L11 Molecular Symmetry Representations

What are totally symmetric orbitals

Don’t change sign with any symmetry operation.

For water’s point group it is called A₁

What about the other MOs

They change sign with different symmetry operations. Tables can be drawn out for them and a -1 written whenever a symmetry operation changes their sign. The B implies there is some anti-symmetry as opposed to A. The numbering is just to distinguish.

This p orbital has its own symmetry, what does that tell you

That it does not combine with any of the other MOs

A₂ character table

For d orbitals, hence it is not in water

Irreducible representation properties

Finding the reducible representation from the atomic orbitals

You can sum up the result of symmetry operations form the atomic orbitals.

Add 1 if the sign does not chnage

Subtract 1 if the sign does change

Ignore it (0) if the orbital moves

Ther planes of symmetry go through the molecule, not the atom on which the orbital is centred.

How does increasing the n of the principal axis affect the irreducible representations

you can have numbers different from 1 and -1. The p_x and p_y orbitals can be rotated 90 degrees to give a 0, and they are no longer treated separately

Consequences of x,y being treated together in representations of dimension > 1

Energy degeneracy relation to symmetry