step 9

Molecular Orbital Mixing

More detail was added to this answer in response to input and questions from students in the class of 2008. If you have suggestions or contributions please e-mail me.

First of all while the stage 1 (pre mixing diagram) of diatomics is very easy to produce, the mixing in diatomics is very difficult to evaluate because more than two orbitals are involved. The total energy of the molecule must be stabilised. This means that very occasionally an occupied MO can move up in energy as long as the occupied MOs move down more in energy. If only two MOs mix then one always goes up and one down, and the one that goes up better be unoccupied. However, once a third MO starts mixing strongly the situation is extremely complex, and this is what has happened here.

Remember:
necessary requirements before mixing can occur:
  • MOs must be of the same symmetry
  • mixing must stabilise the total energy of the molecule
mixing tends to be large when at least one of the following criteria are met:
  • MOs are close in energy
  • one of the MOs is non-bonding
  • one of the MOs unoccupied
  • MOs are in the HOMO-LUMO region

Mixing occurs between all the 3σ, 4σ, 5σ and 6σ MOs because they are of the same symmetry. The 3σ MO is very deep in energy and unlikely to contribute significantly to the final mixed MOs, this leaves the 4σ and 5σ which lie close in energy, but are both occupied, while the 6σ lies very high in energy. Because the 6σ is unoccupied it can be strongly destabilised on mixing without costing the molecule energy. Overall the destabilisation of the 5σ must be less than the stabilisation of the 4σ for the total energy of the molecule to go down.

The actual mixing in this molecule is complex and in this situation a calculation needs to be carried out to determine the final form of the MOs. Look here to see the real MOs

copy the mixed orbitals onto your diagram shifting the energy of the orbitals appropriately ... see the diagram below!

MOs in Inorganic Chemistry course What should you do when faced with an example like this and you don't have recourse to a calculation?
State which MOs will mix, list the "rules" for mixing (Lecture 3), draw a reasonable set of mixed orbitals showing the direction of stabilisation or destablisation (ideally with annotations, showing you know how to draw mixed orbitals), and state that calculations are required before the exact mixing, and movement of energy levels can be determined.
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