Estimating the energy of intramolecular bifurcated (three-centered) hydrogen bond by X-ray, IR and ¹H NMR spectroscopy, and QTAIM calculations

The structure of a series of the 2-substituted pyrroles containing the intramolecular N–H⋯O[dbnd]C hydrogen bond and the 2,5-disubstituted pyrroles having the three-centered intramolecular C[dbnd]O⋯H(N)⋯O[dbnd]C hydrogen bond was studied by X-ray, IR, NMR spectroscopy, and quantum chemical calculations, including calculations in terms of Quantum Theory of Atoms in Molecules (QTAIM). The X-ray diffraction data show that the intramolecular r_{H … O} and R_{N … O} distances increase upon conversion from a two-centered hydrogen bond to a three-centered hydrogen bond, indicating a weakening of the last interaction. The topological parameters of the hydrogen bond obtained from the QTAIM calculations (electron density ρ^BCP and potential energy density V at the critical point of the hydrogen bond) made it possible to quantify the hydrogen bond energy in the studied compounds. The energy of intramolecular N–H⋯O[dbnd]C hydrogen bond in the 2-substituted pyrroles is in the range from 5.5 to 6.0 kcal mol⁻¹ (moderate hydrogen bond), whereas the energy of the components of the three-centered intramolecular C[dbnd]O⋯H(N)⋯O[dbnd]C hydrogen bond in the 2,5-disubstituted pyrroles is reduced to 2.5–3.5 kcal mol⁻¹ (weak hydrogen bond). For weak components of the three-centered hydrogen bond, the principle of the additivity of effects on the spectral parameters influenced by the hydrogen bond (change in the vibration frequency of the N–H bond, Δν_N‒H, and the chemical shift of bridge proton, Δδ_NH) was proposed. For this reason, the ½Δν_N-H and ½Δδ_NH values also were used for estimating the energy of the two-centered components of the three-centered C[dbnd]O⋯H(N)⋯O[dbnd]C hydrogen bond. These estimates are in good agreement with those obtained from the ρ^BCP and V parameters. Consequently, the ½Δν_N-H and ½Δδ_NH parameters can be used as an energy descriptor for two-centered components in the case of a symmetric intramolecular three-centered hydrogen bond.