L1-2 Molecular symmetry

Why is knowing the symmetry of a molecule useful

Starting definition of molecular symmetry

A molecule has symmetry if we can do something to it, and the result is indistinguishable – looks unchanged – from what we started with.

What is rotation symmetry

Rotating the molecule around a certain axis leaves it looking unchanged

What is a symmetry element

A point, line or plane around which a symmetry operation can be performed

What is a symmetry operation

A symmetry opeation is caried out on a symmetry element e.g. rotating around an axis symmetry element. One symmetry element can have more thna one symmetry operation done on it.

In the case of water, it has a C₂ axis symmetry element

If C₂ is “rotate by 180°” then what is C₂.C₂

Rotate by 180° twice i.e. 360° 

What is rotating 360° effectively equal to

The “identity” labelled “E” that is shared by all molecules

What is another way to write C₃.C₃

C₃² - equivalent to 240° rotation

What is the principal axis

it is the axis with the highest order n in C_n e.g C₃ in BF_3.

not all molecules have a principal axis

The principal axis is by convention the z axis

When is there not a principal axis

If there are multiple axes with the same, highest n

Or if the molecule has no rotations

For instance methane here has 4 C₃ axes which pass through the carbon atom and 1 of the 4 hydrogens.

How are mirror planes in a molecule labelled + if the pass through the principal axis

the v means it is vertical

σ_h and σ_d

h is for horizontal axes in planar molecules

d id for dihedral and these planes bisect the angle between C₂ axes

Inversions

inversion i swaps (x,y,z) with (-x,-y,-z) through a centre of inversion

What is Improper Rotation

Denoted by S_n. It is rotation + reflection

Inversion itself “i” is equivalent to S₂ 

it is a C₂ rotation followed by reflection in a plane perpendicular to the rotation axis. It leaves the molecule in an indistinguishable state

The rotations and reflections do not have to be working symmetry operations for the molecule

What is a point group

What happens when you “multipy” together two symmetry operations in the same point group

It results in another symmetry operation from the point group. This could be the identity or something else.

What does the number in the point group names typically mean

The order of the principal rotation axis in the molecule.

What do point groups tell you

What symmetry the molecule has

WHat is the order of a point group

The number of symmetry operatiosn within that group

Overview of some ways to determine a molecule’s point group

Point group illustrative/cartoon example

Sub group connections

Some groups can be considered subsets of others i.e. all the symmetry operations form a group + more are contained within another group with more symmetry operations. Substitutions may lower the symmetry of a molecule, losing some of its operatiosn but preserving the rest.