This mixing of wavefunctions will always happens when the two original wavefunctions have the same symmetry.
Instead of the potential energy
curves crossing over each other, the two
wavefunctions will mix, and the curves for the better,
mixed, states will not cross.
The Non-
Crossing Rule:
Potential energy
curves corresponding to
electronic states
of the same symmetry cannot cross
This effect is important - avoided crossings are often the reason why chemical reactions have a barrier.
The Rule applies to molecular orbitals as well as wavefunctions for whole molecules.
For example, consider a situation where a molecule has two molecular orbitals. The energies of these MOs are altered by a geometric change in the molecule.
·
Each MO can be categorized with respect to the symmetry of the
molecule.
·
Suppose the molecule has a plane of symmetry, then the MOs must
be either symmetric, S, (unchanged)
or antisymmetric, A, (all signs of
the MO changed by reflection in this plane.
As the geometry of the molecule changes, the energies of the MOs will
change.
·
Suppose there are two orbitals, I and II, and I is lower in
energy at the beginning of the geometrical change, while II is lower at the
end.
·
The potential energy curves will be different depending on the
symmetries of the two orbitals.
Here are the
two situations when the MOs have either the same or different symmetries:
·
If the two orbitals have
the same symmetry, they can overlap and interact.
· This mixing together of the two original orbitals produces two new orbitals, one lower and one higher in energy than the original orbitals.
·
The interaction gets
stronger as the two original orbitals come closer together in energy. If the orbitals can overlap, they will, and
will mix to give an avoided crossing.
· On the other hand, if they have different symmetries, they cannot overlap, and so the energy curves can cross each other.