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.
Rappaport
Shay M
SM
Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
Rzepa
Henry S
HS