Black-box determination of temperature-dependent susceptibilities for crystalline organic radicals with complex magnetic topologies

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: A reliable tool for spin-density based properties

Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.

Multi-state formulation of the frozen-density embedding quasi-diabatization approach

We present a multi-state implementation of the recently developed frozen-density embedding diabatization (FDE-diab) methodology [D. G. Artiukhin and J. Neugebauer, J. Chem. Phys. 148, 214104 (2018)] in the Serenity program. The new framework extends the original approach such that any number of charge-localized quasi-diabatic states can be coupled, giving an access to calculations of ground and excited state spin-density distributions as well as to excitation energies. We show that it is possible to obtain results similar to those from correlated wave function approaches such as the complete active space self-consistent field method at much lower computational effort. Additionally, we present a series of approximate computational schemes, which further decrease the overall computational cost and systematically converge to the full FDE-diab solution. The proposed methodology enables computational studies on spin-density distributions and related properties for large molecular systems of biochemical interest.

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.

Antiferromagnetic ordering based on intermolecular London dispersion interactions in amphiphilic TEMPO ammonium salts

Antiferromagnetic coupling in TEMPO-based radicals can be enhanced via self-assembly through London dispersion interactions in amphiphilic solids. The synthesis, magnetic characterization, and three crystal structures of the solid radical ion salts (R-DMAT-n)X with various counterions X and alkyl chain lengths n are reported. Magnetic susceptibility and absolute EPR signal intensity measurements show singlet-triplet transitions in a number of cases, which is discussed in relation to the crystal structures. Antiferromagnetic ordering effects are sensitive to both the length of the alkyl chain and the counter anion.

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.

Verdazyls as Possible Building Blocks for Multifunctional Molecular Materials: A Case Study on 1,5-Diphenyl-3-(p-iodophenyl)-verdazyl Focusing on Magnetism, Electron Transfer and the Applicability of the Sonogashira-Hagihara Reaction

This work explores the use of Kuhn verdazyl radicals as building blocks in multifunctional molecular materials in an exemplary study, focusing on the magnetic and the electron transfer (ET) characteristics, but also addressing the question whether chemical modification by cross-coupling is possible. The ET in solution is studied spectroscopically, whereas solid state measurements afford information about the magnetic susceptibility or the conductivity of the given samples. The observed results are rationalized based on the chemical structures of the molecules, which have been obtained by X-ray crystallography. The crystallographically observed molecular structures as well as the interpretation based on the spectroscopic and physical measurements are backed up by DFT calculations. The measurements indicate that only weak, antiferromagnetic (AF) coupling is observed in Kuhn verdazyls owed to the low tendency to form face-to-face stacks, but also that steric reasons alone are not sufficient to explain this behavior. Furthermore, it is also demonstrated that ET reactions proceed rapidly in verdazyl/verdazylium redox couples and that Kuhn verdazyls are suited as donor molecules in ET reactions.

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.

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

We report on a series of eight diaryl-6-oxo-verdazyl radicals containing a tert-butyl group at the C(3) position with regard to their crystal structure and magnetic properties by means of magnetic susceptibility measurements in combination with quantum chemical calculations using a first-principles bottom-up approach. The latter method allows for a qualitative prediction and detailed analysis of the correlation between the solid-state architecture and magnetic properties. Although the perturbation in the molecular structure by varying the substituent on the N-aryl ring may appear small, the effects upon the structural parameters controlling intermolecular magnetic coupling interactions are strong, resulting in a wide spectrum of cooperative magnetic behavior. The non-substituted 1,5-diphenyl-tert-butyl-6-oxo-verdazyl radical features a ferromagnetic one-dimensional spin ladder type magnetic network-an extremely rarely observed phenomenon for verdazyl radicals. By varying substituents at the phenyl group, different non-isostructural compounds were obtained with widely different magnetic motifs ranging from linear and zigzag one-dimensional chains to potentially two-dimensional networks, from which we predict magnetic susceptibility data that are in qualitative agreement with experiments and reveal a large sensitivity to packing effects of the molecules. The present study advances the fundamental understanding between solid-state structure and magnetism in organically based radical systems.