Q2(c). Bond orders of H₂⁺, Ne₂, CN⁻, NO and HF; order of stability

Method: fill the molecular orbitals in order of energy with all the electrons (valence electrons for second-row atoms) and count bonding (N_b) and antibonding (Nₐ) electrons.

1. H₂⁺ (1 electron): (σ₁ₛ)¹. Bond order =12(1-0)= 0.5 A one-electron bond: it exists (in discharges) but is weak and long.
2. Ne₂ (16 valence electrons): (σ₂ₛ)²(σ*₂ₛ)²(σ₂ₚ)²(π₂ₚ)⁴(π*₂ₚ)⁴(σ*₂ₚ)². Bond order =12(8-8)= 0 Antibonding electrons cancel the bonding ones: Ne₂ does not exist as a stable molecule.
3. CN⁻ (4+5+1=10 valence electrons, isoelectronic with N₂ and CO): (σ₂ₛ)²(σ*₂ₛ)²(π₂ₚ)⁴(σ₂ₚ)². Bond order =12(8-2)= 3 A triple bond, all electrons paired: diamagnetic.
4. NO (5+6=11 valence electrons): (σ₂ₛ)²(σ*₂ₛ)²(σ₂ₚ)²(π₂ₚ)⁴(π*₂ₚ)¹. Bond order =12(8-3)= 2.5 One unpaired electron in π*: NO is paramagnetic. Losing it gives NO⁺ (bond order 3), which is why NO is easily oxidised.
5. HF: only the H 1s and F 2p_z orbitals have the right symmetry and similar energy to overlap. They form one bonding σ MO (mostly F in character) and one σ*. The F 2s, 2pₓ and 2p_y electrons are non-bonding (three lone pairs). (2s)²(σ)²(2pₓ)²(2p_y)²(σ*)⁰. Bond order =12(2-0)= 1

Order of stability

1. A larger bond order means more net bonding electrons, a shorter bond and a higher bond energy. Stability (bond strength) therefore follows bond order: 3pt] Ne₂ (0) < H₂⁺ (0.5) < HF (1) < NO (2.5) < CN⁻ (3)
2. Ne₂ is least stable (no net bond). CN⁻ is most stable: its triple bond is why cyanide is a strong, persistent ligand.
3. The HF single bond is unusually strong (574 kJ mol⁻¹, H–F 91.7 pm) because the large electronegativity difference adds ionic character. Bond order compares the number of shared electron pairs; for bonds between very different atoms polarity also counts.

Application. the same counting explains why CN⁻ and CO bind strongly to iron in haemoglobin and cytochrome oxidase, and why NO⁺ (bond order 3) forms stable nitrosonium salts such as [NO]⁺[BF₄]⁻.