In this study, the effect of the secondary structure of the protein on the acid strength of three structures of random (R), alpha helix (α) and beta sheet () were investigated theoretically. These structures are related to the cationic amino acids of histidine and lysine in the polypeptide chain of eight-glycine residue. Computational methods at the HF, B3LYP, X3LYP and M05-2X levels in the gas and solution phases were applied. Implicit CPCM solvation model and explicit 2-layer ONIOM methods for the computations in solution were used with the 6-31G (d) basis set. Comparison of pKa values of histidine-based peptide shows that acid strength is accorded to: > α > R. But in the case of lysine, acid strength is accordance to: α >  > R. Based on the obtained data, ONIOM method is unable to predict the pKa values in the explicit solvation model. NBO analysis showed that one of the main reasons for increase in the acidity of the solution phase, is increase in delocalization energy difference (ΔEdelocal) of the neutral acid and the corresponding cation. Topological analysis of quantum theory of atoms in molecules for the electron charge density at the bond critical points of the hydrogen bonds of the secondary structures in the presence of the solvent does not show a meaningful correlation with the interaction energy or acid strength. The absolute average ratio of 1.37 and 1.34 for the kinetic energy density to the local potential energy density of lysine and histidine-based peptides, respectively reveals the non-covalent nature of the O…H bonds. Finally, based on the obtained results, pKa of the proteins can be predicted as a function of hydrogen bond characters and their delocalization energy differences between the cationic and neutral forms.

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