Peptide frontier-orbital gaps narrow by backbone electrostatics
Wu, X.; Fu, W.
Show abstract
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) =<g_f>-{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.
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