Proton transfer through the water gossamer

Abstract

The diffusion of protons through water is understood within the framework of the Grotthuss mechanism, which requires that they undergo structural diffusion in a stepwise manner throughout the water network. Despite long study, this picture oversimplifies and neglects the complexity of the supramolecular structure of water. We use first-principles simulations and demonstrate that the currently accepted picture of proton diffusion is in need of revision. We show that proton and hydroxide diffusion occurs through periods of intense activity involving concerted proton hopping followed by periods of rest. The picture that emerges is that proton transfer is a multiscale and multidynamical process involving a broader distribution of pathways and timescales than currently assumed. To rationalize these phenomena, we look at the 3D water network as a distribution of closed directed rings, which reveals the presence of medium-range directional correlations in the liquid. One of the natural consequences of this feature is that both the hydronium and hydroxide ion are decorated with proton wires. These wires serve as conduits for long proton jumps over several hydrogen bonds.

Fig. 1.

The average of the symmetrized PT coordinates for pairs of consecutive PT events (double PT jumps) on the x axis vs. the collective compression of the wire on the y axis. On the x axis, and are the symmetrized PT coordinates defined as the difference in distance of the transferring proton along the hydrogen bond [ and ]. The species O(1), O(2), and O(3) are consecutive oxygen atoms along a wire that house the proton at some point during PT. Associated with each PT coordinate is the distance between the oxygen atoms along the wire: , , and the y axis shows the sum of these two distances. This plot is strikingly similar to the “banana” plots in the stepwise PT jumps (9). Here, instead double jumps are facilitated by collective compressions (see SI Appendix for similar plot for the extent of correlations in groups of triple PT events).

Fig. 2.

(A) Burst and rest behavior of the proton is shown for one trajectory. On the y axis, we show the distance that the proton jumps with respect to a reference starting point at the beginning of the trajectory. The motion of the proton goes through periods of bursts where it can jump rather long distances due to correlated proton hopping followed by resting periods. The regions labeled B indicate points where there is a burst in activity and R are regimes where the proton is going through a resting period. (B) Proton history correlation function (44) [, where h is 1 when a tagged species in the system is a proton or 0 if it is not] is shown for individual proton species in the system as well as the ensemble average. The two blue curves, for example, illustrate two limiting cases involving a trapped proton and a very short-lived proton transiently formed during concerted PT events. The red, green, and violet curves shown, interpolate between these two limiting cases. The black curve represents the average over all PT events from different trajectories, whereas the dashed magenta curve is a fit to this average using several exponentials.

Fig. 3.

A illustrates the hypercoordinated hydroxide, which accepts four hydrogen bonds and donates one weaker hydrogen bond. B illustrates the undercoordinated hydroxide ion, which accepts three hydrogen bonds while the donating hydrogen bond is left dangling pointing to a closed ring.

Fig. 4.

This figure shows distribution of the total number of rings for protons in long-lived (blue) vs. short-lived (green) traps illustrated using a clustered bar chart. The blue bars tend to be larger at smaller ring values (less than ), whereas the green bars tend to be larger at larger ring values (greater than ).

Fig. 5.

A and B show for two directed six-membered rings, and C shows the distribution of obtained for neat water. When (A), the ring is made up of only DA water molecules, whereas when , the ring consists of one DD, one AA, and four DA water molecules. The blue-colored paths show possible realizations of obtained for these rings. In particular for the ring, the longest outgoing path from the tagged DA water (surrounded by a blue sphere) to waters other than itself, is shown by the blue path that is made of five hydrogen bonds. This path ends at the water surrounded by a yellow sphere. For (B), a realization of the longest outgoing wire for a DD water molecule (surrounded by a blue sphere) is shown by the blue path made up of three hydrogen bonds. This path ends at the water surrounded by the yellow sphere. For clarity, in these figures we only show examples of six-membered rings. However, as discussed in the text, the same features hold for rings of all sizes. The distributions of of charged systems are quite similar (SI Appendix).

Fig. 6.

The upper panels show snapshots of the environment of the H₃O⁺ (A) and OH⁻ (B) ions, which is made of closed rings. For clarity, not all of the rings threading the ions are shown. Wires along the rings are also shown around each ion. Note that the OH⁻ ion accepts four hydrogen bonds and donates a weak hydrogen bond in this case. As mentioned in the text, the H₃O⁺ acts as a DD water in the ring, whereas the OH⁻ acts as an AA for the majority of the rings they participate in. The figure illustrates that both the H₃O⁺ and OH⁻ are characterized by many outgoing and incoming wires, respectively. C and D compare the distribution of for neat water [DD (blue) and AA (red)], H₃O⁺ (blue), and OH⁻ (red) systems.

Fig. 7.

A illustrates how the interconversion of rings, in this case a five- and seven-membered ring, result in concerted PT. On the y axis, the symmetrized PT coordinates for the concerted PT events, , , and (corresponding to the black, red, and green curves, respectively) are shown. (B) Coupling between the ring interconversions and the umbrella inversion mode of the hydronium during PT events. The data series shows the umbrella inversion mode coordinate on the y axis along with four snapshots from the molecular dynamics trajectory. The purple triangle is formed by the base of three protons, which is used to illustrate the role of the inversion mode. The inversion coordinate is defined by the perpendicular distance between the oxygen atom of the hydronium ion and the plane formed by the hydrogen atoms. In the first example (A), the inversion mode does not change and hence does not play a role in the PT. However, in the second example, the inversion mode changes, which facilitated the formation and breakage of a 4M ring and is coupled to PT. For clarity, we note that in the first 2 ps the oxygen lies below the triangular blue base, whereas between 2 and 6 ps the oxygen lies above the triangular base.