Apply LCAO to homonuclear diatomic molecules

Combine orbitals with matching symmetry

The linear combination of atomic orbitals approach starts with atomic orbitals of suitable symmetry and comparable energy. Each pair produces a lower-energy bonding combination and a higher-energy antibonding combination.

For homonuclear diatomic molecules, the two atoms contribute equivalent atomic orbitals. This makes H₂, O₂ and F₂ useful models for seeing how orbital shape, energy and occupancy fit together.

LCAO rules for a diatomic molecule

N atomic orbitals form N molecular orbitals. In-phase addition gives the bonding combination; out-of-phase subtraction gives the antibonding combination.

Orbitals can combine effectively only when they have compatible symmetry about the internuclear axis and sufficiently similar energies. End-on overlap gives σ partners; side-on overlap gives π partners.

From H₂ to O₂ and F₂

In H₂, two 1s orbitals form σ(1s) and σ*(1s). The bonding orbital has no internuclear node; the antibonding orbital has one. The two electrons fill σ(1s).

For O₂ and F₂, the 2s orbitals form σ(2s) and σ*(2s). The 2p orbital aligned with the bond axis forms σ(2p) and σ*(2p), while the two perpendicular 2p pairs form two degenerate π(2p) and two degenerate π*(2p) orbitals.

For O₂ and F₂, use the valence ordering σ2s < σ*2s < σ2p < π2p < π*2p < σ*2p. The number and symmetry of the combinations come from the parent orbitals; electron count decides their occupancy later.

Worked example: one pair of 2p orbitals

Take one 2p orbital from each atom aligned along the bond axis. In-phase end-on overlap increases density between the nuclei and gives σ(2p); out-of-phase overlap creates an internuclear node and gives σ*(2p).

If the two 2p orbitals are parallel but perpendicular to the axis, the same phase choices instead give π(2p) and π*(2p).

Practise counting the resulting orbitals

Keep orbital count separate from electron capacity. Two atomic orbitals provide two basis functions, so they always produce two molecular orbitals.

A degenerate π pair comes from two separate perpendicular directions, such as 2pₓ and 2pᵧ when the bond is taken as the z-axis.

Apply LCAO to F₂

F₂ has the same set of valence molecular-orbital shapes as O₂ because both are formed from two equivalent second-period atoms. It differs in the number of electrons placed into those levels.

Do not invent extra orbitals for extra electrons. The basis-orbital count fixes the number of molecular orbitals.

Common mistake: counting lobes as orbitals

A p orbital has two lobes of opposite phase, but both lobes belong to one wavefunction. Two p orbitals do not become four molecular orbitals just because four lobes are drawn.

Another common mistake is to combine orbitals with incompatible symmetry. A p orbital perpendicular to the axis cannot form a σ combination with an s orbital in a homonuclear diatomic molecule.

Check your understanding

For H₂, O₂ and F₂, be ready to show parent orbitals, phase, symmetry, bonding character and relative energy. Occupancy and bond order belong in the diagram lesson that follows.

Next, extend the same LCAO reasoning from two centres to benzene and linear polyenes with several aligned p orbitals.