DFT study of H-bonds in the peptide secondary structures: The backbone–side-chain and polar side-chains interactions

The backbone–side-chain interactions in the peptide secondary structures are studied by the density functional theory methods with/without periodic boundary conditions. The alanine-based two-stranded β-sheet structure infinite models and the cluster models of the C5 structures modified by the glutamic acid residue are considered. Several low-energy structures have been localized in the BLYP/plane-wave and the BLYP/6-311++G** approximations. Combined use of the quantum-topological analysis of the electron density and frequency shifts enables us to detect and describe quantitatively the non-covalent interactions and H-bonds. We found that the strongest backbone–side-chain interaction (∼37 kJ/mol) is due to the intra-chain H-bond formed by the CO backbone group and by the COOH side-chain group. The OH…O distance equals to 1.727 Å and the frequency shift of the OH stretching vibration is 370 cm−1. The polar side-chains interaction is studied in the infinite model of the alanine-based two-stranded β-sheet structure modified by the glutamic acid/lysine residues. Moderate inter-chain H-bond (∼40 kJ/mol) is formed by glutamic acid COOH group and lysine NH2 group. The OH…N distance equals to 1.707 Å and the frequency shift of the OH stretching vibration is 770 cm−1.