Q.What do you understand by Linear combination of atomic orbitals in MO theory?

Molecular Orbital Theory — MO Diagrams, Bond Order & Magnetism

The big idea. When atoms bond, their atomic orbitals combine (LCAO) into molecular orbitals that belong to the whole molecule. Each pair of atomic orbitals gives one bonding MO (lower energy, electron density between the nuclei) and one antibonding MO (higher energy, marked with a *). Fill these with the molecule's electrons, and you can read off its bond order, stability and — crucially — its magnetism.

The two orderings

For second-period homonuclear diatomics there are two energy orderings, because s–p mixing pushes the σ2p up:

• Li₂ through N₂ (≤ 14 valence e⁻) — s–p mixing order: σ2s, σ2s, (π2px = π2py), σ2pz, (π2px = π2py), σ2pz. Here the π2p bonding MOs sit below σ2pz.
• O₂, F₂, Ne₂ — normal order: σ2s, σ2s, σ2pz, (π2px = π2py), (π2px = π2py), σ2pz. Here σ2pz sits below the π2p.

Bond order

Bond order = ½ (N_bonding − N_antibonding).

Fill the MOs (Aufbau, Pauli, Hund) and count. Standard values:

Ions follow from adding/removing electrons: O₂⁺ 2.5, O₂⁻ (superoxide) 1.5, O₂²⁻ (peroxide) 1; N₂⁺ and N₂⁻ both 2.5; He₂⁺ 0.5; NO 2.5, NO⁺ 3, CN⁻ 3, CO 3.

Magnetism — MOT's triumph

A species is paramagnetic if it has unpaired electrons, diamagnetic if all are paired. MOT famously predicts that O₂ is paramagnetic — its last two electrons go singly into the degenerate π*2p orbitals (Hund's rule) — which the simple Lewis structure O=O cannot explain. B₂ is also paramagnetic (two electrons singly in π2p).

Bond order, length, energy — and adding/removing an electron

Higher bond order means a shorter bond and a higher dissociation energy. Whether ionisation raises or lowers the bond order depends on which MO the electron leaves or enters:

• O₂ → O₂⁺ removes an antibonding π* electron → bond order rises (2 → 2.5).
• O₂ → O₂⁻ adds an antibonding π* electron → bond order falls (2 → 1.5). …