Reflecting on symmetry

The concept of symmetry is introduced in GCSE mathematics, but provides an incredibly powerful tool for understanding molecular behaviour in topics such as spectroscopy and quantum mechanics. The way that simple symmetry elements apply to molecular structures can be introduced by working in two dimensions and considering planar molecules.

Extending these principles to three dimensions is much easier using molecular models, and hand-held models probably have an advantage over computer generated ones.¹ Recent advances in 3D printing provide interesting opportunities in this area.² However, more homemade teaching aids can be just as effective, for example: a collection of objects showing different symmetry; a magnet-backed mirror and a set of modified molecular models; and a frame to demonstrate different symmetry axes.³

Xenia Xistouri and Demetra Pitta-Pantazi from the University of Cyprus have suggested students’ mathematical performance in reflective symmetry tasks can be predicted by their general mathematical achievement, perspective taking abilities and spatial rotation abilities, in descending order of importance.⁴ Ji-Won Son from the State University of New York in Buffalo, US, has also suggested that there is confusion between reflection and rotation among both students and pre-service teachers.⁵

We saw in a previous article⁶ that the position of any point (and consequently any atom) can be defined in terms of its x and y coordinates, denoted as (x,y). If we can understand the behaviour of individual points when symmetry operations are applied, and identify appropriate symmetry elements (mirror planes, rotational axes and inversion centres), then we will be able to combine several points and study molecules.

Paul Yates discusses how to move from reflection symmetry and rotation symmetry to molecular symmetry, rotation and inversion.