Phenalenyl is a triangular aromatic molecule made of three fused benzene rings, carrying an unpaired electron, and many of its derivatives show crystal structures with stacked radicals. Here, we investigate the inter-molecular binding in phenalenyl dimers by state-of-the-art computational methods and phenomenological models. Aside from being important for the supramolecular assembly of such radical molecules, the theoretical insight is relevant in methodological aspects, due to the interplay of long-range exchange coupling effects and van der Waals forces. We used comparative wave function-based and density functional theories. Drawing the potential energy surfaces as a function of inter-planar separation and mutual rotation of the monomer units, we found an interesting pattern which is not discovered in previous computational reports on the title systems. The dependence can be nicely interpreted by a transparent phenomenological model based on an orbital overlap paradigm of exchange coupling. We also brought forth a simplified phenomenological valence bond (VB) model of inter-molecular coupling, which is realized on the background of the VB spin model inside of the aromatic monomers and calibrated with the corresponding ab initio data. As the systems can be considered good candidates with potential applications in spintronics and organic magnetism, the theoretical rationalization opens up prospective ways to realize such promises.

We present a series of pyrazolato-bridged copper complexes with interesting structures that can be considered prototypic patterns for tri-, hexa- and hepta- nuclear systems. The trinuclear shows an almost regular triangle with a μ3-OH central group. The hexanuclear has identical monomer units, the Cu6 system forming a regular hexagon. The heptanuclear can be described as two trinuclear moieties sandwiching a central copper ion via carboxylate bridges. In the heptanuclear system, the pyrazolate bridges are consolidating the triangular faces, which are sketching an elongated trigonal antiprism. The magnetic properties of these systems, dominated by the strong antiferromagnetism along the pyrazolate bridges, were described transparently, outlining the energy levels formulas in terms of Heisenberg exchange parameters J, within the specific topologies. We succeeded in finding a simple Kambe-type resolution of the Heisenberg spin Hamiltonian for the rather complex case of the heptanuclear. In a similar manner, the weak intermolecular coupling of two trimer units (aside from the strong exchange inside triangles) was resolved by closed energy formulas. The hexanuclear can be legitimately proposed as a case of coordination-based aromaticity, since the phenomenology of the six-spins problem resembles the bonding in benzene. The Broken-Symmetry Density Functional Theory (BS-DFT) calculations are non-trivial results, being intrinsically difficult at high nuclearities.

We obtained thorough insight into the capabilities of various computational methods to account for the ligand field (LF) regime in lanthanide compounds, namely, a weakly perturbed ionic body and quasidegenerate orbital multiplets. The LF version of the angular overlap model (AOM) was considered. We intentionally took very simple idealized systems, the hypothetical [TbF]2+, [TbF2]+ and [Tb(O2NO)]2+, in order to explore the details overlooked in applications on complex realistic systems. We examined the 4f and 5d orbital functions in connection to f–f and f–d transitions in the frame of the two large classes of quantum chemical methods: wave function theory (WFT) and density functional theory (DFT). WFT methods are better suited to the LF paradigm. In lanthanide compounds, DFT faces intrinsic limitations because of the frequent occurrence of quasidegenerate ground states. Such difficulties can be partly encompassed by the nonstandard control of orbital occupation schemes. Surprisingly, we found that the simplest crystal field electrostatic approximation, reconsidered with modern basis sets, works well for LF parameters in ionic lanthanide systems. We debated the largely overlooked holohedrization effect that inserts artificial inversion symmetry into standard LF Hamiltonians.

Aromatic hydrocarbons with fused benzene rings and regular triangular shapes, called n-triangulenes according to the number of rings on one edge, form groundstates with n-1 unpaired spins because of topological reasons. Here, we focus on methodological aspects emerging from the density functional theory (DFT) treatments of dimer models of the n = 2 triangulene (called also phenalenyl), observing that it poses interesting new problems to the issue of long-range corrections. Namely, the interaction comprises simultaneous spincoupling and van der Waals effects, i.e., a technical conjuncture not considered explicitly in the benchmarks calibrating long-range corrections for the DFT account of supramolecular systems. The academic side of considering dimer models for calculations and related analysis is well mirrored in experimental aspects, and synthetic literature revealed many compounds consisting of stacked phenalenyl cores, with intriguing properties, assignable to their long-range spin coupling. Thus, one may speculate that a thorough study assessing the performance of state-of-the-art DFT procedures has relevance for potential applications in spintronics based on organic compounds.