Three-dimensional fully pi-conjugated macrocycles : when 3D-aromatic and when 2D-aromatic-in-3D?

Several fully pi-conjugated macrocycles with puckeredor cage-type structures were recently found to exhibit aromaticcharacter according to both experiments and computations. Weexamine their electronic structures and put them in relation to 3D-aromatic molecules (e.g.,closo-boranes) and to 2D-aromaticpolycyclic aromatic hydrocarbons. Using qualitative theorycombined with quantum chemical calculations, wefind that themacrocycles explored hitherto should be described as 2D-aromaticwith three-dimensional molecular structures (abbr. 2D-aromatic-in-3D) and not as truly 3D-aromatic. 3D-aromatic molecules havehighly symmetric structures (or nearly so), leading to (at least) triplydegenerate molecular orbitals, and for tetrahedral or octahedralmolecules, an aromatic closed-shell electronic structure with 6n+ 2 electrons. Conversely, 2D-aromatic-in-3D structures exhibitaromaticity that results from the fulfillment of Hu??ckel's4n+ 2 rule for each macrocyclic path, yet their pi-electron counts arecoincidentally 6n+ 2 numbers for macrocycles with three tethers of equal lengths. It is notable that 2D-aromatic-in-3D macrocycliccages can be aromatic with tethers of different lengths,i.e., with pi-electron counts different from 6n+ 2, and they are related tonaphthalene. Finally, we identify tetrahedral and cubic pi-conjugated molecules that fulfill the 6n+ 2 rule and exhibit significantelectron delocalization. Yet, their properties resemble those of analogous compounds with electron counts that differ from 6n+2.Thus, despite the fact that these molecules show substantial pi-electron delocalization, they cannot be classified as true 3D-aromatics