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Local Initiation Conditions for Water Autoionization

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Local Initiation Conditions for Water Autoionization Local initiation conditions for water autoionization Mahmoud Moqadama,1, Anders Lervika,1,2, Enrico Riccardia, Vishwesh Venkatramana, Bjørn Kare˚ Alsberga,3, and Titus S. van Erpa,b,2 aDepartment of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway; and bCenter for Molecular Modeling, Ghent University, B9000 Ghent, Belgium Edited by Phillip L. Geissler, University of California, Berkeley, CA, and accepted by Editorial Board Member R. D. Levine April 5, 2018 (received for review August 9, 2017) The pH of liquid water is determined by the infrequent process in local order parameters are not suitable to describe the event. which water molecules split into short-lived hydroxide and hydro- Hassanali et al. (17) studied the reverse recombination reaction nium ions. This reaction is difficult to probe experimentally and (i.e., neutralization of ionized water molecules) with standard ab challenging to simulate. One of the open questions is whether initio MD and reported that this event takes place by a collec- the local water structure around a slightly stretched OH bond is tive compression of the water wire bridging the ions, followed actually initiating the eventual breakage of this bond or whether by a triple concerted proton jump. The OH− ion which is neu- this event is driven by a global ordering that involves many water tralized remains in a hypercoordinated state and Hassanali et molecules far away from the reaction center. Here, we investigated al. (17) hypothesized that it could serve, together with the com- the self-ionization of water at room temperature by rare-event ab pression of the wire, as a nucleation site for autoionization. initio molecular dynamics and obtained autoionization rates and This view opposes the statement of Geissler et al. (16) that the activation energies in good agreement with experiments. Based dissociation event is primarily triggered by nonlocal structural on the analysis of thousands of molecular trajectories, we identi- fluctuations. We note that concerted proton transfers and col- fied a couple of local order parameters and show that if a bond lective compression of water wires have also been observed for stretch occurs when all these parameters are around their ideal the recombination of a weak base in water (18). range, the chance for the first dissociation step (double-proton Both of these studies give important information about the jump) increases from 10−7 to 0:4. Understanding these initiation autoionization mechanism, although they do not unambiguously triggers might ultimately allow the steering of chemical reactions. reveal the conditions that need to accompany a bond stretch fluc- tuation to initiate the reaction. In this work, we aim to tackle autoionization j water j path sampling j machine learning j this ambiguity and quantitatively identify initiation conditions ab initio molecular dynamics for water autoionization. Simulating the dissociation events may not be sufficient as the apparent initiation conditions observed mong all possible chemical reactions that occur in water, in trajectories that lead to dissociation may also be present in Athe most fundamental is the water dissociation reaction (1), trajectories with an initial bond stretch but still fail to dissociate. which is of major importance in many areas of chemistry and Also nonreactive or “almost reactive” trajectories contain impor- biology (2). Water plays an important role as a universal sol- tant information as these allow for identification of effective vent for a wide variety of chemical processes and can act both initiation conditions that really matter: those that discriminate as an acid and as a base. In aqueous solution, water will self- − + ionize and form hydroxide (OH ) and hydronium (H3O ) ions Significance which take on Eigen- or Zundel-like structures (2–6). Experi- ments show that the mean lifetime for an individual molecule The dissociation of water is arguably the most fundamen- before undergoing autoionization is about 11 h (7, 8). tal chemical reaction occurring in the aqueous phase. Despite The autoionization event has not been directly probed by CHEMISTRY that the splitting of a water molecule very seldom occurs, experiments and the dissociation rate is obtained using the water the reaction is of major importance in many areas of chem- dissociation equilibrium constant and the rate for the much istry and biology. Direct experimental probing of the event faster recombination reaction (7, 8). The experimental chal- is still impossible and also simulating the event via accurate lenges make the autoionization event a pertinent target for computer simulations is challenging. Here, we achieved the computer simulations for which previous constrained ab initio latter via specialized rare-event algorithms estimating rates simulations have given important information about the mech- of dissociation in agreement with indirect experimental mea- anism (9–11). However, the use of constraints leads to a loss of surements. Even more interestingly, by a rigorous analysis of the spontaneous dynamics of the system and the selection of a our results we identified anomalies in the water structure reaction coordinate that accurately measures the progress of the that act as initiators of the reaction, a finding that suggests reaction is challenging. These limitations can be avoided by path- paradigms for steering and catalyzing chemical reactions. sampling methods such as transition path sampling (TPS) (12) or replica exchange transition interface sampling (RETIS) (13, 14) Author contributions: A.L. and T.S.v.E. designed research; M.M., A.L., E.R., and T.S.v.E. which are specifically designed for sampling rare events without performed research; M.M., A.L., V.V., and B.K.A. analyzed data; and M.M., A.L., E.R., V.V., altering the dynamics while less influenced by the choice of the and T.S.v.E. wrote the paper. order parameter (15). Geissler et al. (16) applied TPS with ab The authors declare no conflict of interest. initio molecular dynamics (MD) to simulate just 10 uncorrelated This article is a PNAS Direct Submission. P.L.G. is a guest editor invited by the Editorial autoionization events and demonstrated that the mechanism Board. involves transfer of protons along a hydrogen bond wire with Published under the PNAS license. concomitant breaking of the wire. In their work, local solvent 1 M.M. and A.L. contributed equally to this work. properties (e.g., ion coordination numbers and the presence of 2 To whom correspondence may be addressed. Email: [email protected] or specific hydrogen bonds) were used to interpret the destabi- [email protected]. lization that leads to ionization. The absence of clear visually 3 Deceased December 27, 2017. observable correlations led to the conclusion that the destabi- This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. lization is caused by rare electric-field fluctuations which arise 1073/pnas.1714070115/-/DCSupplemental. primarily from long-range electrostatic interactions and thus that Published online April 30, 2018. www.pnas.org/cgi/doi/10.1073/pnas.1714070115 PNAS j vol. 115 j no. 20 j E4569–E4576 Downloaded by guest on October 1, 2021 between reactive and nonreactive trajectories. To collect this it to the closest oxygen. Note that the definition of the order information, we applied the RETIS method and harvested reac- parameter does not require a threshold for defining a chemi- tive and nonreactive trajectories which we analyzed using the cal bond nor does it constrain the order parameter to specific recently developed predictive power method (19) and we built a water molecules for the duration of the simulation. This means predictive machine-learning model (20). This allowed us to quan- that we compute the rate of dissociation of any water molecule titatively examine the importance of local order parameters and in the system instead of a single targeted O–H bond or water initiation conditions for water autoionization. Based on this anal- molecule. ysis we identify important initiation triggers and calculate the full From our RETIS simulations, the water dissociation rate con- rate of dissociation. stant, kD, can be obtained as the product of a flux, fA, and a (conditional) probability, PA(λN jλ0): Results and Discussion The autoionization event was investigated using ab initio RETIS kD = fA × PA(λN jλ0): [1] simulations as described in Materials and Methods. For the RETIS simulations, we used a relatively simple geometric dis- Here, λ0 and λN are interfaces defining the initial (λ < λ0) and tance order parameter, λ, as illustrated in Fig. 1: When the final (λ>λN ) states and PA(λN jλ0) is the probability of reach- ing the final state before (possibly) reentering the initial state, system consists of only H2O species, λ is the largest covalent O–H bond distance, and when the system contains OH− and given that the initial interface λ0 has been crossed. The flux, fA, + is a measure of the frequency of crossings with λ0. Since we con- H3O species, λ is taken as the shortest distance between the − + sider the dissociation of any water molecule in our system, we oxygen in OH and the hydrogen atoms in H3O . In the follow- ing, we refer to the oxygen atom used for the order parameter have normalized fA by the number of water molecules present. λ − + Typically, for rare events, the crossing probability is very small as O . The type of species (OH ,H2O, or H3O ) was iden- and in practice, PA(λN jλ0) is calculated by first positioning sev- tified by allocating to each hydrogen a single bond connecting eral more interfaces λ0 < λ1 < : : : < λN between the initial and the final state. The overall crossing probability is then obtained as a product of several (history-dependent) conditional prob- A B abilities (14). The conditional probabilities are calculated in a separate path ensemble simulation where the [i +] path ensem- ble defines the collection of paths crossing λi .
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