Two applications of the rules of qualitative MO theory

We will illustrate the three rules of qualitative MO theory for Li₂ and Be₂. The minimal basis (i.e., the smallest possible basis) for these molecules has four orbitals. We have a 1s and a 2s orbital on each nucleus. The energies of the 1s and the 2s orbitals are far apart. According to rule II we can neglect the interaction of the 1s orbitals with the 2s orbitals. The reason why the energy of the 1s orbital is smaller than that of the 2s orbital is that it's much more compact. This means that an electron in the 1s stays much closer to the nucleus than an electron in the 2s. Consequently, the overlap between the 1s orbitals is also much smaller than that between the 2s orbitals. According to rule III, the (de)stabilization of the orbitals formed from the 1s orbitals is small. In fact, they are so small that we can neglect the 1s orbitals. This is quite general. We can distinguish between core orbitals and valence orbitals . The core orbitals do not participate in bond formation. Only the orbitals with the highest energy and the most diffuse orbitals form bonds. These are the valence orbitals. For Li and Be the 1s orbital is a core orbital. So for the bond formation we can focus only on the two 2s orbitals. These form a bonding and an anti-bonding orbital. In Li₂ only the bonding orbital is filled. For Be₂ both the bonding and the anti-bonding orbital is completely filled. Because of rule I this means an increase in energy. MO theory predicts that Be₂ is not stable. Indeed, Be₂ forms only a very weak bond.

Qualitative MO theory.

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