An extensive discussion developed regarding my post on a fascinating helical -annulene. Topics included the nature of the ring current sustained by the π-electrons and in particular the bond-length alternation around the periphery and whether this should alter if the electron count were to be changed to that of a 4n+2 system (i.e. a dication). Whilst the -annulene itself is hypothetical, it emerged that some compounds known as expanded porphyrins have very similar (albeit smaller scale) helical structures. X-ray structures for two such provide useful reality checks on the calculations. Here‡ I include the (3D) coordinates of these two systems so that you can explore for yourself their helicity.
I include below Δrmeso, being the mean unsigned difference in bond length (Å) at the meso positions of the porphrin ring, the calculations being at the 6-311G(d,p) level using the DFT procedure indicated below. The linking number analysis for such systems will be reported elsewhere.
‡The WordPress system operated here does not enable 3D coordinates to be inserted into the comment section of a post, only the main body.
- S.M. Rappaport, and H.S. Rzepa, "Intrinsically Chiral Aromaticity. Rules Incorporating Linking Number, Twist, and Writhe for Higher-Twist Möbius Annulenes", J. Am. Chem. Soc., vol. 130, pp. 7613-7619, 2008. http://dx.doi.org/10.1021/ja710438j
- H.S. Rzepa, "Lemniscular Hexaphyrins as Examples of Aromatic and Antiaromatic Double-Twist Möbius Molecules", Organic Letters, vol. 10, pp. 949-952, 2008. http://dx.doi.org/10.1021/ol703129z