Q4(a). LCAO; bonding, non-bonding and antibonding orbitals of H₂
What is LCAO? What are bonding, non-bonding and anti-bonding orbitals? Illustrate with a suitable diagram with an example of H₂ molecule within the framework of molecular orbital (MO) theory.
Answer in brief
LCAO writes a molecular orbital as a linear combination of atomic orbitals, ψ=c_Aφ_A+c_Bφ_B. In-phase combination gives a lower-energy bonding MO (σ1s), out-of-phase a higher-energy antibonding MO (σ*1s); an AO that finds no partner keeps its energy as a non-bonding MO. H₂ is (σ1s)², bond order 1.
Key points
- near each nucleus an electron of the molecule behaves much as in the atom, so the MO is built from the atomic orbitals: ψ=c_Aφ_A+c_Bφ_B. For a homonuclear molecule c_A=± c_B. n AOs always give n MOs. AOs combine effectively…
- ψ₊=N₊(1s_A+1s_B). The waves add in phase: electron density is built up between the nuclei and attracts both, so the energy falls below that of 1s. Cylindrically symmetric: σ1s.
- ψ₋=N₋(1s_A-1s_B). The waves cancel midway: a nodal plane between the nuclei, density pushed outside, energy raised. It is raised more than the bonding MO is lowered (Δ E*>Δ E, because of overlap), so filling both is net…
- an AO of the wrong symmetry or very different energy has no partner and stays at its atomic energy, neither bonding nor antibonding. In HF the F 2pₓ and 2p_y orbitals (π symmetry) cannot overlap the H 1s orbital (σ symmetry):…
The full model answer
Written out in full, as it should go in the answer booklet. The solution page with its diagrams follows it.
- LCAO: near each nucleus an electron of the molecule behaves much as in the atom, so the MO is built from the atomic orbitals: ψ=c_Aφ_A+c_Bφ_B. For a homonuclear molecule c_A=± c_B. n AOs always give n MOs. AOs combine effectively only if they have comparable energy, the same symmetry about the bond axis and appreciable overlap.
- Bonding MO: ψ₊=N₊(1s_A+1s_B). The waves add in phase: electron density is built up between the nuclei and attracts both, so the energy falls below that of 1s. Cylindrically symmetric: σ1s.
- Antibonding MO: ψ₋=N₋(1s_A-1s_B). The waves cancel midway: a nodal plane between the nuclei, density pushed outside, energy raised. It is raised more than the bonding MO is lowered (Δ E*>Δ E, because of overlap), so filling both is net antibonding: σ*1s.
- Non-bonding MO: an AO of the wrong symmetry or very different energy has no partner and stays at its atomic energy, neither bonding nor antibonding. In HF the F 2pₓ and 2p_y orbitals (π symmetry) cannot overlap the H 1s orbital (σ symmetry): they become non-bonding lone pairs. In H₂ there is none.
- H₂: two electrons, paired, in σ1s: H₂: (σ1s)², b=12(N_b-Nₐ)=12(2-0)=1 A single bond, diamagnetic; bond length 74 pm, dissociation energy 432 kJ mol⁻¹.
- Test of the model: H₂⁺ (σ1s)¹, b=12, exists but is weaker; He₂ (σ1s)²(σ*1s)², b=0, is not a stable molecule.
Application. the same diagram, with 2s and 2p orbitals, explains the paramagnetism of O₂ and the bond orders of N₂, O₂⁺ and O₂⁻; photoelectron spectra show the MO energies directly.
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All parts of Question 4
- 4(a) LCAO; bonding, non-bonding and antibonding orbitals of H₂10 marks
- 4(b) Capillary action, contact angle and γ=12hρ gr10 marks
- 4(c) Does a KCl salt bridge eliminate the liquid junction?10 marks
- 4(d) Diamagnetic [Ni(CN)₄]²⁻ and paramagnetic [NiCl₄]²⁻10 marks
- 4(e) Why d–d transitions are forbidden, weak, and yet observed10 marks