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