An analytic potential energy function is proposed and applied to evaluate the amide-amide and amide-water hydrogen-bonding interaction energies in peptides. The parameters in the analytic function are derived from fitting to the potential energy curves of 10 hydrogen-bonded training dimers. The analytic potential energy function is then employed to calculate the N-H...O=C, C-H...O=C, N-H...OH2, and C=O...HOH hydrogen-bonding interaction energies in amide-amide and amide-water dimers containing N-methylacetamide, acetamide, glycine dipeptide, alanine dipeptide, N-methylformamide, N-methylpropanamide, N-ethylacetamide and/or water molecules. The potential energy curves of these systems are therefore obtained, including the equilibrium hydrogen bond distances R(O...H) and the hydrogen-bonding energies. The function is also applied to calculate the binding energies in models of beta-sheets. The calculation results show that the potential energy curves obtained from the analytic function are in good agreement with those obtained from MP2/6-31+G** calculations by including the BSSE correction, which demonstrate that the analytic function proposed in this work can be used to predict the hydrogen-bonding interaction energies in peptides quickly and accurately.
A method is proposed to rapidly predict the hydrogen bond cooperativity in N-methylacetamide chains. The parameters needed are obtained from the fittings to the hydrogen bonding energies in the formamide chains containing 2 to 8 monomeric units. The scheme is then used to calculate the individual hydrogen bonding energies in N-methylacetamide chains containing 2 to 7 monomeric units. The cooperativity predicted is in good agreement with those obtained from MP2/6-31+G** calculations by including the BSSE correction. Our scheme is further employed to predict the individual hydrogen bonding energies in larger N-methylacetamide chains containing up to 200 monomeric N-methylacetamide units, to which the MP2 method cannot be applied. Based on our scheme, a cooperative effect of over 170% of the dimer hydrogen bonding energy in long N-methylacetamide chains is predicted. The method is also applied to heterogeneous chains containing formamide, acetamide, N-methylformamide, and N-methylacetamide. The individual hydrogen bonding energies in these heterogeneous chains are also in good agreement with those obtained from MP2 calculations with the BSSE correction, further demonstrating that our method is reasonable.
In this work, we tentatively propose that the hydrogen-bonding strength E (referring to the minimal hydrogen-bonding energy) and its corresponding hydrogen-bond (HB) distance (referring to the optimal HB distance d) for simple mono-HB systems have an exponential relationship on the basis of MP2 and DFT computational results. We take a step further and propose that the hydrogen-bonding indices of the donor (I) and acceptor (I), reflecting their intrinsic contributions to hydrogen-bonding strength, also have an exponential relation with the hypothetical effective hydrogen-bond radii of the donor (r) and acceptor (r), respectively. On the basis of extensive quantum-mechanical calculations, relevant assumptions about the hydrogen-bonding index are rationalized. Moreover, the hydrogen-bonding index is also suggested as an additional prefiltering criterion for virtual screening besides the widely accepted Lipinski's rule of five. Finally, a "Hydrogen-Bond Index Estimator (HBIE)" module has been implemented in our Visual Force Field Derivation Toolkit (VFFDT) program to approximately and rapidly estimate the hydrogen-bonding indices of any small molecules in batch and screen possible stronger donors or acceptors from the small-molecule database. To the best of our knowledge, the concept of the hydrogen-bonding index and its potential application are proposed here for the first time.
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