A General Definition of Ring Puckering Coordinates

Abstract

A unique mean plane is defined for a general monocyclic puckered ring. The geometry of the puckering relative to this plane is described by amplitude and phase coordinates which are generalizations of those introduced for cyclopentane by Kilpatrick, Pitzer, and Spitzer. Unlike earlier treatments based on torsion angles, no mathematical approximations are involved. A short treatment of the four-, five-, and six-membered ring demonstrates the usefulness of this concept. Finally, an example is given of the analysis of crystallographic structural data in terms of these coordinates. © 1975, American Chemical Society. All rights reserved.