Validation Challenge of Density-Functional Theory for Peptides: Example of Ac-Phe-Ala$_5$-LysH$^+$

We assess the performance of a group of exchange-correlation functionals for predicting the secondary structure of peptide chains, up to a new many-body dispersion corrected hybrid density functional, coined PBE0+MBD*. For the purpose of validation, we first compare to published, high-level CCSD(T) benchmark conformational energy hierarchies for 73 conformers of small three-residue peptides, establishing that the van der Waals corrected PBE0 functional yields an average error of only $\approx$ 20 meV ($\approx$ 0.5 kcal/mol). This compares to $\approx$ 40-50~meV for non-dispersion corrected PBE0 and 50-100~meV for different empirical force fields. For longer peptide chains that form secondary structure, CCSD(T) level benchmark data are currently unaffordable. We thus turn to the experimentally well studied Ac-Phe-Ala$_5$-LysH$^+$ peptide, for which four closely competing conformers were experimentally established. For comparison, an exhaustive conformational space exploration yields at least eleven competing low energy minima. We show that (i) the many-body dispersion correction, (ii) the hybrid functional nature of PBE0+MBD*, and (iii) zero-point corrections are needed to reveal the four experimentally observed structures as the minima that would be populated at low temperature.