A new set of puckering coordinates for four-membered ring molecules

Abstract

A set of two independent internal coordinates “polar angles” are proposed which allow description of arbitrary finite bond-bending puckering deformations of four-ring molecules with constant bond length. In particular for four-ring systems of the type xyyx and xxxx, whose conformations have symmetry C 2 v - C s , D 2 h - C 2 v and D 4 h - D 2 d , respectively, a rather complete set of relations expressing geometrical parameters leke bond angles, puckering angles, torsional angles, height and diagonals by the polar angles and their implications are discussed. Using Born-Oppenheimer approximation, a qualitative illustration of the ring-bending puckering potential function as expressed by polar angles is given.