Concerted Hydrogen-Bond Dynamics in the Transport Mechanism of the Hydrated Proton: A First-Principles Molecular Dynamics Study

First-principles molecular dynamics calculations performed in a fully converged basis set are used to reveal new details about the mechanism of the anomalous proton-transport process in water, a fundamental question dating back over 200 years. By separating actual structural diffusion from simple rattling events, wherein a proton shuttles forth and back in a hydrogen bond, it is found that the former are driven by a concerted mechanism in which hydronium begins to accept a hydrogen bond from a donor water molecule while the proton-receiving water molecule simultaneously loses one of its acceptor hydrogen bonds. The kinetics of the process are found to be in good agreement with recent experiments.

Figure 1

Mean-square displacement (a) of the hydronium oxygen, ${\mathrm{O}}^{*}$. Results are shown for the current DVR-based study (solid line) and an analogous plane-wave-based study using the protocol of Ref. 28 (dashed line), along with the calculated diffusion constants. Continuous population correlation function (b) (see text) with rattling events included (solid line) and excluded (dashed line). Thinner solid and dashed lines indicate the integrated correlation functions corresponding to the exchange lifetime ${\tau }_{\mathrm{exch}}$ with and without rattling, respectively.

Figure 2

RDFs and ICNs of ${\mathrm{O}}_{\mathrm{next}}^{*}$ (black and red, respectively) and RDFs for the two other nearest neighbors of ${\mathrm{O}}^{*}$ (blue) averaged over 20 fs intervals for long times before a PT event (500–480 fs) and for intervals prior to and approaching a PT event (180–160 fs, 60–40 fs, and 20–0 fs). PT occurs in panel (d).

Figure 3

RDFs and ICNs of ${\mathrm{O}}^{*}$ (black and red, respectively) averaged over 20 fs intervals for long times before a PT event (480–500 fs) and for intervals approaching a PT event (160–180 fs, 40–60 fs, and 0–20 fs). PT occurs in panel (d).

Figure 4

Snapshots of an example proton-transfer event from the actual simulation. ${\mathrm{O}}^{*}$ is blue, oxygen atoms are red, hydrogen atoms are white, and HBs are purple. See text for mechanistic details.