Discussion
According to simple HMO theory, which one of the following statements about butadiene is true ?
Answer: C
The true statement is that exciting an electron from the HOMO to the LUMO will not change the π charge densities.
Butadiene is an alternant hydrocarbon. By the Coulson-Rushbrooke pairing theorem its bonding and antibonding Huckel orbitals come in pairs with coefficients of equal magnitude at every atom. Since the HOMO and LUMO coefficients have the same squares at each carbon, moving an electron from one to the other leaves every π charge density at 1.
The bond orders do change, because the HOMO is bonding and the LUMO antibonding between C1-C2, while the reverse holds for C2-C3, so option B is false. Butadiene's four MOs have energies α ± 1.618β and α ± 0.618β, none non-bonding, and electrophiles attack the terminal carbons, which have the largest HOMO coefficients.
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