*“A task that invokes fearful symmetry: **Form point groups from elements’ litanies. **Planes and axes, inversions; **These abstract immersions **Unpack complex structures‘ consistencies.”*

Continuing the week of poetic homages, the 24 April 2019 limerick used as its central theme a memorable phrase–*“*fearful symmetry*”*— from William Blake’s “The Tyger.”

Symmetry is an important concept in chemistry, as many of the properties that molecules exhibit can be predicted from the types of symmetry displayed in their three-dimensional shapes. (For this highly visual topic, I have relied on several outstanding resources constructed and written by many others, and I have provided several pertinent links to their much more detailed information.)

“**A task that invokes fearful symmetry:/ ****Form point groups from elements’ litanies.”**

Molecular symmetry is typically presented in advanced chemistry coursework. It is complex, challenging, and rewarding; characterizing its associated tasks via Blake’s phrasing of “fearful symmetry,” in the first line, seems apt!

The second line introduces pertinent vocabulary. A molecule can contain different types of symmetry elements (separate from the periodic table’s definition!), which in turn represent particular symmetry operations. For instance, a square has “four-fold rotational symmetry”: we can imagine repeatedly turning a perfect square 90 degrees clockwise; we’d achieve four equivalent, indistinguishable square shapes, in total. We would denote this set of symmetry operations (the four rotations) with a symmetry element called a C_{4} proper axis; this is the axis around which the rotations occur.

A list of all the elements exhibited by a given molecule (i.e., the “litany” of its symmetry elements) constitutes its symmetric designation: the point group of that molecule.

**“Planes and axes, inversions; / These abstract immersions / Unpack complex structures‘ consistencies.”**

Along with axes of rotation, internal mirror planes and centers of inversion are also types of symmetry elements. Considering the symmetry of a molecule is a rigorous exercise and often requires a complex thought process: an “abstract immersion.” For instance, an analysis of the molecule benzene, discussed previously, involves characterizing two dozen symmetry operations.

Understanding a molecule’s symmetry provides a valuable introduction to its spectroscopic and geometric properties. If two molecules are in the same point group, then even though they may be made up of completely different atoms, they will display similar behaviors in some respects; understanding their symmetries can help “unpack [these] consistencies.”