Three-Dimensional Fully pi-Conjugated Macrocycles: When 3D-Aromatic and when 2D-Aromatic-in-3D?

28 March 2022, Version 3
This content is a preprint and has not undergone peer review at the time of posting.


Several fully pi-conjugated macrocycles with puckered or cage-type structures were recently found to exhibit aromatic character according to both experiments and computations. We examine their electronic structures and put them in relation to 3D-aromatic molecules (e.g., closo-boranes) and to 2D-aromatic polycyclic aromatic hydrocarbons. Using qualitative theory combined with quantum chemical calculations, we find that the macrocycles explored thus far should be described as 2D-aromatic with three-dimensional molecular structures (abbr. 2D-aromatic-in-3D) and not as truly 3D-aromatic. 3D-aromatic molecules have highly symmetric structures (or nearly so), leading to (at least) triply degenerate molecular orbitals, and for molecules with tetrahedral or octahedral structures an aromatic closed-shell electronic structure results with 6n + 2 electrons. On the other hand, 2D-aromatic-in-3D structures exhibit aromaticity that results from the fulfillment of Hückel’s 4n + 2 rule for each individual macrocyclic path, yet, their pi-electron counts are coincidentally 6n + 2 numbers for macrocycles with three tethers of equal lengths. The 3D-macrocyclic molecules, suggested to be 3D-aromatic, are instead similar to naphthalene. It is notable that 2D-aromatic-in-3D macrocyclic cages can be aromatic with tethers of different lengths, i.e., when their pi-electron counts differ from 6n + 2. Finally, we identify tetrahedral and cubic pi-conjugated molecules that fulfill the 6n + 2 rule and exhibit significant electron delocalization. Yet, their properties resemble those of analogous compounds with electron counts that differ from 6n + 2. Thus, despite that these tetrahedral and cubic molecules show substantial pi-electron delocalization they cannot be classified as true 3D-aromatics.


Electron delocalization
Hückel's rule
Baird's rule
Cage compounds

Supplementary materials

Electronic Supporting Information
ACID and EDDB plots, tables with current strengths, EDDB results on delocalization, analysis of potential 3D-aromaticity of P4, Si4(4-) and closo-borane B12H12(2-), Cartesian coordinates, absolute energies


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