Concerted versus stepwise mechanisms of cyclic proton transfer: Experiments,simulations, and current challenges

Proton transfer (PT) is a process of fundamental importance in hydrogen (H)-bonded systems. At cryogenic or moderate temperatures, pronounced quantum tunneling may happen due to the light mass of H. Single PT processes have been extensively studied. However, for PT involving multiple protons, our understanding remains in its infancy stage due to the complicated interplay between the high-dimensional nature of the process and the quantum nature of tunneling. Cyclic H-bonded systems are typical examples of this, where PT can happen separately via a "stepwise" mechanism or collectively via a "concerted" mechanism. In the first scenario, some protons hop first, typically resulting in metastable intermediate states (ISs) and the reaction pathway passes through multiple transition states. Whilst in the concerted mechanism, all protons move simultaneously, resulting in only one barrier along the path. Here, we review previous experimental and theoretical studies probing quantum tunneling in several representative systems for cyclic PT, with more focus on recent theoretical findings with path-integral based methods. For gas-phase porphyrin and porphycene, as well as porphycene on a metal surface, theoretical predictions are consistent with experimental observations, and enhance our understanding of the processes. Yet, discrepancies in the PT kinetic isotope effects between experiment and theory appear in two systems, most noticeably in water tetramer adsorbed on NaCl (001) surface, and also hinted in porphycene adsorbed on Ag (110) surface. In ice I_h, controversy surrounding concerted PT remains even between experiments. Despite of the recent progress in both theoretical methods and experimental techniques, multiple PT processes in cyclic H-bonded systems remain to be mysterious.