From the diagram, it appears that local and global aromaticity are related to how the aromatic coupling is arranged in the macrocycle. Local aromaticity is characterized by aromatic coupling within individual rings or regions with little conjugation between. Such structures are planar within their aromatic rings/regions, but generally have nonplanar geometry in-between. Global aromaticity involves aromatic coupling throughout the macrocycle, with strong conjugation between rings and an extended planar structure.
Adding electrons can alter the mode of aromaticity if the electrons enter orbitals that are predominantly bonding between rings (converting local to global) or in the reverse fashion predominantly bonding within rings (converting global to local).
This effect can be seen in a simpler system, [a,e]dibenzocyclooctetraene:
Zhu et al. 1 considered the reduction of this molecule from the neutral state to the dianion using alkali metals. The neutral molecule is clearly aromatic only locally within the benzene rings, with a nonplanar structure in the intervening cyclooctatetraene ring. When the molecule is reduced, it becomes fully planar suggesting that aromatic coupling has become globalized. (Figure from Ref. 1)
We can use the Hückel model to show semiquantitatively how this change comes about. Using this model we can calculate the pi-bond order between each pair of neighboring atoms, obtaining the following for the neutral molecule:
We have nearly a full pi bond across the mirror plane between the benzene rings, while the neighboring benzylic linkages have much reduced pi bonding. This suggests that in the neutral molecule the aromatic coupling is predominantly localized to the benzene rings, agreeing with the locally planar but globally nonplanar molecular geometry shown above.
When the alkali metal is added and two additional electrons are inserted, they go into an orbital that the Hückel model identifies as bonding in the benzylic linkages but antibonding in most other linkages, particularly in the bridges that close the benzenoid rings and the previous nearly-isolated pi bonds in the middle of the structure. The bond orders are thereby shifted:
The newly occupied orbital, selectively bonding in the benzylic linkages, strengthens conjugation there while weakening the bonds that close the smaller rings. The aromatic coupling has shifted away from the individual benzenoid rings to cover the full macrocycle, becoming global.
- Yikun Zhu, Zheng Zhou, Zheng Wei, and Marina A. Petrukhina (2020). "Two-Fold Reduction of Dibenzo[a,e]cyclooctatetraene with Group 1 Metals: From Lithium to Cesium", Organometallics, 39, 24, 4688–4695.