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. 

 

 

Next: Hückel Theory