Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge / 2024 / Paper 1 / 2 / d

The elementary valence-MO model gives $\boxed{\text{bond order}({\mathrm{C}}_2)=2}$. Each carbon supplies four $n=2$ valence electrons, so fill eight electrons in the ordering appropriate to the lighter second-row diatomics:The two ${\pi }_u$ orbitals are degenerate, as are the two ${\pi }_g^{\ast }$ orbitals. The $2s$ bonding and antibonding occupations cancel; four net p-bonding electrons remain, giving $(6-2)/2=2$. Mixing between sigma orbitals of compatible symmetry places the occupied ${\pi }_u$ pair below the empty p-derived ${\sigma }_g$ orbital in this diagram. All occupied orbitals are paired.

The omitted $1s$ orbitals form filled ${\sigma }_{g}1s$ and ${\sigma }_u^{\ast }1s$ levels. Their contributions to the formal bond order cancel, and their low energies and small spatial extent make them largely core-like. Omitting them simplifies this valence diagram without claiming they do not exist or have exactly no effect on molecular energies.