Microscopic dynamics of charge separation at the aqueous electrochemical interface

John A. Kattirtzia,b, David T. Limmerc,d,e,1, and Adam P. Willarda,1

aDepartment of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02138; bCollege of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China; cDepartment of Chemistry, University of California, Berkeley, CA 94609; dKavili Energy NanoScience Institute, University of California, Berkeley, CA 94609; and eMaterial Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94609

Edited by Michael L. Klein, Temple University, Philadelphia, PA, and approved June 6, 2017 (received for review March 7, 2017) We have used molecular simulation and methods of importance the process of aqueous ion association (forward reaction above) sampling to study the thermodynamics and kinetics of ionic or dissociation (reverse reaction above) is deceptively simple. charge separation at a liquid water–metal interface. We have con- The expression omits the cooperative role of solvent, which sidered this process using canonical examples of two different must restructure to accommodate transitions between the asso- classes of ions: a simple alkali–halide pair, Na+I−, or classical ions, ciated and dissociated states (2, 11). This restructuring, which + − and the products of water autoionization, H3O OH , or water is driven by thermal fluctuations, is both collective (extending ions. We find that for both ion classes, the microscopic mecha- beyond the first solvation shell) and fleeting (12–14). These nism of charge separation, including water’s collective role in the microscopic processes are difficult to probe experimentally (15), process, is conserved between the bulk liquid and the electrode so atomistic simulation has played an important role in reveal- interface. However, the thermodynamic and kinetic details of the ing their molecular-level details. Simulations based on state- process differ between these two environments in a way that of-the-art quantum chemical methods reveal important infor- depends on ion type. In the case of the classical ion pairs, a higher mation about the structure and energetics of these systems; free-energy barrier to charge separation and a smaller flux over however, without additional importance sampling or embedding, that barrier at the interface result in a rate of dissociation that they are too computationally demanding to characterize collec- is 40 times slower relative to the bulk. For water ions, a slightly tive room-temperature dynamics (16–19). Classical simulations higher free-energy barrier is offset by a higher flux over the bar- overcome this limitation by treating some interactions empiri- rier from longer lived hydrogen-bonding patterns at the interface, cally, thereby enabling the characterization of the equilibrium resulting in a rate of association that is similar both at and away dynamics of extended molecular systems. The tools of mod- from the interface. We find that these differences in rates and sta- ern statistical mechanics, combined with computational tech- bilities of charge separation are due to the altered ability of water niques for efficiently sampling reactive trajectories (20), enabled to solvate and reorganize in the vicinity of the metal interface. a detailed characterization of the reaction mechanism, thermo- dynamics, and kinetics of these processes. These tools have been chemical kinetics | catalysis | surface science | ion pairing previously applied to investigate ion pair dissociation in the bulk liquid, which has revealed that the dissociation of classical ions n aqueous solution, the association or dissociation of oppo- and water ions are both crucially driven by electrostatic fluctu- Isitely charged ions requires the collective rearrangement of ations of the aqueous environment (2, 6). The characteristics of surrounding water molecules (1, 2), which solvate bound ion these electrostatic fluctuations are similar between the two types pairs differently than individual ions (3–6). The solvent fluc- tuations that enable these collective rearrangements drive the Significance dynamics of ion pairing and unpairing and therefore play a fun- damental role in many chemical reactions. Near the surface of Aqueous electrode interfaces serve as the backdrop for many an electrode, these collective solvent fluctuations can differ sig- important chemical processes in nature and technology. These nificantly from that of the bulk liquid (7, 8), and these differ- interfaces continually garner much interest due to their abil- ences can affect the rates and mechanisms of aqueous electro- ity to facilitate and even catalyze certain electrochemical reac- chemical reactions. In this work, we use molecular simulation tions. Charge separation is a fundamental step in nearly all to investigate the microscopic processes of aqueous ion pair- catalytic processes that occur at metal interfaces. Traditional ing when it takes place near, but not in direct contact with, electrochemical measurements are able to observe the conse- an extended metallic electrode. We identify the specific effects quences of charge separation but are limited in their ability of the electrode interface by comparing our results to those to reveal direct molecular details. By studying detailed molec- generated in the environment of the bulk liquid. We find that ular models of charge transfer at water metal interfaces, we the presence of an electrode has little effect on the mecha- have uncovered the microscopic dynamics of this fundamental nistic details of ionic charge separation, but can significantly process. Elucidating the altered thermodynamics and kinetics influence the thermodynamics and kinetics of the process. We of charge separation at water–metal interfaces and identify- highlight that this influence is different for simple monova- ing their molecular underpinnings will inform the interpreta- + − lent salts like Na and I , whose transport is limited by the tion of macroscopic measurements and the design of better mobility of an aqueous solvation shell (9), than it is for water catalysts. + − ions, like H3O and OH , whose transport is limited by the concerted hopping of protons along hydrogen-bonding chains Author contributions: D.T.L. and A.P.W. designed research; J.A.K., D.T.L., and A.P.W. per- (10). This fundamental difference is controlled by the micro- formed research; J.A.K., D.T.L., and A.P.W. analyzed data; and J.A.K., D.T.L., and A.P.W. scopic details of electrode–water interactions and thus has impli- wrote the paper. cations for the nanoscale design of aqueous electrochemical The authors declare no conflict of interest. systems. This article is a PNAS Direct Submission. When described in terms of a chemical reaction, 1To whom correspondence may be addressed. Email: [email protected] or dlimmer@ berkeley.edu. + − This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. A(aq) + B(aq) AB(aq), 1073/pnas.1700093114/-/DCSupplemental.

13374–13379 | PNAS | December 19, 2017 | vol. 114 | no. 51 www.pnas.org/cgi/doi/10.1073/pnas.1700093114 Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 ntebl,adtedt lte nbu orsodt osa h lcrd interface. al. electrode et the Kattirtzi at yellow. ions in to correspond highlighted blue is in ion plotted charged data negatively the the and and bulk, green, of the in function in highlighted a is as ion profile positive free-energy The the respectively. ions, water and ions 1. Fig. platinum extended an of interface we associ- electrochemical work, are an this that with In changes ated environmental environment. the aqueous specifically the consider in differ- changes affected be by can they ently mechanisms, different via occurs ions (OH ion hydroxide (H charged hydronium negatively formed newly molecule near- a water a neutral to a in from of proton result a of making/breaking fluctuations relocation spontaneous the correlated These and bonds. fluctuations hydrogen known field process simula- electric a initio induced solvent- ions, of ab coordination water well-timed sim- the bound with requires of autoionization, of shown as that dissociation been the from has that different It tion thus salts. is monovalent ions ple water mediating in of role separation solvent’s sim- The of the (21). those leads ions from feature monovalent differ to sized This ions ilarly hydrogen- (6). water of transport aqueous properties rapid solvation the the and delocalized into for pro- of tons integrate shuttling Grotthuss-like the easily leverage and network bonding molecule. can water individual ions an from These and to transfer proton of ucts thermal typical of order the temperature. on is emergence that energies, the barrier free-energy to a leads thermodynam- of reorganization over- usually solvent the is dissociation favorable, although ion ically that, aqueous revealed of have process all efforts process numerous These this in 14). and role water’s (1–4, dissociation, quantifying at aimed ion been have aqueous efforts the for as solva- identified step been sepa- ionic has rate-limiting to polarized reorganization solvent ions oppositely This of and shells. tion separate pair two trans- bound and into a deconstructed be formed of for must shell dipole order solvation dipolar electric In this rate, the pair. to ion whose molecules response bound water the in by polarized dressed are are Simi- whose charge. ions orientations molecules ionic of the pairs water to bound of response larly, shell in solvation polarized are a orientations by dressed are they differ structures solvation their that fact significantly. the despite pairs, ion of eas h ae-eitdsprto fwtradclassical and water of separation water-mediated the Because prod- the are hydronium, and hydroxide specifically ions, Water solution, aqueous in solvated are ions classical simple When A A C and k B T B where , oti yia npht on rmarcmie tt bakbree ae)t iscae tt rdbree ae)frclassical for panel) (red-bordered state dissociated a to panel) (black-bordered state recombined a from going snapshots typical contain k B sBlzanscntn and constant Boltzmann’s is 3 h neincsprto o lsia osadwtrin,rsetvl.Tedt lte nrdcrepn oions to correspond red in plotted data The respectively. ions, water and ions classical for separation interionic the R, O + 6 2,laigbhn a behind leaving 12), (6, ) − ). T sthe is D B eodwsdsge osuytercmiaino ae ions, water of recombination study the pair, to study ion H to designed classical designed was was a first second used of We The dissociation electrode. systems: the platinum model extended different with an we contact two of interface, in surface electrode water (111) aqueous liquid the of the simulations at atomistic dynamics performed ion study To Environments Heterogeneous in Events Rare of Simulating dynamics slow their the into to monolayer directly water. couple the adsorbed thus of and part shell dra- liq- incorporate solvation the pure this can at with For ions interface comparison however, (26). itself; uid in monolayer liquid the subtle of bulk is slowdown matic effect adjacent this the systems, of 1 water dynamics Fig. and in shown ture are separation interface charge that electrode along and than taken the slower Snapshots near magnitude (8). trajectories liquid of bulk orders the are of relax- that molecular 25). dynamics exhibiting (24, ation hydrophobic, monolayer be can water The the monolayer to 23). electrode-adsorbed This leads (22, an and surface strong of typically the formation is of formed and plane bond site that the chemical top partial way the along on the pointing centered is oxygen dipole its its interfaces with them, these to of binds water feature unique A electrode. e,w sda biii oe fwtrbsdo est func- density on based water of sys- model (6). model initio theory and second tional ab the making an in the used Thus, we by bonds. tem, facilitated OH dynamics is covalent the of transport breaking whose describe ions, classical to water this inadequate of Unfortunately, is (26). model electrode nondissociative the at from behaviors away between changes and halides qualitative alkyl consistent other of shown mobility. on mobilities have and studies and energies previous free pair, hydration as adsorption ion the water ion particular this liquid of studied of we measures Although dynamics experimental and as repro- structure accurately well molecular to the effi- demonstrated This been duce particles. has charge sim- combination point ions cient the symmetric describe spherically we as and (27), describe ilarly, model we SPC/E Specifically, the fields. using force water classical using solution ous 3 O hssol vligwtrmnlyrafcstestruc- the affects monolayer water evolving slowly This B. + and OH − PNAS ntefis oe ytm edsrb h aque- the describe we system, model first the In . | eebr1,2017 19, December | o.114 vol. Na C + and and D | oti lt of plots contain o 51 no. I − n the and , | 13375 A

CHEMISTRY SPECIAL FEATURE For both model systems, the electrode and its interaction with plateau. The second contribution is due to distortions in the ionic water molecules is described following the model of Siepmann solvation shell that arise in response to the changes in interionic and Sprik (28). In this model, each electrode atom includes distance that occur during transitions between the bound and a fluctuating partial charge that varies to maintain a constant charge separated states. These distortions determine character- potential condition. In this way, fluctuations in the charge distri- istics such as the size and shape of the free-energy barrier. bution of the aqueous environment induce corresponding fluctu- As indicated in Fig. 1, aqueous contributions to the free energy ations in the electronic polarization of the electrode. These fluc- depend on both the identity of the charged particles and also tuations mimic the electrostatic contributions of image charges on the details of the aqueous environment. We focused on the and are consistent with a textbook description of a metal in that latter by comparing the charge separation free energy for ions they obey the Johnson–Nyquist relation (29). As found in other at the electrode interface to that of ions in the bulk liquid. We studies (30–32), this description of the electrostatic environ- observed that near an electrode, both water ions and classical ment results in an electrostatic potential that is rapidly varying ions faced an increased free-energy barrier for recombination. near the electrode, but homogeneous in the bulk, with concomi- However, this barrier increase was larger for water ions than it tant Gaussian electric field fluctuations (24). Other electronic was for classical ions. This differing influence of the electrode on degrees of freedom, such as those that determine the details of the charge separation free energy of classical ions and water ions water–platinum binding, are described implicitly by using empir- reflects water’s differing role in the charge separation mechanism ical interaction potentials. This electrode model captures impor- for these two systems. That is, the electrode’s influence on charge tant aspects of molecular physics that are unique to electrode separation is determined by water’s specific role in the micro- interfaces, such as electronic polarization and site-specific water scopic process. To understand this influence more thoroughly, adsorption, at a fraction of the computational cost associated we now describe the mechanistic details for each case separately, with an ab initio description of the metal. focusing specifically on the indirect role of the electrode on the We analyzed charge separation in terms of both thermody- water-mediated aspects of charge separation. namics and kinetics. We quantified the thermodynamics by com- puting the free energy along the microscopic coordinate that The Mechanism of Charge Separation for Simple Ions characterizes transitions between the bound and charge sepa- The mechanism of ionic charge separation involves an inter- rated states. For the classical ion system, we computed this free play between ion and water dynamics. To understand this inter- energy using standard umbrella sampling techniques (33), and play and how it is affected by the electrode interface, we first we computed the dissociation rate constant from the side–side identified the reaction coordinate that encodes the microscopic correlation function (34). These methods are direct and accu- details that are relevant to the dynamical process. An appro- rate but they are too computationally demanding to be applied priate reaction coordinate must be capable of (i) distinguishing to the water-ion system, which relies on relatively expensive between the bound and charge separated states, and (ii) prop- ab initio molecular dynamics simulations. Thus, for water-ion erly characterizing the transition state ensemble (TSE), which recombination, we used our limited ensemble of trajectories to are those configurations that have equal probability of commit- construct a Markov state model (MSM), and we analyzed this ting to either the bound or charge separated state (1). The one- model to infer the thermodynamics of charge recombination dimensional coordinate of Fig. 1 accomplishes the former, but (35). To construct this model, we discretized the charge sepa- not the latter. It omits the fundamental role of the solvation envi- ration order parameter defined in SI Appendix into a series of ronment in facilitating transitions between the bound and charge metabasins, and then we used these metabasins as a basis for a separated states. MSM. The MSM was parameterized by specifying the transition The configuration of water molecules in the system determines rates between metabasins, which we computed directly from our the electrostatic environment of an ion pair. Collective rear- trajectory ensemble. This MSM framework allowed us to infer rangements of water molecules control the electrostatic varia- the thermodynamic consequences associated with subtle differ- tions that drive the process of ionic charge separation. We can ence between simulations carried out in the bulk and at the elec- quantify these variations by computing the solvent-induced elec- trode interface. We analyzed the kinetics of water-ion pairs by trostatic potential, also known as the Madelung potential, analyzing the statistics of recombination times as derived from N H2O simulation data and an associated model of charge recombina- q± X qi ψ± = , [1] tion dynamics. 4π0 |ri − r±| i Thermodynamics of Interfacial Charge Separation where the summation is taken over all of the atoms that belong The thermodynamics of aqueous charge separation can be eval- to water molecules, qi and ri is the charge and position of the th uated by considering the free energy, or reversible work, to sepa- i water atom, q+ and r+ are the charge and position of the + rate two oppositely charged particles in solution, such as plotted Na ion, and 0 is the vacuum permittivity. This quantity reports in Fig. 1 C and D. As this figure illustrates, the free energy to directly on water’s collective contribution to the electrostatic separate water ions and the free energy to separate classical ions environment of the Na+ ion, and similarly the analogous quan- − bear a similar general structure. That is, both systems exhibit tity for I , ψ−, reports on collective water fluctuations around it. a stable free-energy basin at small interionic spacing, which we Their sum, ψ = ψ+ + ψ−, is thus the total electrostatic potential identify as the bound state, and a plateau-like region at larger acting on the ionic pair, from the surrounding solvent; for conve- interionic spacing, which we identify as the charge-separated nience, we report it in units of 1/β = kBT . state. In both cases, these two states are separated by a transi- The quantity ψ exhibits different statistics when the ions are tion region that includes a small (∼ 2kBT ) free-energy barrier in in their bound state compared with when they are independently the direction of association. solvated. This result can be seen in Fig. 2, which contains a plot The thermodynamics of charge separation depends signifi- of the charge separation free energy as a function of ψ and cantly on the solvation free energy of the ion pair. This free R. When resolved in these coordinates, the bound and charge energy is shaped by the properties of the aqueous environment separated states are connected via a pathway that is mutually through two primary contributions. The first contribution is due elongated in both ψ and R, clearly indicating the importance to differences in the solvation free energy between the bound of collective water fluctuations in ionic charge separation. Fur- and charge separated states. This free-energy difference controls thermore, members of the TSE harvested with transition path the relative heights of the bound basin and the charge separated sampling are distributed along this free-energy path, suggesting

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Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 atrz tal. et Kattirtzi nfe-nrybrirhih obn oyedteanomalously the yield to combine height barrier evolving free-energy in slowly this governing electrode, in timescale to dynamics the the increases couples significantly near process which monolayer, ions separation For charge ori- water–electrode the dynamics. slow mono- experience Strong relaxation water monolayer (8). adsorbed this entational within an liquid molecules of and bulk formation layer, the the to in lead interactions are they than free- the and in interface barrier electrode the over the surface. flux of energy the affect that differences to these envi- identical that bulk the not that is is discrepancy ronment apparent this to 2C, resolution Fig. The in shown that function find correlation we side–side the via directly, k exp(1.5) tt hoy dnia ytm ihabrirhih difference height conse- barrier a have with to systems of expected identical transition on theory, is Based state kinetics. height dissociation electrode. relative the barrier the of for quences presence in the difference by liquid This the on imposed straints ovn eraiaini agra h lcrd nefc,by interface, electrode for cost the free-energy at the larger that ∼ is coordinate reveals the reorganization 2B, onto Fig. solvent energy in free plotted the result, projecting by cess (SI TSE the of members Appendix). suitability across this analysis commitor confirmed performing have by We coordinate. of reaction coordinate suitable 2D the that shown fits linear with (blue), interface and (red) black. bulk in for the potential for points Madelung ions black the (C classical of (blue). as interface function shown and a are (red) as bulk TSE energy the Free the (B) of surface. 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Fig. BC A elec 1.5k ae yaisaemr lgiha h lcrd interface electrode the at sluggish more are dynamics Water eioae ae’ otiuint h hresprto pro- separation charge the to contribution water’s isolated We 1.5k ≈ B B 0.2k reeeg sa as energy Free (A) NaI. for dissociation pair ion of Mechanism T T ≈ hni si h uklqi— osqec fcon- of consequence liquid—a bulk the in is it than , bulk r rdce ohv ae htdfe yafco of factor a by differ that rates have to predicted are hti,bsdo are egtaoe eexpect we alone, height barrier on based is, That 4.5 k ψ elec oehr hsrdcddfuinadteincrease the and diffusion reduced this Together, . oee,we iscainrtsaecomputed are rates dissociation when However, . ≈ 0. 02k bulk (ψ, ulodro antd different. magnitude of order full a , n h oa aeugpotential, Madelung total the and R, iesd orlto ucinfrthe for function correlation Side–side ) R ) aifisteciei ob a be to criteria the satisfies ψ The . ψ , hspoesa h lcrd nefc ssoni i.1B. Fig. in shown is of interface illustration electrode An the molecules. at water an process intermediate this of three shuttling or the two of drives the fluctuation from field proton excess electric large a cess, hog h ocre rnfro rtn ln hi fhydro- the of connect chain that a bonds along gen protons occurs of process transfer concerted recombination is the The through which spontaneous. recombination, and charge help rapid focus of both the to process with chose time-reversed therefore even the We on simulate, techniques. to event-sampling difficult rare dissociates of thus state is stable and exceptionally reluctantly This molecules. water of tral state Ions bound Water The for Separation Charge of Mechanism The water collective large such for require different not reorientations. do fundamentally dissociation which is pairs, in ion influence slowdown water significant electrode’s presence a The the to rates. above, lead by described of molecules affected reorientations ions water is collective classical the role simple on constraints the that electrode-induced For dynam- how electrode. the and the driving pairs in of influ- ion role This specific of water’s environment. ics by aqueous controlled is interfacial ence the by mediated elec- and bulk the between interface. rate trode dissociation in difference large fhdoe od.Tert o hspoesi ucino the of function a is process this for rate The chains bonds. short hydrogen through mechanism, of concerted charges a the via Second, recombine, molecule. can water neighboring single and a ion water First, the a to events. bond dynamic hydrogen of a H along types hop two can recombi- of proton charge terms the describes in of model nation connectivity The the network. bond and hydrogen molecules, water surrounding their of value the model, water predict This ciently within of data. details model more coarse simplified in this described a from of derivable use recombination ion the sim- with (our statistics statistics improved poor includes to due data quantify ulation to in difficult are shown ferences as large-τ However, the distributions. in the differences discernible revealed interface of of separation time ion initial with tory computing by the statistics on effect subtle How- a ions. had water electrode of the of statistics that dynamics effect observed of little we recombination has case ever, average electrode the the the of unlike on presence and the salts, Notably, monovalent respectively. of interface, trode times recombi- charge recombination rapid and average facilitate with chains molecules. nation, bond water intermediate hydrogen two These via bonds hydrogen pairs secutive ion Water barrier. by the to separated is diffusion time not with that associated are dis- but that recombine, larger ions just to from time the Starting quantitative the that basin. affects bound large tances the sufficiently to is committed distance already this 1D, Fig. hydronium– of fixed a separation with hydroxide con- equilibrated of been ensemble have Because an that state. from figurations initialized bound trajectories the compared only reach to time, ions the τ water computing separated by quantified tially we which nation, 3 eed estvl nteiiilsprto ftein,we ions, the of separation initial the on sensitively depends eqatfidteeetoesefc ntercmiaintime recombination the on effect electrode’s the quantified We recombi- ion water of kinetics the considering by began We h nuneo h lcrd ntedsoito fin is ions of dissociation the on electrode the of influence The O τ + elec hspoo opn eut na xhneo oiin of positions of exchange an in results hopping proton This . τ Comparing . 0 = τ . . 40 5 PNAS r yial rde ycan ftrecon- three of chains by bridged typically are A ˚ sfrin ntebl iudada h elec- the at and liquid bulk the in ions for ps | H P ≈200 eebr1,2017 19, December 3 P (τ H O 5 (τ 3 + ) .Fo h reeeg ucinin function free-energy the From A. ˚ O τ H o osi h ukadteelectrode the and bulk the in ions for h rbblt htagvntrajec- given a that probability the ), and needn rjcois.W thus We trajectories). independent + ie h oiin of positions the given 3 O othe to + sdsge oeffi- to designed is Appendix, SI OH and 5 ilhv recombination a have will A ˚ − OH OH | ssml aro neu- of pair a simply is hs dif- these Appendix, SI o.114 vol. − − i h participation the via 6.Drn hspro- this During (6). OH | τ bulk − H o 51 no. 3 rfo the from or O 0 = τ o ini- for , + , al of tails | . OH 35 13377 − ps ,

CHEMISTRY SPECIAL FEATURE number of hydrogen bonds in the chain. We simulated charge charge between the hydroxide and the hydronium species, as recombination with a kinetic Monte Carlo (KMC) algorithm for given by, fixed configurations of the hydrogen bond network. We com-   puted the rates of the processes in the KMC model directly from 1 X X Q = q − q , [2] our simulation data. 2  i j  Fig. 3A contains a plot of P(τ) computed by applying our i∈H3O+ j ∈OH− KMC model across the ensemble of initial conditions used in where the two summations are taken over all of the atoms our ab initio simulations. We observed that recombination in the belonging to the hydronium or hydroxide ion, respectively, and bulk and at the electrode interface have similar mean behavior, qi is the Mulliken charge on the ith atom. We define the hydrox- but differ in the tails of their recombination time distributions. ide and hydronium based on nuclear coordinates by first associ- Specifically, it is more likely that an ion pair at the electrode ating each hydrogen with its nearest oxygen, as described in SI interface has an abnormally long recombination time. This large Appendix, and then identifying an oxygen with only one associ- difference involves very low probability events, and thus does ated hydrogen as a hydroxide center and an oxygen with three not manifest itself in the mean behavior. We attribute the differ- associated hydrogens as a hydronium center. These water-ion ence in these curves to subtle differences in the topology of the centers and their associated hydrogens are thus included in the hydrogen-bond network between the bulk and the interface. Pro- summations in Eq. 2∗. This continuously varying quantity was ton dynamics in our model are constrained by the hydrogen-bond formulated so that Q = 1 when the hydronium and hydroxide are network and thus especially sensitive to the details of network fully charged and Q = 0 when the two species are charge neu- structure. Specifically, the interfacial hydrogen-bond network is tral. By analyzing the statistics of Q, sampled over an ensemble distorted along the plane of the interface. This distortion leads of recombining trajectories, we can compute the free energy for to a slight reduction in the relative number of hydrogen-bond charge recombination. chains along which recombination can occur (see SI Appendix Fig. 3B shows the probability distributions for Q for water ion for details). This reduction is balanced by an increase in the recombination in the bulk and at the electrode interface, com- probability that a proton transfer will increase the separa- puted directly from the ensemble of recombination trajectories†. tion between the ions, thus leading to an increase in recombi- These profiles reveal that the barrier height to recombination is nation time. slightly larger at the electrode interface than it is in the bulk liquid. The electronic and nuclear rearrangements that accompany This barrier height difference is ∼1.5kBT , similar to that found in water ion recombination are driven by electrostatic fluctuations the case of the classical ions described above. However, the kinetic of the aqueous environment. These fluctuations are reflected in consequences of this observation are not apparent when compar- the distribution of electronic charge in the system, which is dif- ing the recombination times, which are nearly identical near and ferent for the bound and charge separated states. One way to away from the electrode interface. We can thus conclude that the quantify this difference is to compute the imbalance of electronic kinetic effect of an increased barrier height is compensated by an increase in flux along the coordinate Q. We explain the molecular origins of the enhanced flux in Q in terms of the equilibrium dynamics of hydrogen bonding. The A concerted proton hops that drive recombination are directed along chains of multiple hydrogen bonds. This process is there- fore contingent on the stability of these chains. Fluctuations that destabilize or sever hydrogen-bond chains will have a negative effect on recombination. Along a liquid water interface, such fluctuations are suppressed due to geometric constraints that lead to more stable and longer lived hydrogen bonds (36, 37). The consequences of these constraints can be quantified by com- puting the distribution of hydrogen-bond lifetimes, P(τHB). In Fig. 3C, we see that the hydrogen-bond lifetimes are larger at the electrode interface than they are in the bulk. Hydrogen-bond chains at the interface are thus longer lived, which allows more time for the environmental fluctuations to induce the electronic reorganization associated with charge recombination. BC Implications for Electrochemistry The aqueous environment of an electrode interface differs from that of the bulk liquid. These differences affect the microscopic processes that underlie many electrochemical applications. In this work, we have highlighted specifically the microscopic pro- cess of ionic charge separation and shown that the electrode’s influence can depend significantly on the identity of the ionic species. This dependence is controlled by water’s specific role in

∗In rare instances, we observed the delocalization of a single water ion to form a cluster of three connected water ions. Our method for defining the water ions in these cases is described in SI Appendix. †This sample population reflects our simulation protocol in which trajectories are auto- Fig. 3. Mechanism for water ion association for bulk (red) and the inter- matically terminated shortly after recombination. Therefore, the relative weights of the face (blue). (A) The distributions of recombination times, τ.(B) Distribu- bound and charge separated states in these nonreweighted free-energy profiles do not tion function of the net system charge. (C) Distribution of hydrogen bond reflect that of equilibrium. We find that the difference in the barrier height between lifetimes. bulk and electrode interface is preserved upon an equilibrium reweighting.

13378 | www.pnas.org/cgi/doi/10.1073/pnas.1700093114 Kattirtzi et al. Downloaded by guest on September 27, 2021 Downloaded by guest on September 27, 2021 4 ulnR,Se E eesB(04 rnmsincefiins omtos n solvent and committors, coefficients, Transmission (2014) B Peters JE, Shea RG, Mullen 14. simu- dynamics molecular DFT-based from constants Acidity (2010) M Sprik M, Sulpizi 11. 1 ohG 20)Cmue iuaino rtnslainadtasoti aqueous in transport and solvation proton of simulation Computer (2006) GA Voth Throw- sampling: path 21. Transition (2003) PL Geissler C, Dellago D, Chandler electrodes. PG, Pt Bolhuis hydrogen-covered on 20. layers water elec- of platinum Structure (2013) charged A to Groß T, transfer Roman Proton 19. (2010) E Spohr W, Schmickler F, Wilhelm 18. Sk 17. proton during state transition Zundel-like a of Observation (2009) al. et ST, Roberts 15. in Autoionization (2001) M K Parrinello B, J, Reischl Hutter 13. D, Chandler C, Dellago PL, Geissler 12. currents. electrical by liquids of decomposition of Theory (1806) C Grotthuss de 10. 6 ile ,Bj M, Nielsen 16. atrz tal. et Kattirtzi clefcsaentaprn ntetemdnmc n are and dynam- thermodynamics these the Notably, in apparent 39). dynam- not 38, the are (22, on effects separation influence ical charge different a of have ics water- and may geometry surface energy different a binding such with metal, or copper, different or a gold platinum(111) of as made a electrode use an we however, results, electrode; these control In thus effects. interactions dynamical electrode–water these the of separa- charge details ionic The of fluctuations, tion. dynamics environ- molecular microscopic the aqueous govern to that couple the timescales which of interac- the as properties Electrode-water such equilibrium ment, dynamical. the is alter pairs tions ion of separation systems. type, electrochemical ion of on design dependence the for their analo- important and is the effects, and however, these Understanding affected. for magnitude; barely accounting is of ions water order for process an electrode gous comprising an over ions near by slowed for is interface that separation find charge We salts, monovalent dynamics. pair ion mediating .Knsa ,RsihJ,Lne-elR,LeS 19)Sletsrcue dynamics, structure, Solvent (1998) SH Lee RM, Lynden-Bell JC, Rasaiah S, Koneshan 9. can surfaces metal of Hydration (2013) D Chandler P, Madden Fundamental AP, Willard surfaces: DT, solid Limmer with water 8. of interaction The (1987) TE Madey PA, hydro- hydrated of Thiel recombination the the 7. On of (2011) M nature Parrinello H, The Eshet MK, (1999) Prakash A, M Hassanali Parrinello 6. J, Hutter ME, Tuckerman D, Marx chloride sodium pair a 5. of ion structure Solvation chloride (1986) JA Sodium McCammon M, (1984) Berkowitz PJ AC, Belch Rossky 4. JA, McCasmon water. OA, in Karim dissociation M, ionic of Berkowitz mechanism 3. the Toward (2012) in C dissociation Dellago pair AJ, ion Ballard of pathways 2. Kinetic (1999) D Chandler C, Dellago PL, Geissler 1. motnl,tedmnn nuneo h lcrd nthe on electrode the of influence dominant the Importantly, oriae ninpi dissociation. ion-pair in coordinates water. liquid lations. (Paris) Phys Chim n imlclrsystems. biomolecular and dark. the in passes, mountain rough over ropes ing Today Catal study. trajectory dynamics molecular A trodes. calculations. theory functional density of 114:18182–18197. basis the on reactions lution interfaces. electrode–electrolyte electrochemical of eling solutions. hydroxide aqueous in transfer water. liquid 25 at solutions aqueous in mobility ion and hydrophobic. 4205. and heterogeneous dynamically be aspects. water. in ions hydroxide and nium water. in proton excess water. in pair ion simulation. Computer water: in interaction B Chem Phys water. lsnE ta.(00 oeigteeetohmclhdoe xdto n evo- and oxidation hydrogen electrochemical the Modeling (2010) al. et E, ulason ´ hsCe B Chem Phys J hsCnesMatter Condens Phys J ufSiRep Sci Surf figrJ elg 20)Tesaitc feeti edflcutosin fluctuations field electric of statistics The (2009) C Dellago J, ofinger ¨ 202:183–190. reu E asnM,RsmilJ(05 oad rtpicpe mod- principles first Towards (2015) J Rossmeisl MH, Hansen ME, orketun ¨ o Phys Mol Science 116:13490–13497. 58:54–74. mCe Soc Chem Am J 7:211–385. 291:2121–2124. 103:3706–3710. 107:495–502. 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(2001) B Smit D, Frenkel treat- efficient 33. computationally A (2012) in GA moments Voth HS, dipole White and R, field Kumar electric MK, Petersen local of 32. Fluctuations (2015) A Onuki K, Takae 31. walls metal between water of simulation dynamics Molecular (2015) capacitors. A Onuki nanoscale K, Takae in fluctuations 30. Charge (2013) al. et potential DT, electrostatic Limmer and topology 29. surface of Influence poten- (1995) pair M effective a Sprik in JI, term Siepmann at missing The 28. exchange (1987) T Water Straatsma J, (2015) Grigera H, D Berendsen Chandler 27. PA, Madden AP, water Willard for DT, model General Limmer (2003) 26. DA King electrochemical PL, Andres an de at VA, Water Ranea (2009) A, D Michaelides Chandler 25. PA, Madden SK, Reed AP, electrodes. Pt Willard at hydrogen-covered on water 24. layers of water of perspective Structure (2013) molecular A Groß A T, Roman (2012) A 23. Michaelides A, Hodgson J, Carrasco 22. yUiest fClfri,Bree,Cleeo Chemistry. later of and College Berkeley, Science was California, D.T.L. Theoretical A.P.W.). of for and University Center by J.A.K. Princeton Department the (to MIT by funds Sci- supported the faculty National initially junior and by A.P.W.) through supported (to Chemistry was CHE-1654415 of work This Grant simulations. Foundation initio ence ab the up ting ACKNOWLEDGMENTS. More pseudopotentials. in GTH found be and can correction details dispersion 1 D3 sizes with cell 3 functional with sizes cell simulations simulation initio with ab up classi- set The of were potential. number simulations electrode constant cal applied a and with temperature, ensemble volume, an particles, in performed were simulations All significant these predict Methods to insufficient thus effects. continuum interfacial are aque- Traditional the interface. (40) and electrode models shell, the solvation at dynamics describes their explicitly ous ions, that between model interplay a without the predict to difficult thus lcrlt nefc:Apiaint xdeetoeptnil,itrailcapaci- interfacial potentials, charge. electrode zero of fixed potentials and to tances, Application interface: electrolyte interface. solid–liquid electrified Poisson-Boltzmann modified and theory functional density theory. of Combination faces: TiO water/rutile interfaces. model. state Markov unbiased using approximation. state transition Applications potential. constant a at held 116:4903–4912. cells electrochemical polarizable of ment walls. metal between water reversal. field after dynamics and response B Dielectric Chem field: electric an under 111:106102. systems. water/electrode on tials. collective. and rare is 24024. electrode platinum hydrated surfaces. metal noble and Lett transition close-packed on adsorption monomer study. simulation interface—A Today Catal interfaces. metal 90:216102. hsChem Phys J hsRvB Rev Phys 119:9377–9390. hmPy Lett Phys Chem 202:183–190. Aaei,NwYr) o 1. Vol York), New (Academic, lsnE Bj E, ulason ´ 2 PNAS a Mater Nat 10 interface. (110) 91:6269–6271. 77:245417. IAppendix SI etakDrte oz o sitnewt set- with assistance for Golze Dorothea thank We | nesadn oeua iuain rmAgrtm to Algorithms From Simulation: Molecular Understanding reu E rpoi ,NrkvJ 20)Mdln the Modeling (2008) JK Nørskov V, Tripkovic ME, orketun ¨ 386:218–224. eebr1,2017 19, December 11:667–674. hmPhys Chem J hmPhys Chem J aaa Discuss Faraday hmPhys Chem J hmPy Lett Phys Chem hsCnesMatter Condens Phys J hmTerComput Theor Chem J . hsRvB Rev Phys × 102:511–524. 143:154503. 1 68:2959–2970. × 141:423–441. m h atrue h PBE the used latter The nm. 2 466:68–71. 86:075140. | o.114 vol. hsCe C Chem Phys J 26:244102. 11:276–285. × 3 | × o 51 no. m n the and nm, 6 hsCe C Chem Phys J hsRvLett Rev Phys 119:24016– | hsRev Phys 13379 Phys J

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