Energetics and dynamics of proton transfer reactions along short water wires

Proton transfer (pT) reactions in biochemical processes are often mediated by chains of hydrogen-bonded water molecules. We use hybrid density functional calculations to study pT along quasi one-dimensional water arrays that connect an imidazolium-imidazole proton donor-acceptor pair. We characterize the structures of intermediates and transition states, the energetics, and the dynamics of the pT reactions, including vibrational contributions to kinetic isotope effects. In molecular dynamics simulations of pT transition paths, we find that for short water chains with four water molecules, the pT reactions are semi-concerted. The formation of a high-energy hydronium intermediate next to the proton-donating group is avoided by a simultaneous transfer of a proton from the donor to the first water molecule, and from the first water molecule into the water chain. Lowering the dielectric constant of the environment and increasing the water chain length both reduce the barrier for pT. We study the effect of the driving force on the energetics of the pT reaction by changing the proton affinity of the donor and acceptor groups through halogen and methyl substitutions. We find that the barrier of the pT reaction depends linearly on the proton affinity of the donor but is nearly independent of the proton affinity of the acceptor, corresponding to Brønsted slopes of one and zero, respectively.