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 anti-clockwise), 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.

5) Improper rotation (Rota-reflex) axis. Sn

Rotation Cn followed by reflection in a reflection in a perpendicular plane.

Allene