Electronic Energies Are Not Enough: An Ion Mobility-Aided, Quantum Chemical Benchmark Analysis of H+GPGG Conformers.

Peptides and proteins exist not as single, lowest energy structures but as ensembles of states separated by small barriers. In order to study these species we must be able to correctly identify their gas phase conformational distributions, and ion mobility spectrometry (IMS) has arisen as an experimental method for assessing the gas phase energetics of flexible peptides. Here, we present a thorough exploration and benchmarking of the low energy conformers of the small, hairpin peptide H+GPGG with the aid of ion mobility spectrometry against a wide swath of density functionals (35 dispersion-corrected and uncorrected functionals represented by 21 unique exchange-correlation functionals) and wave function theory methods (15 total levels of theory). The three experimentally resolved IMS peaks were found to correspond to three distinct pairs of conformers, each pair composed of species differing only by the chair or boat configuration of the proline. Two of the H+GPGG conformer pairs possess a cis configuration about the Pro-Gly1 peptide bond while the other adopts a trans configuration. While the experimental spectrum reports a higher intensity for the cis-1 conformer than the trans conformer, 13 WFT levels of theory, including a complete basis set CCSD(T) extrapolation, obtain trans to be favored in terms of the electronic energy. This same effect is seen in 14 of the 18 dispersion-corrected density functionals studied, whereas the remaining 17 functionals show more variety. Only when Gibbs free energies are considered do the WFT methods and dispersion-corrected functionals reflect the experimental distribution. CAM-B3LYP-D3BJ emerges as the best-performing density functional, matching the experimental distribution and the CCSD(T)/CBS relative energies within 6%. Further analysis reveals the trans conformer to be favored electronically, but entropically disfavored, leading to the experimental preference of the cis-1 conformer. These results highlight the danger in considering only the electronic energies, which is common practice in electronic structure theory predictions of conformational energy distributions. Additionally, the effects of temperature and scaling of the frequencies used in obtaining the Gibbs free energies are explored.