Intrinsically chiral aromaticity. Rules incorporating linking number, twist, and writhe for higher-twist Mobius annulenes

The geometries of coiled annulenes belonging to the chiral C-2 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 Calugareanu-White-Fuller theorem). While the value of L-k can been equated with single-twist (L-k = 1 pi), double-twist (L-k = 2), and higher-order (L-k > 2) twisted (Mobius-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.