mol-ecule shows signs of rapid intra-molecular H-atom exchange typical for this class of compounds and spectroscopic data are provided in addition to the crystal structure. The triazole compound appears to be a side-product of the verdazyl synthesis.

Synthesis and Magnetic Properties of Stable Radical Derivatives Carrying a Phenylacetylene Unit

A nitronyl nitroxide derivative, 2-phenylethynyl-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-1-oxyl-3-oxide (1), and two verdazyl derivatives carrying a phenylacetylene unit, 1,5-diphenyl-3-phenylethynyl-6-oxo-1,2,4,5-tetrazin-2-yl (2) and 1,5-diisopropyl-3-phenylethynyl-6-oxo-1,2,4,5-tetrazin-2-yl (3), were synthesized and their packing structures were studied by X-ray crystallographic analysis and magnetically characterized in the solid state. While 1 and 3 had an isolated doublet spin state, 2 formed an antiferromagnetically coupled pair (2J/k_B = −118 K). Density functional theory (DFT) calculations reveal that the spin density polarized in the phenyl group decreases as the dihedral angle between the phenyl ring and radical plane increases.

Strong intermolecular antiferromagnetic verdazyl-verdazyl coupling in the solid state

Strong magnetic couplings are generally observed intramolecularly in organic diradicals or in systems in which they are promoted by crystal engineering strategies involving, for example, transition metal ligation. We herein present a strong intermolecularly coupling verdazyl radical in the solid state without the use of such design strategies. The crystal structure of an acetylene-substituted verdazyl radical shows a unique antiparallel face-to-face orientation of the neighboring verdazyl molecules along with verdazyl-acetylene interactions giving rise to an alternating antiferromagnetic Heisenberg chain. Single crystal structural data at 80, 100, 173, and 223 K show that one of the π-stacking distances depends on temperature, while heat capacity data indicate the absence of a phase transition. Based on this structural input, broken symmetry DFT calculations predict a change from an alternating linear Heisenberg chain with two comparable coupling constants J₁ and J₂ at higher temperatures towards dominant pair interactions at lower temperatures. The predicted antiferromagnetic coupling is confirmed experimentally by magnetic susceptibility, solid-state EPR and NMR spectroscopic results.