On the recombination of hydronium and hydroxide ions in water Ali Hassanali1, Meher K. Prakash, Hagai Eshet, and Michele Parrinello Department of Chemistry and Applied Biosciences, Eidgenössiche Technische Hochschule Zurich and Università della Svizzera Italiana, via G. Buffi 13, CH6900 Lugano, Switzerland Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved October 17, 2011 (received for review July 30, 2011) The recombination of hydronium and hydroxide ions following species as intermediates. In the context of recombination, the un- water ionization is one of the most fundamental processes deter- derstanding of the diffusion of the ions up to contact distance mining the pH of water. The neutralization step once the solvated lends itself to the ideas of the Grotthuss mechanism. Eigen and ions are in close proximity is phenomenologically understood to be de Maeyer phenomenologically proposed that reorganization of fast, but the molecular mechanism has not been directly probed the hydrogen bond network would drive the neutralization pro- by experiments. We elucidate the mechanism of recombination cess from this contact distance. in liquid water with ab initio molecular dynamics simulations, The model proposed by Eigen and de Maeyer serves effectively and it emerges as quite different from the conventional view of when the ions are far away from each other; however, it does not the Grotthuss mechanism. The neutralization event involves a shed light on the molecular mechanism of the recombination pro- collective compression of the water-wire bridging the ions, which cess once the ions reach contact distance. A representative situa- þ − occurs in approximately 0.5 ps, triggering a concerted triple jump tion at contact distance, with the H3O and hydroxide (OH ) of the protons. This process leaves the neutralized hydroxide in a separated by approximately 6 Å and two intermediate waters hypercoordinated state, with the implications that enhanced col- is shown in Fig. 1. Whether the dynamics of the proton from here lective compressions of several water molecules around similarly occurs in a stepwise fashion, transferring over one intermediate hypercoordinated states are likely to serve as nucleation events for water at a time analogous to the Grotthuss mechanism, or in a the autoionization of liquid water. concerted way (7) has been a critical missing piece in the formu- lation of a complete recombination mechanism of hydronium and acid-base chemistry ∣ concerted proton transfer ∣ hydronium and hydroxide ions in bulk water. In this work we advance the model hydroxide recombination put forward by Eigen and de Maeyer (11) by unravelling the re- combination mechanism as the ions transition from the diffusive he mechanisms of proton transfer and transport through dif- regime to contact distance. Tferent media has been a subject of great interest in the fields The time-reversed process, namely, the autoionization of of chemistry and biology (1–6). Several processes involving pro- liquid water, has previously been studied by using trajectories ton transfer, such as proton conduction through proton wires from advanced sampling methods (2, 14). These studies showed in proteins, and acid-base neutralization have been receiving ele- that rare electric field fluctuations resulted in ionization and a vated attention (7–9). Water is a common solvent for many of rapid structural diffusion of the proton away from the OH− within these processes. As an ionizable medium with hydrogen bonds 100 fs forming a solvent-separated hydrogen-bonded wire (Fig. 1). that continuously break and reform, water presents a rich envir- Our results confirm these basic features but unveils a critical onment for sustaining several complex reactions. Perhaps one of slower step occurring on the subpicosecond time scale during the the most fundamental studies in this regard is the dissociation of recombination which involves a collective motion of the wire that water and the consequent recombination of the ions. This process was not previously reported (2). We establish that, besides the forms the cornerstone of textbook acid-base chemistry (10). The fast proton transfer and formation of a hydrogen-bonded wire K acid dissociation constant of water ( W ) at room temperature is between the ions that was observed in earlier studies (2), the col- 1 × 10−14 , which means that H2O rarely autodissociates and the lective compression of the wire is a necessary condition for the subsequent ionic products quickly recombine. Elucidating the final neutralization step. The collective compression of several molecular mechanisms of the autodissociation of water and water molecules is likely to be one of the critical rate-limiting recombination of the ions has far-reaching consequences in steps in the autoionization of liquid water. These dynamical pro- enriching our understanding of the anomalous conductivity of cesses of the wire now provide a physical basis for the fast proton protons in different environments. transfer observed in the recombination and autoionization steps Most of the acid-base neutralization studies are interpreted which is strikingly different from the slower picosecond time scale within the framework of the model proposed by Eigen and de of proton motion expected in bulk water (1, 3, 4). The specific Maeyer (11). This model attributes the rate-limiting step of solvent motions that we elucidate form the molecular basis for recombination to the approach of the solvated ionic species by the electric field fluctuations involved in the recombination of a Grotthuss-like structural diffusion, until a contact distance of the ions and the time-reversed process (2). This work reveals the about 6 Å (12). At contact distance, the hydronium and hydroxide molecular mechanism of the neutralization and demonstrates ions are separated by two water molecules, which form a water þ − that the annihilation of the H3O and OH ions involves a wire between the ions as shown in Fig. 1 (11, 12). The Grotthuss concerted triple jump of protons through a water wire, which is mechanism (13) was proposed to explain how the excess proton þ occurring as H3O diffuses much faster than expected from its hydrodynamic radius (13). The general consensus on the modern Author contributions: A.H., M.K.P., H.E., and M.P. designed research, performed research, view of the 200-yr-old Grotthuss mechanism (13) is that the analyzed data, and wrote the paper. þ excess proton diffuses with a proton transfer from H3O to the The authors declare no conflict of interest. neighboring water when the solvation conditions of the surround- This article is a PNAS Direct Submission. ing environment are suitable (3). The hydronium ion moves one 1To whom correspondence should be addressed. E-mail: [email protected]. molecular length at a time, continuously interconverting between This article contains supporting information online at www.pnas.org/lookup/suppl/ covalent and hydrogen bonds, with the Eigen cation and Zundel doi:10.1073/pnas.1112486108/-/DCSupplemental. 20410–20415 ∣ PNAS ∣ December 20, 2011 ∣ vol. 108 ∣ no. 51 www.pnas.org/cgi/doi/10.1073/pnas.1112486108 Downloaded by guest on September 26, 2021 2 A 1.6 B 8.4 1.4 1.2 8 1.5 1 900 950 1,000 7.6 Water wire length (Å) 7.2 Propagating O-H bonds (Å) 1 0 500 1,000 0 500 1,000 Time (fs) Time (fs) 2.4 9.0 C 2.2 D þ − 2.0 Fig. 1. A schematic water wire linking the H3O and OH is shown. Within 8.5 the paradigm of the modern view of the Grotthuss mechanism, the propaga- 1.8 – 1.6 tion of the proton is expected in three consecutive steps (1 3) resulting from 8.0 sequential compressions. In contrast, we observe that it is a cooperative 1.4 1.2 motion of the water wire (4) that results in a concerted motion of the protons 7.5 (Fig. 2). 1.0 Length of water wire (Å) 0.8 7.0 intriguingly different from the classical and modern views of the 0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.5 1.0 1.5 2.0 2.5 Number of ionized species Average propagating O−H bond lengths (Å) Number of ionized species Grotthuss mechanism (1, 13). Fig. 2. (A) The collective compression of the water wire in a typical trajec- Results and Discussion tory is illustrated with the sum of the three O-O distances. (B) The change Collective Compression and Proton Triple Jump. In order to under- in the bond lengths associated with the transferring protons is shown. stand the mechanism of recombination and to treat the proton- The striking feature of a global compression of the water wire and the con- certed flux of protons is highlighted with dashed circles and in the inset. This transfer events explicitly, we performed state-of-the-art ab initio feature is in sharp contrast to the mechanisms expected within the frame- molecular dynamics simulations. The system consists of a box of work of Grotthuss diffusion. These features are seen for an ensemble of re- 64 waters periodically replicated in space which allows for a rea- combination trajectories (density plots C and D), which exemplify these listic treatment of ions separated at contact distance. The ioniza- processes as a function of the number of ionic species in the system. The den- þ − tion of water yielding H3O and OH ions is an activated process sity plots for the individual pairwise oxygen distances along the wire exhibit and will not spontaneously occur on the time scales affordable to similar trends to those shown in A.SeeSI Appendix for details along with the ab initio simulations (2). To study the recombination mechanism, definition of the number of ionic species in the system and a collection of we artificially constrain two different waters to exhibit the struc- other individual trajectories.