Internal rotation and space groups

Abstract

Relationships between crystallographic space groups and the symmetry groups of molecular models with multiple internal rotations were explored. With position vectors defined as functions of internal rotation coordinates and after defining unit cells for internal rotation models, it was possible to transform these unit cells into unit cells of two- or three-dimensional space groups. Specific examples are given for models with two or three internal rotations. The vector of the symmetry numbers σ j of the internal rotation model is the equivalent of the wavevector k in crystals.