Peptide frontier-orbital gaps narrow by backbone electrostatics

Aromatic side chains carry the optical and redox chemistry of peptides, and lengthening one is widely expected to extend its conjugation and narrow its HOMO-LUMO gap. We test that expectation with plane-wave density functional theory on 22 isolated neutral peptides NH2-(X)n-COOH (X = Phe, Tyr, Trp, Cys; n = 1 to 5, and n = 10 for Cys and Trp). The gap does narrow, at the same rate for all three aromatic residues, i.e., -0.17 to -0.18 eV per residue, even though benzene, phenol and indole are very different chromophores. Residue-resolved projections reveal why: nothing delocalises. Every aromatic frontier orbital is 97 to 100 % confined to a single residue and the HOMO participation number saturates at one ring. Each residue instead keeps its own local gap: for Trp it is invariant to within 0.03 eV over n = 2 to 10, while over that same span the global gap falls by 1.19 eV. The global gap is therefore an extreme-value functional of the residue site energies, gap(n) =-{Delta}(n), whose alignment penalty accounts for the entire effect: the polar backbone generates a monotonic internal electrostatic ramp that leaves the two gap edges at opposite ends of the chain, 32 [A] apart. We set out the resulting design rules for peptide-based bio-organic semiconductors.