The Density Functional Theory Account of Interplaying Long-Range Exchange and Dispersion Effects in Supramolecular Assemblies of Aromatic Hydrocarbons with Spin

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.

Formations of bimolecular barbituric acid complexes through hydrogen bonding interactions: DFT analyses of structural and electronic features

Formations of bimolecular barbituric acid (BA) complexes through hydrogen-bonding (HB) interactions were investigated in this work. BA has been known as a starting compound of pharmaceutical compounds developments, in which the molecular and atomic features of parent BA in homo-paring with another BA molecule were investigated here. The models were optimized to reach the stabilized structures and their properties were evaluated at the molecular and atomic scales. Density functional theory (DFT) calculations were performed to provide required information for achieving the goal of this work. Six dimer models were obtained finally according to examining all possible starting dimers configurations for involving in optimization calculations. N-H . . . O and C-H . . . O interactions were also involved in dimers formations besides participation of the X-center of parent BA in interaction. Molecular and atomic scales features were evaluated for characterizing the dimers formations. As a consequence, several configurations of BA dimers were obtained showing the importance of performing such structural analyses for developing further compounds from BA.

Grassmannians and Cluster Structures

Cluster structures have been established on numerous algebraic varieties. These lectures focus on the Grassmannian variety and explain the cluster structures on it. The tools include dimer models on surfaces, associated algebras, and the study of associated module categories.

Dimers in a bottle

We revisit D3-branes at toric CY3 singularities with orientifolds and their description in terms of dimer models. We classify orientifold actions on the dimer through smooth involutions of the torus. In particular, we describe new orientifold projections related to maps on the dimer without fixed points, leading to Klein bottles. These new orientifolds lead to novel $$ \mathcal{N} $$ N = 1 SCFT’s that resemble, in many aspects, non-orientifolded theories. For instance, we recover the presence of fractional branes and some of them trigger a cascading RG-flow à la Klebanov-Strassler. The remaining involutions lead to non-supersymmetric setups, thus exhausting the possible orientifolds on dimers.

Combinatorial Reid's recipe for consistent dimer models

Reid's recipe for a finite abelian subgroup $G\subset \text{SL}(3,\mathbb{C})$ is a combinatorial procedure that marks the toric fan of the $G$-Hilbert scheme with irreducible representations of $G$. The geometric McKay correspondence conjecture of Cautis--Logvinenko that describes certain objects in the derived category of $G\text{-Hilb}$ in terms of Reid's recipe was later proved by Logvinenko et al. We generalise Reid's recipe to any consistent dimer model by marking the toric fan of a crepant resolution of the vaccuum moduli space in a manner that is compatible with the geometric correspondence of Bocklandt--Craw--Quintero-V\'{e}lez. Our main tool generalises the jigsaw transformations of Nakamura to consistent dimer models. Comment: 29 pages, published version