Polygonal current models for polycyclic aromatic hydrocarbons and graphene sheets of various shapes

Abstract

Assuming that graphene is an "infinite alternant" polycyclic aromatic hydrocarbon resulting from tessellation of a surface by only six-membered carbon rings, planar fragments of various size and shape (hexagon, triangle, rectangle, and rhombus) have been considered to investigate their response to a magnetic field applied perpendicularly. Allowing for simple polygonal current models, the diatropicity of a series of polycyclic textures has been reliably determined by comparing quantitative indicators, the p-electron contribution to I B , the magnetic field-induced current susceptibility of the peripheral circuit, to n k and to r k ðCMÞ52NICS k ðCMÞ, respectively the out-of-plane components of the magnetizability tensor and of the magnetic shielding tensor at the center of mass. Extended numerical tests and the analysis based on the polygonal model demonstrate that (i) n k and r k ðCMÞ yield inadequate and sometimes erroneous measures of diatropicity, as they are heavily flawed by spurious geometrical factors, (ii) I B values computed by simple polygonal models are valid quantitative indicators of aromaticity on the magnetic criterion, preferable to others presently available, whenever current susceptibility cannot be calculated ab initio as a flux integral, (iii) the hexagonal shape is the most effective to maximize the strength of p-electron currents over the molecular perimeter, (iv) the edge current strength of triangular and rhombic graphene fragments is usually much smaller than that of hexagonal ones, (v) doping by boron and nitrogen nuclei can regulate and even inhibit peripheral ring currents, (vi) only for very large rectangular fragments can substantial current strengths be expected.

The pseudo-π model of the induced magnetic field: fast and accurate visualization of shielding and deshielding cones in planar conjugated hydrocarbons and spherical fullerenes

“…This picture denotes the presence of seven strong local diatropic currents at Clar aromatic rings, a weak global peripheral diatropic current and additionally weak diatropic currents at the inner CC bonds connecting the outer Clar aromatic rings, precisely recovering ring current maps obtained with RC analysis. 47,48 The NICS pzz scan profiles of 14 ( Fig. 6b) support this interpretation.…”

Optoelectronic Properties of Polycyclic Benzenoid Hydrocarbons of Various Sizes and Shapes for Donor‐π‐Acceptor Systems: A DFT Study

“…Large flakes of graphene or an extended PAH system can be termed as nanographene, [3,18–23] the properties of them are largely influenced by the size and edge shape [24–28] . As the size of the PAH increases, the number of isomers possible also increases [29] .…”

Consequences of Curvature on Induced Magnetic Field: The Case of Helicenes

“…Furthermore, the helical topology leads to the typical shielding cones obtained in planar rings to be reduced, owing to a deshielding region that grows along the helical axis as the number of turns increases. This implies that the most important contributions of the total magnetic response in the helical structures come from the σ‐ and core electrons, and not from the π‐ones as occurs in the case of PAHs …”