The pseudohelical hydrocarbons (
R)-
6, (
S)-
7,
and (
R)-
8 and the helical hydrocarbon (
P)-
9, formally derivedfrom the helical hydrocarbon (
P)-
4 by stepwise replacement of each of the four-membered rings by afive-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-h
anded dextrorotatory helix, while(
P)-
9 represents the unusual case of a right-h
anded levorotatory helix. To rationalize these facts, DFTcalculations of the rotatory power of (
P)-helices of three-, four-,
and five-membered rings have beenperformed. The results show a very good agreement with the experimental data for the rigid helices ofthree-membered rings
and always show the correct sign
and order of magnitude for the flexible helicesof four-
and five-membered rings for which Boltzmann-averaged optical rotations of up to six conformershad to be used. Within the conformers of the latter, a set of large dihedral angles for the bonds of theinner sphere correspond to a high specific rotation,
and a set of small dihedral angles correspond to alow specific rotation. As a consequence, the Boltzmann-averaged values markedly depend on the geometry
and weight of the conformers involved.