Potential functions for hydrogen bond interactions. III. Empirical potential function for the peptide N-H...O=C hydrogen bond

Abstract

A careful comparison of the distribution in the (R, θ )-plane of all NH ... O hydrogen bonds with that for bonds between neutral NH and neutral C=O groups indicated that the latter has a larger mean R and a wider range of θand that the distribution was also broader than for the average case. Therefore, the potential function developed earlier for an average NH ... O hydrogen bond was modified to suit the peptide case. A three-parameter expression of the form V_ℏδ = V_min + p₁ Δ² + q₁ e^p3 Δ , θ² with ∃ = R - R_min, was found to be satisfactory. By comparing the theoretically expected distribution in R and θ with observed data (although limited), the best values were found to be p₁ = 25,p₃ = - 2 and q₁ = 1 x 10^-3, with R_min = 2.95 Å and V_min = - 4.5 kcal/mole. The procedure for obtaining a smooth transition from V_hb to the non-bonded potential V_nb for large R and θ is described, along with a flow chart useful for programming the formulae. Calculated values of ΔH, the enthalpy of formation of the hydrogen bond, using this function are in reasonable agreement with observation. When the atoms involved in the hydrogen bond occur in a five-membered ring as in the sequence a different formula for the potential function is needed, which is of the form V_ℏδ = V_min +p ₁∃² +q ₁ x ² where x = θ - 50° for θ ≥ 50°, with p₁ = 15, q₁ = 0.002, R_min = 2.8 Å and V_min = - 2.5 kcal/mole.