Molecular Symmetry and Chirality
Introduction and Overview
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The symmetry of a molecule describes how its different parts relate to one another geometrically. symmetry plays an important role in many areas of chemistry, with effects on:

  • physical properties: e.g. dipole moment, chirality
  • spectroscopic properties: transition intensities, geometric equivalence of groups or nuclei
  • bonding interactions: bonds require overlap of atomic orbitals of correct symmetry
Terms and Definitions

Symmetry Operation: a spatial manipulation performed on a molecule that leaves it in an configuration identical to and superimposable upon the original configuration.

Symmetry Element: an axis, plane, or point about which a symmetry operation is performed.

Point Group: a symbol that identifies all the symmetry elements present in a molecule.

Symmetry Elements and Operations

Element Operation Symbol ANotes
none identity
(no operation)
  • a molecule is always unchanged if no operation is performed, so all molecules possess E
  • E = C1
    i.e. rotation by 360° about any axis is just like doing nothing
rotation axis
rotate by
  • axis with highest value of n is the principal axis
  • C2 axes perpendicular to the principal Cn are called C2' axes
mirror plane reflection σ
  • σ parallel to and containing Cn is vertical: σv
  • σ parallel to Cn and bisecting two C2' axes is dihedral: σd
  • σ perpendicular to Cn is horizontal: σh
inversion i
  • all atoms are moved through inversion centre to an equal distance on opposite side
  • i may or may not be an atomic centre
rotation axis
rotate by 360º/n, then reflect ^ to axis Sn
  • combination rotation/reflection operation
  • odd n value requires both Cn and σh (e.g. BF3 has an S3 axis, and also has both a C3 and a σh)
  • even n value may or may not have Cn and σh (e.g. CH4 has an S4 axis, but has neither a C4 nor a σ perpendicular to the S4)
  • S1 = σ, S2 = i

Effects on Molecular Properties

To be chiral, a molecule must lack both i and σ.*
Molecules belonging to groups Cn (including E) and Dn are chiral.

* This is a small oversimplification. The most precise requirement for chirality is the lack of any Sn element, but because hardly anybody really knows what those look like, there are a series of increasingly precise shortcuts used to Spotting a Chiral Compound. Or, you can just skip to the summary at the end.

To be polar, a molecule must lack all of i, C2' axes, and σh.
Molecules belonging to groups Cs, Cn (incl E) and Cnv (including Cv) may be polar.

This page is maintained and copyright by W. Stephen McNeil at UBC Okanagan.