Relationship between torsional angles and ring-puckering coordinates

Abstract

A relationship between torsional angles and ring puckering coordinates, applicable to any puckered ring, is deduced assuming infinitesimal displacements from a planar reference conformation. For equilateral polygons there is only one maximum torsion angle θ m and one phase angle φ m for each value of m, whereas for non-equilateral polygons there is one maximum θ m j,j+1 and a correction, ϵ m j,j+1 , to be applied to the phase angle φ m for each torsion angle θ j,j+1 . The resulting expressions for equilateral pentagons and hexagons are equivalent to the empirical ones proposed previously.