An analysis of hydrated proton diffusion in ab initio molecular dynamics.

A detailed understanding of the inherently multiscale proton transport process raises a number of scientifically challenging questions. For example, there remain many (partially addressed) questions on the molecular mechanism for long-range proton migration and the potential for the formation of long-lived traps giving rise to burst-and-rest proton dynamics. Using results from a sizeable collection of ab initio molecular dynamics (AIMD) simulations (totaling ∼2.7 ns) with various density functional approximations (Becke-Lee-Yang-Parr (BLYP), BLYP-D3, Hamprecht-Cohen-Tozer-Handy, B3LYP) and temperatures (300-330 K), equilibrium and dynamical properties of one excess proton and 128 water molecules are studied. Two features in particular (concerted hops and weak hydrogen-bond donors) are investigated to identify modes in the system that are strongly correlated with the onset of periods of burst-and-rest dynamics. The question of concerted hops seeks to identify those time scales over which long-range proton transport can be classified as a series of sequential water hopping events or as a near-simultaneous concerted process along compressed water wires. The coupling of the observed burst-and-rest dynamics with motions of a fourth neighboring water molecule (a weak hydrogen-bond donor) solvating the protonated water molecule is also investigated. The presence (absence) of hydrogen bonds involving this fourth water molecule before and after successful proton hopping events is found to be strongly correlated with periods of burst (rest) dynamics (and consistent with pre-solvation concepts). By analyzing several realizations of the AIMD trajectories on the 100-ps time scale, convergence of statistics can be assessed. For instance, it was observed that the probability for a fourth water molecule to approach the hydronium, if not already proximal at the beginning of the lifetime of the hydronium, is very low, indicative of the formation of stable void regions. Furthermore, the correlations of the neighboring water atoms are identified as the fourth water approaches the hydronium. Finally, the temperature effects on structural and dynamical properties are studied.