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
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
proper rotation axis
rotate by 360º/n
axis with highest value of n is the principal axis
C2 axes perpendicular to the principal Cn are called C2' axes
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
all atoms are moved through inversion centre to an equal distance on opposite side
i may or may not be an atomic centre
improper rotation axis
rotate by 360º/n, then reflect ^
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 C∞v) may be polar.