The three rules of qualitative MO theory

To determine the electronic structure of small molecules it is often enough to use just three rules of thumb.

Rule I : Two orbitals that interact form two new orbitals. The one with the lower energy is called a bonding orbital , the one with higher energy an anti-bonding orbital . The stabilization of the bonding orbital (i.e., the downward shift of its MO energy when it's formed) is smaller than the destabilization of the anti-bonding orbital (i.e., the upward shift of its MO energy).

The difference in stabilization and destabilization is relevant for repulsion. It explains, for example, why He₂ is not stable. If both the bonding and the anti-bonding orbital are completely filled, then the energy increases. It's also necessary for this that the overlap is not neglected. If we neglect the overlap, then we find that the energy doesn't change when both orbitals are completely filled. Overlap neglect is allowed, however, if only the bonding orbital is occupied.

Rule II : The (de)stabilization of the (anti-)bonding orbital is smaller when the difference of the energies of the orbitals from which the bonding and anti-bonding orbital are formed is larger.

This can be seen when we solve the secular equation for different orbitals. The (de)stabilization has the difference of the energies of the orbitals in the denominator. This rule is very useful when the initial orbitals are far apart in energy. If the difference is large enough, it may be appropriate to neglect the interaction altogether.

If the interacting orbitals each have one electron, then the difference in energies may lead to different bond types. If the difference is small, then the original orbitals contribute about equally to the orbitals that are formed. The electrons end up in the bonding orbital that spreads out over both original orbitals. This is a covalent bond . If the difference is large, then the bonding orbital will resemble the original orbitals with the lower energy. This orbital gets two electrons, whereas it originally only had one. This is an ionic bond .

Rule III : The (de)stabilization of the (anti-)bonding orbital is smaller when the overlap of the orbitals from which the bonding and anti-bonding orbital are formed is smaller.

This can also be seen if we make the reasonable assumption that the non-diagonal elements of the Fock matrix (b) are proportional to the corresponding elements of the overlap matrix (S). In lowest order the (de)stabilization is linear in the overlap for identical interacting orbitals, and even quadratic for different interacting orbitals. This rule is very useful for core orbitals. These orbitals have only a very small overlap. Their energy hardly changes when bonds are formed. Consequently we can ignore them when we look at bond formation.

Qualitative MO theory.

• Derivation of the secular equation.
• Identical interacting orbitals.
• Different interacting orbitals.
• The three rules of qualitative MO theory (this page).
• Two applications of the rules of qualitative MO theory.