Abstract
On the basis of a variable neighbourhood search with the AutoGraphiX software, it is conjectured that for even numbers of atoms the fully conjugated acyclic π system of maximum HOMO–LUMO gap is a `comb' in which each vertex of a backbone carries a single pendant edge. Chemically, this represents C n H 3 n/2+2 , an α, ω-diene with methylene groups attached at all intermediate positions. As n increases without limit, the conjectured asymptotic dimensionless gap is 2 2 −2 . Odd-numbered graphs that would have maximum gap as singly charged π systems are reported for up to 41 vertices; they are related to comb graphs.
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