With the specific aim of calculating the acid dissociation constant of three different random, alpha helix and beta sheet structures of cationic amino acid Histidine with 8 glycines in the solution phase were investigated. Corresponding pKa values were evaluated using the Gaussian 09 computational software and with the HF and B3LYP density functional theory calculations for the gas phase. The solvated model CPCM / UFF for solution phase calculations with the basis set of 6-31G (d) is performed. In this study, two different thermodynamic cycles, namely the direct method and the proton exchange method (Figure 1) have been used. Chemical accuracy in pKa calculations is difficult to achieve, because an error of 1.36 kcal/mol in the change of free energy for deprotonation in the solvent results in an error of 1 pKa unit. One of the main sources of error is the energy of hydrogen ions and hydronium cation which are used in the first and second cycles, respectively. The results show that the proton exchange method is more accurate than (close to the experimental values) derived from the pKa of the direct method. Comparison of pKa values of three structures of random, alpha helix and beta sheet (Figure 2) shows that the acid strength of beta, alpha and random decreases, respectively. To study this phenomenon, the structural analysis and calculation natural bond orbital (NBO) have been used. Structural analysis showed that this phenomenon is due to the formation of hydrogen bonds in the structures of alpha and beta. NBO analysis showed that one of the main reasons for the increase of the solution phase acidity is the delocalization energy ( E delocal) elevation for the neutral acid relative to the positively charged ones. To understand the strength of hydrogen bonding of atoms in molecules analysis (AIM) was performed which showed the strength of hydrogen bonds in the structure of the beta is more than alpha and random structures. Electron density and Laplacian analysis confirm the previous results, too.

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