Advanced Inorganic Chemistry/Symmetry Elements

Advanced Inorganic Chemistry/Symmetry Elements (1.1)

Symmetry elements of the molecule are geometric entities: an imaginary point, axis or plane in space, which symmetry operations : rotation, reflection or inversion, are performed. [1],[2] Their recognition leads to the application of symmetry to molecular properties and can also be used to predict or explain many of a molecule’s chemical properties. Symmetry elements and symmetry operations are two fundamental concepts in group theory, which is the mathematical description of symmetry properties that describe the structure, bonding, and spectroscopy of molecules.

Contents 1. Point of symmetry operations 1.1. Identity, E     1.2. Proper Rotation, Cn     1.3. Reflection, σ 1.4. Inversion, i 1.5. Improper Rotation, Sn  2. Point groups 3. Example: symmetry of benzene

1. Point symmetry operations Point symmetry of a molecule results when there exists at least one point in space that remains indistinguishable from the original molecule after any symmetry operation is applied. In other words, a rotation, reflection or inversion operations are called symmetry operations if, and only if, the newly arranged molecule is indistinguishable from the original arrangement. There are five kinds of point of symmetry elements that a molecule can possess, thus, there are also five kinds of point of symmetry operations. All symmetry elements in a molecule must share at least one point in common and this point occurs at the center of the molecule.

1.1. Identity, E Identity operation comes from the German ‘Einheit’ meaning unity. This symmetry element means no change. All molecules have this element.

4. References [1] Pfenning, Brian W. (2015). Principles of Inorganic Chemistry. Hoboken: John Wiley & Sons, Inc.. pp. 195. [2] https://www-e.openu.ac.il/symmetry/symmetry-tutorial.html