Symmetry
Many molecules have symmetric shapes.
The symmetry of molecules determines many
of their properties.
Very powerful statements about molecular
properties can be (easily) made based on their
symmetries.
The study of molecular symmetry is
important in:
Bonding – which bonds (σ, π, …) composed
of which atomic orbitals.
Vibrations – how many vibrations of each
‘type’, how many active in IR spectra, how
many in Raman.
Electronic Spectroscopy – which transitions
are allowed and if forbidden what makes
them weakly observable.
Reactivity – if reacting molecules approach in
a symmetric manner, what parts of their
electronic structure are involved in reactions.
Symmetry operations.
A symmetry operation is an operation
performed on a molecule that leaves it
apparently unchanged.
Example, rotation about a symmetry axis.
Reflection in a mirror plane:
There are 5 distinct symmetry operations:
1) Identity
2) Rotation about an axis
3) Reflection in a plane
4) Inversion symmetry – centre of
symmetry
5) Improper rotations (Rota-reflex)
1) Identity: No action taken. Leave the
molecule alone. Rotation by 360o
Symbol: E (or I in some texts)
2) Rotation about an axis. Rotation by
(360/n)o, n - integer. (180, 120, 90, 72, 60
degrees)
Symbol Cn . The largest value of n is called
the Principle Axis of Rotation.
Examples:
(360°/n) = 120° so n = 3 (Principle).
There are 3 C2 axes as well.
The principal rotation axis of the benzene
molecule is a C6 axis running perpendicular
to the molecule.
There are 2 C6
(clockwise and anticlockwise), 2 C3 and a
C2 about this same
axis.
Also there are 6 C2 axes in the plane of the
molecule
3) Reflection in a plane.
Symbol σ
If the molecule has a principle axis:
Planes containing the principle axis and
bonds (e.g. H2O, NH3 …) σv
Planes containing the principle axis and
bisecting bonds (e.g. ) σd
Planes perpendicular to the principle axis,
σh.
(Were are the mirror planes in benzene?).
4) Centre of symmetry. i.
H
H
C
H
C
H
i
5) Improper rotation (Rota-reflex) axis. Sn
Rotation Cn followed by reflection in a
reflection in a perpendicular plane.
Allene