Computer-Aided Identification of Symmetry Relating Groups of Molecules

Abstract

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 pointgroup 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.

Plans vs Reality: Reflections on Chemical Crystallography Online Teaching During COVID-19

“…In emergency circumstances like the present, performing the practice is very difficult, but not impossible, thanks to advanced online alternatives. It is worth noting that there are a number of interactive teaching tools and dynamic simulations that have been developed so far to depict various crystallographic principles, many of which are freely available on the Internet. − They all significantly bolster the adoption of crystallographic concepts, thus facilitating the education in the domain of crystallography. A great step forward in the area of the dynamic simulations of SCXRD was made by Barbour who made them more realistic by introducing the real motion of the diffractometer.…”

Leveraging cognitive resources to investigate the impact of molecular orientation on students’ activation of symmetry resources

“…These include activities using various objects (Herman and Lievin, 1977;McKay and Boone, 2001;Flint, 2011), shapes (Gallian, 1990), artwork (Glasser, 1967), dice (Grafton, 2011), and guided inquiry activities (Luxford et al, 2012;Rattanapirun and Laosinchai, 2021) and virtual visualization tools (Cass et al, 2005;Korkmaz and Harwood, 2004;Meyer and Sargent, 2007;Tuvi-Arad and Gorsky, 2007;Sein, 2010;Tuvi-Arad and Blonder, 2010). Additionally, a virtual tool has been developed to help students understand how inter-molecular symmetry can be invoked to relate collections of molecules (Ruiz and Johnstone, 2020). While these reports provide evidence for a rich landscape related to symmetry instruction, our goal for this study was to characterize students' recognition of specific symmetry elements from a cognitive perspective.…”

A new library of 3D models and problems for teaching crystallographic symmetry generated through Blender for use with 3D printers or Sketchfab

“…By its very nature, understanding crystallography requires a strong ability to intuit 3D spatial relationships (Chapuis, 2011;Graz ˇulis et al, 2015). These relationships can be taught to students via mathematical concepts such as matrix algebra, symmetry and group theory, though diagrammatic demonstration of symmetry relationships is of prime importance and utility (Tuvi-Arad & Blonder, 2010;Grafton, 2011;Luxford et al, 2012;Southam & Lewis, 2013;Fuchigami et al, 2016;Girolami, 2016;Penny et al, 2017;Ruiz & Johnstone, 2020). Classically, 2D projections (stereographic projections) of 3D relationships have been used in crystallography (Hardgrove, 1997;Stro ´z ˙, 1997;Chen et al, 2015;Duda et al, 2020).…”