Intrinsically Chiral Aromaticity. Rules Incorporating Linking Number, Twist, and Writhe for Higher-Twist Möbius Annulenes

The geometries of coiled annulenes belonging to the chiral C2 and Dn (n = 2,7) point groups are defined by two chiral indices, Wr and Tw, respectively (writhe and twist), which sum to give an overall integer linking number, Lk (the Cãlugãreanu−White−Fuller theorem). While the value of Lk can been equated with single-twist (Lk = 1π), double-twist (Lk = 2), and higher-order (Lk > 2) twisted (Möbius−Listing) annulenes, we suggest that the correct Huckel molecular-orbital treatment is to use Tw specifically in the 2pπ−2pπ overlap correction first suggested by Heilbronner, rather than Lk. Quantitatively, because many of these systems project much of the finite value of Tw into Wr, a simple mechanism exists to increase the π-electron resonance stabilization beyond what simple Heilbronner theory predicts. Examples of a diverse set of such chiral annulenes are dissected into Wr and Tw contributions, which reveals that those with the minimum value of Tw are associated with the greater delocalized stability.