Computer-Aided Identification of Symmetry Relating Groups of Molecules

Molecular symmetry plays an important role in many areas of chemistry, and students are generally taught to identify intramolecular symmetries at the undergraduate level. Intermolecular symmetry, the symmetry among groups of molecules, is of great importance in topics such as X-ray crystallography, but it receives substantially less attention. Even when familiar with such symmetries as translations, screw rotations, and glide reflections, students rarely obtain the same level of proficiency in identifying these symmetries via inspection as they do with the proper and improper rotations involved in point group symmetry. We describe a tool designed to scaffold the student’s ability to mentally manipulate molecules and identify the presence and nature of intermolecular symmetry. The tool consists of an algorithm that the student follows to generate centroids between atoms in putatively symmetry-related molecules. The easily recognized patterns formed by the centroids provide key information about the presence and nature of any intermolecular symmetry relating the molecules. The theoretical basis for the patterns formed by the centroids is provided along with worked examples, an example problem set, and a prescription for generating new exercises.