Pseudohelical and helical primary structures of 1,2-spiroannelated four- and five-membered rings: syntheses and chiroptical properties

The pseudohelical hydrocarbons (R)-6, (S)-7, and (R)-8 and the helical hydrocarbon (P)-9, formally derived from the helical hydrocarbon (P)-4 by stepwise replacement of each of the four-membered rings by a five-membered ring, have been prepared. Their optical rotations vary systematically, both in magnitude and sign. Of the extremes, (P)-4 represents the usual case of a right-handed dextrorotatory helix, while (P)-9 represents the unusual case of a right-handed levorotatory helix. To rationalize these facts, DFT calculations of the rotatory power of (P)-helices of three-, four-, and five-membered rings have been performed. The results show a very good agreement with the experimental data for the rigid helices of three-membered rings and always show the correct sign and order of magnitude for the flexible helices of four- and five-membered rings for which Boltzmann-averaged optical rotations of up to six conformers had to be used. Within the conformers of the latter, a set of large dihedral angles for the bonds of the inner sphere correspond to a high specific rotation, and a set of small dihedral angles correspond to a low specific rotation. As a consequence, the Boltzmann-averaged values markedly depend on the geometry and weight of the conformers involved.