Location of protons in N–H⋯N hydrogen-bonded systems: a theoretical study on intramolecular pyridine–dihydropyridine and pyridine–pyridinium pairs

Abstract

Two-dimensional potential energy surfaces (PESs) were calculated for the degenerate intramolecular proton transfer (PT) in two N–H⋯N hydrogen-bonded systems, (Z)-2-(2-pyridylmethylidene)-1,2-dihydropyridine (1) and monoprotonated di(2-pyridyl) ether (2), at the MP2/cc-pVDZ level of theory. The calculated PES had two minima in both cases. The energy barrier in 1 was higher than the zero-point energy (ZPE) level, while that in 2 was close to the ZPE. Vibrational wavefunctions were obtained by solving time-independent Schrödinger equations with the calculated PESs. The maximum points of the probability density were shifted from the energy minima towards the region where the covalent N–H bond was elongated and the N⋯N distance shortened. The effects of a polar solvent on the PES were investigated with the continuum or cluster models in such a way that the solute–solvent electrostatic interactions could be taken into account under non-equilibrated conditions. A solvated contact ion-pair was modelled by a cluster consisting of one cation 2, one chloride ion and 26 molecules of acetonitrile. The calculation with this model suggested that the bridging proton is localised in the deeper well due to the significant asymmetry of the PES and the high potential barrier.