Molecular orbital theory

Molecular orbital (MO) theory treats a molecule as a whole. The atomic orbitals of the atoms combine to form molecular orbitals that belong to the whole molecule. This is the LCAO method (linear combination of atomic orbitals). Atomic orbitals combine effectively only if they have similar energy, the same symmetry about the molecular axis, and good overlap.

Two atomic orbitals always give two molecular orbitals:

• a bonding MO, of lower energy, with electron density built up between the nuclei, holding them together; and
• an antibonding MO (marked with *), of higher energy, with a node (zero electron density) between the nuclei, pushing them apart.

The + and – signs on orbital lobes are the phases of the wave function; lobes of the same phase overlap to make a bonding orbital.

Electrons fill the MOs in order of energy, following the Aufbau, Pauli and Hund rules. The order for B₂, C₂ and N₂ is: σ1s, σ1s, σ2s, σ2s, (π2pₓ = π2p_y), σ2p_z, (π2pₓ = π2p_y), σ*2p_z. For O₂ and F₂, σ2p_z comes below the pair of π2p orbitals.

Bond order = ½ (N_b – N_a), where N_b is the number of electrons in bonding MOs and N_a in antibonding ones.

• A positive bond order means a stable molecule; a bond order of zero means the molecule does not exist (He₂, Be₂).
• The higher the bond order, the more stable the molecule and the shorter its bond.

For example, H₂ has 2 bonding electrons and none antibonding: bond order = ½(2 – 0) = 1. H₂⁺ has just one electron: bond order ½, so it exists but is weaker.

Magnetism: if all the electrons are paired, the substance is diamagnetic (weakly pushed away by a magnet). If there are unpaired electrons, it is paramagnetic (attracted by a magnet). O₂ has two unpaired electrons in its π*2p orbitals, so it is paramagnetic, as experiments show. Lewis structures, which show O₂ with all its electrons paired, cannot explain this; MO theory can.