Past exam of the chemistry A course of the University of Cambridge 2021 Paper 1 A4 b ii Solution 2026-10-20
For planar ammonia, the nitrogen valence atomic orbitals have symmetries , and . The hydrogen symmetry orbitals span . Consequently the in-plane orbitals form a bonding orbital, a bonding pair and their antibonding partners. The out-of-plane has no matching hydrogen combination and remains a nonbonding orbital. With the core omitted, the conventional valence occupation isThe preceding ammonia molecular orbital diagram shows the correlation. On pyramidalization, and both correlate with of the C3v point group, permitting s–p orbital mixing. The pure planar lone pair can acquire bonding character, lowering its energy and helping stabilize the pyramid. Symmetry alone does not provide a numerical inversion barrier.[ref]
Both dimers have two electrons in a valence sigma-bonding orbital and a formal valence bond order of one. For hydrogen the minimal-basis configuration is , with the -derived as highest occupied molecular orbital and as LUMO. The bonding combination has no internuclear node; the antibonding combination does.
For lithium, include the filled core pair of levels as well as the valence levels:The first two orbitals are predominantly core combinations whose bonding and antibonding occupations cancel in a simple bond-order count. The highest occupied molecular orbital is predominantly , denoted ; the LUMO is , predominantly the antibonding combination but modified by mixing with compatible contributions. The nearby empty -derived sigma and pi levels must also be shown. Only orbitals of matching symmetry mix, so this does not mean that every combination mixes with every combination.
On a common qualitative energy reference, hydrogen is much lower than lithium's valence , while lithium's core levels lie much deeper. The Li valence bonding–antibonding separation is smaller, consistent with its longer and weaker bond. The figure uses a compressed core region and schematic gaps, not measured orbital energies. The role of symmetry-compatible s–p orbital mixing in the first-row diatomics is illustrated in institutional molecular-orbital notes.[ref]
