Symmetry analysis of periodicity and internal torsional conformers around a single bond

A simple formula to predict the number of equivalent conformations upon internal rotation around a single bond is derived. If the separate parts A and B, of a single bonded molecule A-B, possess N_a and N_b symmetry planes that contain the single bond, the number of symmetrical conformations is found to be Z = N_aN_b/J, where J is the number of these planes which are common. The energy potential for internal rotation then has a period of 2π/Z. Unsymmetrical conformations are infinite in number, but are shown to occur in infinite sets, each set with 2N_aN_b/J equivalent conformations. Extension to three-center molecules is also made.