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Hydroxide Diffuses Slower Than Hydronium in Water Because Its Solvated Structure Inhibits Correlated Proton Transfer

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Hydroxide Diffuses Slower Than Hydronium in Water Because Its Solvated Structure Inhibits Correlated Proton Transfer ARTICLES https://doi.org/10.1038/s41557-018-0010-2 Hydroxide diffuses slower than hydronium in water because its solvated structure inhibits correlated proton transfer Mohan Chen 1,7, Lixin Zheng 1,7, Biswajit Santra 2, Hsin-Yu Ko 2, Robert A. DiStasio Jr 3, Michael L. Klein1,4,5, Roberto Car 2,6* and Xifan Wu 1,5* Proton transfer via hydronium and hydroxide ions in water is ubiquitous. It underlies acid–base chemistry, certain enzyme reactions, and even infection by the flu. Despite two centuries of investigation, the mechanism underlying why hydroxide diffuses slower than hydronium in water is still not well understood. Herein, we employ state-of-the-art density-functional- theory-based molecular dynamics—with corrections for non-local van der Waals interactions, and self-interaction in the elec- tronic ground state—to model water and hydrated water ions. At this level of theory, we show that structural diffusion of hydro- nium preserves the previously recognized concerted behaviour. However, by contrast, proton transfer via hydroxide is less temporally correlated, due to a stabilized hypercoordination solvation structure that discourages proton transfer. Specifically, the latter exhibits non-planar geometry, which agrees with neutron-scattering results. Asymmetry in the temporal correlation of proton transfer leads to hydroxide diffusing slower than hydronium. + he anomalously high mobility of the hydronium, H3O (aq), Importantly, the first AIMD study of hydronium and hydroxide in and hydroxide, OH–(aq), ions solvated in water has fascinated bulk water12 showed that classical thermal fluctuations easily induce scientists since the very beginning of molecular-based physi- proton transfer events on the picosecond time scale. T 1,2 cal chemistry . The two ions can be viewed as opposite topologi- In the case of hydronium, the first molecular simulations con- cal defects in the fluctuating hydrogen-bond (H-bond) network in firmed the long-held view that transfer involves interconversion + liquid water. In this picture, both ions bind to three water molecules of two defect complexes, that is, the solvated H3O (aq) or Eigen 13,14 + 15–23 by donating or accepting H-bonds. Diffusion is not dominated by ion , and the solvated H5O2 (aq) or Zundel ion . Even more hydrodynamics, but by a structural process usually referred to as notable were the results for hydroxide, OH–(aq), which appeared the Grotthuss mechanism3, in which a proton is transferred from a to alternate between two configurations: an unexpected hyperco- hydronium to a neighbouring water molecule or from a water mol- ordinated form with four acceptor H-bonds and a nearly tetrahe- ecule to a neighbouring hydroxide. In this process, a covalent O–H dral form with three acceptor H-bonds and, occasionally, a weak bond breaks while another forms as the topological defect jumps to donor H-bond. Proton transfer only occurred in the latter con- an adjacent site in the network. Not surprisingly, proton transfer has figuration, suggesting a ‘presolvation’ mechanism, that is, access been intensively investigated, both experimentally and theoretically, to the tetrahedral configuration, was necessary for proton trans- for almost a century since the early molecular models4. fer in OH–(aq). Neutron diffraction24 and core-level spectros- Although the Grotthuss mechanism correctly identifies the ori- copy data25 were consistent with the hypercoordinated structure, gin of fast diffusion, some issues remain unresolved. Experimentally, indirectly supporting the presolvation picture. However, analysis diffusivity is obtained via the Nernst equation from the measured of neutron scattering data24 suggested the solvation structure of electrical conductivity of the ions. While the diffusivity describes OH–(aq) had a pot-like shape, differing from the planar structure the combined effect of hydrodynamic and structural processes, predicted by the early AIMD simulations26, which employed the the jump frequency of the protons in the structural process can be generalized gradient approximation (GGA) and treated nuclear extracted from nuclear magnetic resonance (NMR) relaxation times. dynamics classically. Subsequent path integral AIMD simula- Conductivity5–7 and NMR5,8 experiments indicate that hydronium tions, which treated the nuclei quantum mechanically, refined diffuses roughly twice as fast as hydroxide. Predicting the transfer the model by stressing the fluxional character of the defect com- dynamics is difficult as it depends on the cleavage and formation of plexes, but did not change the basic picture as tunnelling was not covalent bonds in a fluctuating liquid medium. Major progress in found to be important26,27. In the latter scenario, proton transfer modelling proton transfer came with the advent of ab initio molecu- events occur randomly due to thermal and/or quantal fluctua- lar dynamics (AIMD)9. In this approach, the forces on the nuclei are tions. However, recent AIMD simulations added a new twist to derived from the instantaneous ground state of the electrons within the story: proton transfer events are highly correlated and hap- density functional theory (DFT)10,11, while the electrons adjust on pen in bursts consisting of multiple jumps closely spaced in time the fly and can thereby access bond breaking and forming events. followed by periods of inactivity28,29. 1Department of Physics, Temple University, Philadelphia, PA, USA. 2Department of Chemistry, Princeton University, Princeton, NJ, USA. 3Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY, USA. 4Department of Chemistry, Temple University, Philadelphia, PA, USA. 5Institute for Computational Molecular Science, Temple University, Philadelphia, PA, USA. 6Department of Physics, Princeton University, Princeton, NJ, USA. 7These authors contributed equally: Mohan Chen, Lixin Zheng. *e-mail: [email protected]; [email protected] NATURE CHEMISTry | www.nature.com/naturechemistry © 2018 Macmillan Publishers Limited, part of Springer Nature. All rights reserved. ARTICLES NATURE CHEMISTRY Results and discussion Table 1 | Computed ratios from the diffusion coefficients D Proton transfer via the hydronium ion. The electronic structure (units: 10–9 m2 s–1) of H O+(aq) (D+) and OH–(aq) (D–), the 3 of H O+(aq) comprises three bonding electron pairs and one lone experimental diffusivity data are computed from the limiting 3 electron pair, which are represented by the maximally localized molar conductivities (units: –1 cm2 mol–1) of H O+(aq) ( +) λ Ω 3 λ Wannier functions39,40 in Fig. 1a. The protons of hydronium are and OH–(aq) ( –) measured at 28 (refs 5,7) and 25 °C (ref. 6) λ positive and ready to be donated to neighbouring water molecules D + D– D +/ D– whereas the oxygen is likely to accept an H-bond from its neigh- PW91 3.24 18.5 0.18 bouring water molecules due to the negative lone electron pair. Since the H-bond is mainly attributed to an electrostatic attraction, 2.83 1.92 1.47 BLYP the ability of donating (accepting) H-bonds can be conveniently HCTH/120 3.25 0.44 7.39 measured by the distance separating the negative electrons from PBE 10.8± 2.7 18.2± 3.7 0.59± 0.27 the positive nucleus, roughly estimating how positive (negative) PBE-TS 12.8± 1.9 8.3± 1.6 1.54± 0.53 the local environment is for a specific proton (oxygen). The result- ing distance between electron pairs with respect to the nuclei, as PBE0-TS 8.3 1.9 3.7 0.4 2.24 0.75 ± ± ± obtained by the PBE0-TS trajectory, are shown in Fig. 1b for sol- a c a c a c Exp. (H2O) 9.6 , 9.4 5.4 , 5.2 1.77 , 1.80 vated ions and neat liquid water. Compared to liquid water, the a c a c a c Exp. (D2O) 6.9 , 6.7 3.2 , 3.1 2.15 , 2.15 proton of hydronium has a stronger ability to donate an H-bond, λ+ λ– λ+/ λ– while the oxygen of hydronium has a weaker ability to receive one Exp. (H O) 364.0a, 351c 206.0a, 195c 1.77a, 1.80c (Supplementary Section 2). Therefore, in the absence of proton 2 transfers, the solvated hydronium is amphiphilic in nature with its Exp. (D O) 261.6a, 252c 121.5a, 117c 2.15a, 2.15c 2 proton (oxygen) site being hydrophilic (hydrophobic)41–45. Hence, a c b a c + λ (H2O)/ λ (D2O) 1.39 , 1.39 , 1.364 1.70 , 1.67 H3O (aq) forms the Eigen complex by stably donating three The simulation data for six exchange-correlation functionals: PW9157, BLYP58,59, HCTH/12060, H-bonds to its neighbouring water molecules as shown in Fig. 1a. PBE, PBE-TS and PBE0-TS, are reported. The data for the first three functionals are from ref. While supported by some experiments46,47, this conventional pic- 26, those for the last three functionals are from the present simulation. We also show the standard ture has been challenged by recent experiments17,21 suggesting that deviations for computed D. The deuterium mass was used for both ions and water molecules in all AIMD simulations listed, while the experimental data (Exp.) based on both H and D are listed. See a long-lived Zundel complex plays a central role in proton solva- + Supplementary Section 4 for more information on the procedures to compute diffusivities based tion and transport. In the Zundel complex (H5O2 (aq)) the excess on the AIMD simulations. The experimental diffusivity data were computed based on the Nernst RT proton has two flanking water molecules, called the special pair, equation D = λ, where R is the gas constant, T is the temperature, and F is Faraday’s constant. F2 which contribute prominently to the observed vibrational spectra. a 5 b 6 c 7 from ref. ; from ref. ; from ref. In the dynamic picture of AIMD simulations, however, there is no sharp distinction between Eigen and Zundel configurations. The hypercoordinated hydroxide form revealed by previous While waiting for a proton transfer event the solvated proton simulations breaks the mirror symmetry of the topological defect remains associated with a particular O atom but the correspond- model between hydronium and hydroxide.
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