Annulenes can twist, and I have blogged about a number of examples (cations and neutrals). The twist can be portioned into a twist associated with the dihedral angle as one progresses around the compound and writhe which is associated with distortion of the annulene into a third dimension.¹

Herges has prepared the 36-annulene 1 where the anthracenyl units were introduced to force the loop out of plane.² Four different conformations of 1 where isolated by crystallization out of different solvents. 1a and 1b were produced in benzene, and they differ by having two half-twists (L_k=2) and one half-twist (L_k=1), respectively. 1c was isolated from DMF, with one half-twist. 1d was isolated from Et₂O/CH₂Cl₂.

1

Computations at the B3LYP/6-31g* level identified 10 low lying conformations, and the ones corresponding to the experimentally observed forms are shown in Figure 1. The computed conformer that matches with 1d differs form the experimental version by a rotation about one single bond, and the computed version has a different topology than the experiment. One item of note is that all of the 10 computed conformers are dominated by the twist (T_w) and have very small writhe.

1a	1b
1c	1d
1e

Figure 1. B3LYP/6-31G* optimized structures of 1a-e.

Though not isolated in experiment, one of the low lying conformers has three half-twists (L_k=3) and is also shown in Figure 1 as 1e. Identification of this highly twisted species would be quite interesting.

References

(1) Fowler, P. W.; Rzepa, H. S., "Aromaticity rules for cycles with arbitrary numbers of half-twists," Phys. Chem. Chem. Phys., 2006, 8, 1775-1777, DOI: 10.1039/b601655c.

(2) Mohebbi, A.; Mucke, E. K.; Schaller, G.; Köhler, F.; Sönnichsen, F.; Ernst, L.; Näther, C.; Herges, R., "Singly and Doubly Twisted [36]Annulenes: Synthesis and Calculations," Chem. Eur. J., 2010, 16, 7767-7772, DOI: 10.1002/chem.201000277,

InChIs

1: InChI=1/C80H52/c1-9-25-65-57(17-1)73-45-41-53-33-35-54(36-34-53)42-46-75-61-21-5-13-29-69(61)79(70-30-14-6-22-62(70)75)51-52-80-71-31-15-7-23-63(71)76(64-24-8-16-32-72(64)80)48-44-56-39-37-55(38-40-56)43-47-74-59-19-3-11-27-67(59)78(68-28-12-4-20-60(68)74)50-49-77(65)66-26-10-2-18-58(66)73/h1-52H/b45-41-,46-42+,47-43-,48-44+,50-49+,52-51-,53-41-,54-42-,55-43-,56-44-,73-45-,74-47-,75-46-,76-48-,77-49-,78-50+,79-51+,80-52+
InChIKey=KXWPWHPRFOXOIX-IFDMNBDGBZ