Local and Collective Reaction Coordinates in the Transport of the

Article pubs.acs.org/JPCB

Local and Collective Reaction Coordinates in the Transport of the Aqueous Hydroxide Ion Sean T. Roberts,†,§ Aritra Mandal,† and Andrei Tokmakoff*,†,‡ †

Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, University of Chicago, Chicago Illinois 60637, United States

‡

S Supporting Information *

ABSTRACT: We investigate local and collective reaction coordinates for the structural diffusion of the hydroxide ion in dilute aqueous NaOH solution using a multistate empirical valence bond (MS-EVB) simulation. We characterize a 15 fs time scale associated with shifting of the equally shared proton within a Zundel-like H3O2− ion to form a water molecule, a 550 fs relaxation from this transition state largely guided by electrostatic fluctuations of the surrounding environment, and a 9.6 ps time scale that corresponds to the solvation of the water molecule formed by the proton transfer event. When individual proton transfer events are examined, we are unable to identify a unique transition state solely on the basis of a decrease in the hydroxide ion’s coordination number. Instead, we find that the collective electric field along the proton transfer direction is better suited to describe the creation and relaxation of Zundel-like transition states that allow structural diffusion of the hydroxide ion.

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“hypercoordinated” configuration, wherein the ion’s oxygen atom accepts four water hydrogen bonds, but find that the number of hydrogen bonds accepted by the ion decreases to three during proton transfer events. This led to the proposal that the rate limiting step for proton transfer is the breakage of a hydrogen bond to the ion. Such a mechanism, termed “presolvation,” can be rationalized by recognizing that adopting a lower coordination number configures the ion to readily reincorporate into water’s hydrogen bonding network upon proton transfer.16,18 Recent calculations on solvated hydroxide clusters put this mechanism into question, finding that the hydroxide ion can accept more than four hydrogen bonds and transfer the proton from a four-coordinate species.20 Although these conduction mechanisms have not gone without scrutiny, much of the published criticism has focused on the relative stability of solvated hydroxide ions with different coordination numbers.21 The role that collective coordinates play in the structural diffusion of the hydroxide ion is not explicitly addressed in the presolvation mechanism. Though a hypercoordinated (or four-coordinate) structure may represent a barrier to proton transfer, once this barrier has been lowered by conversion of the ion to a three-coordinate state, the driving force that then leads to the transfer of a proton to the ion is not obvious. Of course, these two processes are not independent, because the rearrangement of hydrogen bonds is a highly

INTRODUCTION

A molecular description of the reaction mechanism for aqueous proton transfer remains a difficult problem because both local and collective processes play important parts in guiding the motion of individual protons. Proton transfer in solution is commonly described by propagation along a collective solvent coordinate;1−6 however, local hydrogen bonding structure and motions involving only a few key atoms play equally important roles in directing the motion of individual protons.7,8 For example, the dissociation of aqueous HCl involves two key coordinates working in concert, the solvent polarization about the HCl molecule and the shape of the hydrogen bonding network surrounding the H2O molecule that accepts a proton.9 Likewise, simulations have suggested that the transport of protons in aqueous acids involve several hydrogen bond creation and breakage events in the solvent shells about each hydronium ion,10 so that their diffusion depends intimately on hydrogen bond rearrangements of the liquid.11 Collective fluctuation of several water molecules also plays a decisive role in autoionization of water, where the solvent electric field is thought to provide the driving force for water dissociation.6 The collective compression of hydrogen-bonded water wires has been proposed as a key step in the recombination reaction between autoionization products12 and in aqueous proton transfer processes.13 In recent studies of hydroxide ion transport, emphasis has been placed on changes in the local hydrogen bonding structure surrounding the ion that allow it to accept a proton from one of its hydrogen bonding partners.14 Ab initio molecular dynamics (AIMD) simulations15−19 indicate that the most stable form of the aqueous hydroxide ion is a © 2014 American Chemical Society

Special Issue: James L. Skinner Festschrift Received: January 31, 2014 Revised: March 24, 2014 Published: March 25, 2014 8062

dx.doi.org/10.1021/jp501145p | J. Phys. Chem. B 2014, 118, 8062−8069

The Journal of Physical Chemistry B

Article

collective process, involving the loosely correlated motion of many water molecules.22,23 Indeed, a recent work argues that proton transport in aqueous hydroxide is not necessarily triggered by reduction of the coordination number of the ion, but through a collective compression of hydrogen bonded water wires.13 In an effort to investigate the role of collective coordinates in the diffusion of the hydroxide ion, we have studied the dynamics of proton transfer from water to hydroxide ion as simulated by a recent MS-EVB model developed by Ufimtsev et al.24 Although MS-EVB simulation models have been employed for many years to study the transport of the excess proton,25−29 it is only recently that this methodology has been applied to the hydroxide ion.30 Our analysis shows that the solvent electric field projected along the proton transfer coordinate, i.e., along the O−H bonds being broken and formed during the proton transfer process, serves as a good reaction coordinate. It also emphasizes that, in the search of effective metrics for proton transfer, the hydroxide ion coordination number may not include important collective effects that guide the dynamics of the proton. This investigation is also motivated by an interest in establishing connections between proton transfer dynamics in aqueous hydroxide and recent two-dimensional infrared spectroscopy (2DIR) of the participating O−H stretching vibrations.31,32 Considerable evidence indicates that the solvent electric field exerted along an O−H bond in neat water determines the O−H stretch vibrational frequency,33−37 and thereby the shape of the proton potential. It is therefore likely that the same collective variables that influence the proton transfer dynamics also describe the IR spectroscopy.

Figure 1. Illustration defining the variables used in the analysis of aqueous hydroxide structure and proton transfer dynamics.

rH···A = |rH* − rOA|, and the commonly used proton sharing asymmetry parameter is δ = |rH···A − rH···D|. The coordination number, nC, of the ion is defined for a fixed configuration as a count over the number of hydrogen bonds made to OA, using the commonly used geometric hydrogen bonding criteria ROO ≤ 3.5 Å and ∠H*ODOA < 30°.

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RESULTS AND DISCUSSION In recent 2DIR experiments of the O−H stretch of dilute HOD in concentrated NaOD:D2O solutions, two principle time scales associated with the proton transfer process were identified and assigned with the help of this MS-EVB simulation model.31,32 The measurements assigned a 110 fs decay process to the relaxation of Zundel-like DO···H···OD− configurations that exist close to the transition state for proton transfer.31 2DIR surfaces measured over picosecond time scales indicated the presence of an exchange cross peak assigned to the transfer of a deuteron from HOD to an OD− ion, giving a >3 ps time scale for the proton transfer.32 These time scales correlate well with the results of AIMD simulations.18 A simulation employing the B3LYP density functional predicts a 180 fs time scale for “proton rattling” events wherein a proton within a Zundel-like HO···H···OH− configuration preferentially associates with either oxygen of the ion multiple times. Also observed is a 1.7 ps time scale associated with the formation of such Zundellike species from stable structures of solvated hydroxides.18 Although transfer of a proton through a metastable Zundel-like intermediate is possible,14 the close agreement between experiment and simulation argues for a fleeting Zundel-like state. The MS-EVB simulation shows that Zundel-like shared proton configurations are exceedingly short-lived and lie at the transition state for proton transfer. This is seen by calculating the nonequilibrium relaxation from the δ = 0 state using the relaxation function δ(τ). For dynamics, we define a proton transfer event as a simulation time step during which the proton separation asymmetry rH···D − rH···A changes sign and label the time point preceding this event as t0. The time delay relative to the proton transfer event used in these calculations is τ = (t − t0). We use an overbar to indicate a time average over a nonequilibrium time-dependent conditional probability and angle brackets to indicate an equilibrium average. To begin with, we have considered only successful proton transfers where the proton does not switch back to the same water molecule. The relaxation function, which converges to the mean value of the parameter δ at longer times (0.415), is fit to a sum of two exponential decays and an exponentially decaying cosine function. Figure 2 shows that 95% of the rapid relaxation of δ(τ) is completed with a time scale of 15 fs, i.e., much faster than any intermolecular motions of the liquid. This time corresponds to a third of the gas phase period of the proton

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METHODS The MS-EVB simulation model used in the following work has been described in detail elsewhere.24,38 The presented results were calculated from a pair of simulation trajectories consisting of a single NaOH ion pair solvated by 214 H2O molecules (flexible SPC water) in a cubic box with periodic boundary conditions (density = 1.01 g/cm3), which were provided by Ufimtsev and Martinez. The system was equilibrated for 100 ps by using velocity rescaling (T = 303.8 K) before making a production run of 900 ps in the NVE ensemble with the velocity-Verlet integrator. For one trajectory, a 0.5 fs time step was used whereas a 1.0 fs step size was employed for the other, but no discernible differences in the resulting dynamics were detected. Ewald summation was used to account for long-range electrostatic forces. The kinetic energy needed to be rescaled every 10 ps to compensate for minor energy drift. Parameters shown in this work were calculated on the basis of the 372 successful proton transfer events, where the proton did not switch back to the original donor water molecule. For the purpose of our analysis, we define structural labels for atoms participating in the proton transfer process in Figure 1. We denote the water molecule solvating the ion as the proton donor and label the transferring proton as H* and the remaining atoms of the donor as OD and HD. Likewise, we refer to the OH− ion as the proton acceptor and its atoms as OA and HA. For a given proton donor water molecule and adjacent proton acceptor hydroxide, we label their oxygen positions as rOD and rOA, respectively, and ROO = |rOD − rOA|. If the position of the shared proton is rH*, then the distances separating the proton from its nearest neighbor oxygens are rH···D = |rH* − rOD|, 8063



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Figure 2. Ultrafast relaxation of shared proton configurations to its equilibrium value ⟨δ⟩ = 0.415 for successful (blue trace) and unsuccessful (green trace) proton transfers, respectively. The relaxation functions are fit to the following equation: δ(τ) = ∑i=1,2Ai exp(−τ/Ti) + A3 exp(−τ/T3) cos(ωτ + φ) + A4, where Ti are the three relaxation time scales and ω and φ are the frequency and phase of the oscillation respectively. The fits shown (red line for successful and black line for unsuccessful proton transfers) indicate that 95% of the amplitude relaxes with a time scale of 15 fs (T1). This is followed by a relaxation on the time scale of ∼150 fs (T2) and pronounced 190 fs (175 cm−1) (ω) oscillations that damp in ∼550 fs (T3) for a successful proton transfer. Only the T2 time scale changes to ∼300 fs for unsuccessful proton transfers. The inset shows a zoomed in view of the early dynamics of δ(τ). Figure 3. (A) Average number of hydrogen bonds donated from water to OA, nC(τ), during proton transfer events. At τ = 0, the point where δ = 0, nC = 3.27. In this calculation we exclude back-transfer events that do not result in the structural diffusion of the ion. At τ = 0, the distribution of nC is the following: 3.2% nC = 2, 64.2% nC = 3, 30.1% nC = 4, and 2.4% nC = 5. If back-transfer events are included, these results change little: 2.8% nC = 2, 61.8% nC = 3, 33.6% nC = 4, and 1.8% nC = 5. (B) Probability distribution of the values of δ found for three- and four-coordinate OH− ions. For each ion configuration, we identify the minimum value of δ among the hydrogen bonds donated to the complex and only use these values to construct the plotted distributions.

shuttling in the Zundel-like complex,39 indicating ballistic motion of the proton away from the δ = 0 configuration. This is followed by a relaxation on the time scale of ∼150 fs and pronounced 190 fs (175 cm−1) oscillations that damp in ∼550 fs, corresponding to a vibrating hydrogen bond separating the newly formed products. We have also monitored the relaxation function when we consider only the back-transfer events that do not result in a successful proton transfer. The only change in that case is the intermediate time scale, which becomes ∼300 fs. This suggests that on average H* only moves back and forth between the two oxygen atoms of a Zundel-like complex only a sparing number of times during proton transfer before it localizes on OA.31 The authors of ref 18 noted that their slower 1.7 ps time scale matched well the lifetime of four-coordinate hydroxide ion configurations and concluded that the breakage of a hydrogen bond donated to the ion acts to gate the proton transfer event. To compare, we characterize the structural and dynamical character of the hydroxide coordination shell in the MS-EVB model. For all configurations sampled in the two trajectories, we find that three-coordinate species are a significant fraction of species populated at equilibrium, with nC distributed as follows: 0.3% nC = 2, 37.4% nC = 3, 58.2% nC = 4, 4.1% nC = 5. In Figure 3A we plot the average number of hydrogen bonds accepted by the hydroxide ion before and after proton transfer events, nC(τ). In this calculation we exclude proton rattling, that is, back-transfer events that do not result in the structural diffusion of the ion. During proton transfer events, we indeed find that nC decreases from 3.66 to 3.27, supporting the general picture determined from analysis of the AIMD simulations.18 However, nearly 40% of this change occurs during the 15 fs preceding τ = 0, a time that is an order of magnitude faster than large amplitude changes in hydrogen bond configurations. This time scale is better correlated with the fast relaxation of the Zundel-

like shared proton configuration noted above. Additionally, the change in nC on proton transfer is only 0.4, reflecting the fact that roughly 30% of the proton transfer events in the MSEVB simulation occur from four-coordinate configurations where one of the solvating water molecules lead to a δ = 0 configuration. This point is emphasized by Figure 3B, which plots P(δ), the probability distribution of proton sharing asymmetry values found for three and four coordinate configurations. Though three-coordinate configurations have smaller average values of δ than four-coordinate ones, the distributions are broad and overlapping. At δ = 0, a three-coordinate configuration is only 2.3 times as likely when proton rattling is taken into account. These observations illustrate that although the coordination number of the ion is certainly correlated with proton transfer events, it cannot provide a unique identification of the proton transfer transition state. Similarly, a recent AIMD simulation study shows that the proton goes through long “rest” periods between bursts of active movement across multiple water molecules without necessarily requiring a reduction in coordination number.13 8064



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Motivated by previous suggestions that autoionization is driven by transient electric fields that arise due to the collective fluctuations of the liquid,6 and the consensus that O−H vibrational frequencies are dictated by the solvent electric field,33−37 we examined the behavior of the electric field acting along the proton transfer coordinate. At each time step, we identify the water molecule in the solvation shell of the OH− ion that possesses the smallest value of δ, and calculate the magnitude of the field acting on the proton H* along the direction of OA and OD. Writing this for the case of the field from charges qi exerted on the proton from the acceptor direction, EA =

∑ i

qi rH···i 2

(rĤ ···i·rĤ ···A)

Here rH···i is the separation between an external charge and H* and r̂ refers to a unit vector. ED, the field acting on the proton from the direction of the acceptor OD, is defined analogously. When calculating electric fields, we include contributions from the charges of the top two EVB states, weighting their contribution to the field by their EVB amplitude. In addition, for the field calculation the negative charge on the hydroxide oxygen is treated as a single point charge equal to the charge on OD even though it is represented by a ring of 20 smaller charges around the oxygen in calculating the dynamics. This treatment corrects for discontinuities in the calculated fields upon proton transfer. Figure 4A plots probability distribution of EA, P(EA), for all simulation configurations. In general, the field projected along this direction adopts a positive value, indicating that the collective field due to the surrounding solvent acts to prevent the transfer of H* to the OH− acceptor by pushing the proton away from the ion. Also plotted in Figure 4A is probability distribution of the field along this direction for those configurations where the proton is equally shared between OD and OA. At these proton transfer points, we find that the average value of EA has decreased to zero, indicating that the solvent no longer electrostatically opposes the breakage of the donor O−H bond. EA and ED are very well correlated with a correlation coefficient of −0.98, where the negative sign signifies opposite signs for EA and ED. Parts B and C of Figure 4 show the correlation of δ with EA and ED, respectively. Good linear correlation of δ with both EA and ED with opposite sign and similar magnitude indicates that during proton transfer, OA, H*, and OD are almost collinear and the dynamics of EA and ED are well correlated with the dynamics of δ. A free energy surface calculated from this joint probability distribution enables us to predict the barrier for proton transfer reaction to be ∼2.5 kBT (Supporting Information, Figure S1). To characterize the role of fields in the proton transfer dynamics, we can characterize their time-dependence relative to the shared proton configuration. We plot both the time dependence of EA and ED averaged over all successful proton transfer events in Figure 5A. The proton transfer itself results in a rapid, sharp inversion in the signs of both ED(τ) and EA(τ) at τ = 0, implying that the solvent is rearranging in such a way as to destabilize the donor bond in favor of the acceptor bond. The time scale for this inversion (15 fs) is faster than the most rapid librational motions, indicating that changes to the local configuration of oxygens does not play a significant role in this shift. The time scale for the switching of electric fields closely correlates with the ultrafast relaxation of Zundel-like species

Figure 4. (A) Probability distribution of EA in atomic units, the collective electric field due to all atoms in the simulation projected along the acceptor direction r̂H···A, for each simulation time step (black) and for shared proton configurations (δ = 0, dashed red). (B) and (C) Joint probability distribution of δ with EA and ED, respectively. The correlation coefficients for these variables are +0.75 and −0.76, respectively. For each ion configuration, we identify the minimum value of δ among the hydrogen bonds donated to the complex and only use these values to construct the joint probability distributions.

implied by changes in δ. These observations are consistent with the picture that the mobile proton is preferentially localized on one of the water molecules in the donor−acceptor pair, and those electric fields which originate from small amplitude but collective orientational shifts in the surrounding water guide the momentary switching process between these positions. A crude measure of the length scale over which charge fluctuations are important can be obtained by excluding different sets of atoms from the field calculation. Of particular interest is the collective solvent electric field Ecol, which excludes the field contributions of the four donor and acceptor atoms themselves. In Figure 5B we plot the behavior of the solvent field from the acceptor and donor directions, Ecol,A and Ecol,D. The observed behavior is qualitatively identical to that displayed in Figure 5A. Ecol,A(τ) and Ecol,D(τ) exchange about the point of proton transfer, showing that the motion of water molecules outside of the first solvation shell is correlated with the proton transfer event. In this case, the field switches sign approximately with a longer time-scale of ∼150 fs, indicating that changes in hydrogen bond length may contribute to the 8065



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Figure 5. (A) Projection of the total electric field along the donor bond that is broken and the acceptor bond that is formed during proton transfer. (B) Same as in (A), but excluding the field contributions due to the hydroxide ion acceptor and donor water molecule. Figure 6. (A) Hydrogen bonding time correlation function, k(t) for water molecules that do not enter the solvation shell of the OH− ion during the simulation run. The decay time scale for this function is 520 fs, a characteristic time scale for fluctuations of the bath. (B) Solvation energy starting from the point of proton transfer (τ = 0, black trace). It has been fit to a biexponential decay (red line) with time scales of 510 fs and 6.35 ps, respectively.

changes in field. In this case, the asymptotic limits of the field appear to have decreased by roughly an order of magnitude, which is expected given the 1/r2 scaling of the electric field strength with distance.40 In the MS-EVB model for proton transfer to hydroxide, the fluctuating electric field is a better predictor of proton transfer events than four- to three-coordinate switching. Naturally, these processes are closely related because the first solvation shell of the hydroxide ion and the proton donor necessarily make the largest contributions to the electric field. Although the data in Figure 5A display some hydrogen bond oscillations, a biexponential fit to ED gives decay time scales of 15 and 600 fs, respectively. This can be compared to the 520 fs time scale for the fluctuations of the hydrogen bonding network of our simulation model as quantified through the hydrogen bond time correlation function k(t) = ⟨h(t) h(0)⟩, where h(t) is equal to 1 if at time t the examined O−H bond participates in a hydrogen bond and is 0 otherwise (Figure 6A).18,42 This decay rate is similar to the ∼500 fs time scale for the fluctuations of water’s hydrogen bonding network found in this simulation model, suggesting that water dynamics form the heart of the field fluctuations that drive the motion of the proton. Solvation energy, as defined by the difference in energy between the reactant and product wells, is another parameter sensitive to the collective fluctuations in the system and is expected to act as the primary reaction coordinate in a Marcus picture of aqueous proton transfer. As an approximation of the solvation energy, at each simulation time step we alter the OD− H* bond length to 1.0 and 1.5 Å, leaving the remaining atoms of the simulation fixed. These two distances roughly correspond to the potential minima associated with a symmetrically shared Zundel species in our MS-EVB simulation model and the difference in energy associated with these two positions provides an estimate of the solvation energy.31 Figure 6B shows relaxation of the solvation energy starting from the point of proton transport and averaged over all the successful proton transport events, which is a biexponential decay with time scales

of 510 fs and 6.35 ps, respectively. The faster time scale is comparable to the longer decay time scale of ED and k(t), indicating that the same collective motions of the liquid that give rise to hydrogen bond and electric field fluctuations contribute to the preparation of Zundel-like configurations. We now turn our attention to the picosecond solvation dynamics of the newly formed products of the proton transfer reaction. Specifically, we focus on examining the behavior of HA following proton transfer. Prior to proton transfer, the solvation shell surrounding HA adopts an expanded structure characteristic of a weakly interacting proton of the OH− ion, but following proton transfer to the ion, the solvent surrounding HA should adopt a structure closer to bulk water. This transformation reflects the collective solvent dynamics that participate in the proton transfer event. Experimentally, this transformation has been viewed by observing time-dependent shifts in the frequency of the OA−HA stretching transition using 2DIR spectroscopy, which gives a lower bound of >3 ps for the solvation of HA following proton transfer.32 To calculate dynamical quantities for studying long time scale dynamics, we consider only those trajectories where the OH− ion preserves its identity for at least 500 fs prior to a successful proton transfer. This criterion was chosen on the basis of the time-dependent changes in the coordination number of the hydroxide ion following proton transfer (Figure 3A) to ensure that we examine proton transfer reactions that initiate from species that have enough time to fully form a hypercoordinated solvation shell. However, relaxing this constraint makes little difference in the conclusions we draw below (Supporting Information Figure S2). Focusing on HA of the new water 8066



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scale of hA(τ) and RHA···O(τ). This implies that even though the solvation energy of the newly formed product displays a sub-ps decay that we can relate to fluctuations of the hydrogen bonding environment near the central H3O2− species, it takes roughly an order of magnitude longer for this water to adopt bulk-like properties. The long time scale decay of these quantities is slower compared to the average hopping time scale of ∼2.5 ps. This likely reflects that diffusion of the hydroxide ion away from the new water molecule is needed before the product water molecule can behave like a molecule in the bulk. This also suggests that the ion affects waters as far away as the second solvation shell. By affecting these neighbors, this may allow for correlated proton hops involving multiple waters, but that is beyond the scope of this paper. Combining these observations and applying the principle of microscopic reversibility allows one to propose a proton transfer mechanism in aqueous hydroxide that is consistent with earlier work, but in which the emphasis is shifted away from coordination number and toward collective electric fields. The progress of the proton transfer reaction is well described by fields that originate in the collective ordering of water molecules on short (Å) and long (nm) distance scales. These solvating water molecules rapidly evolve their loosely correlated structure through thermal fluctuations. However, long-range persistent configurations of these thermally sampled configurations that give rise to favorable fields for proton transfer are already in place picoseconds before ultrafast shifts in shortrange hydrogen bonding structure finally drive the proton to jump from donor to acceptor. In this picture, the proton is more of an innocent bystander, responding to fluctuations of the dynamic structure of water, rather than an active participant.

Figure 7. Average behavior of structural parameters associated with HA following proton transfer that highlights how quickly the solvation shell surrounding the newly formed water molecule moves to adopt a water-like structure. (A)hA(τ); (B)RHA···O(τ).

molecule, Figure 7A plots the decay of the hydrogen bonding parameter following a proton transfer event, hA(τ). At τ = 0, hA has a value of 0.11, which reflects the hydroxide ion’s predisposition against the formation of a hydrogen bond to its proton. Following the conversion of the OH− ion to a H2O molecule, hA(τ) displays an initial fast increase (263 fs) followed by a slow rise (9.6 ps) toward the expected asymptotic limit of 0.9, indicating the slow formation of a hydrogen bond. Given that equilibrium correlations for h(t) in this model relax roughly an order of magnitude faster, it is not clear why this latter nonequilibrium process is so slow. In investigations into the validity of linear response theory for solvation dynamics, it was observed that nonequilibrium disturbances relax slower than equilibrium correlations for the case of an increase in product charge and decrease in product size.41 This bears some similarity to the present case in which the hydroxide anion is transformed to a neutral water molecule in a locally lower density environment than bulk water. For more insight, we investigated order parameters for the solvation of the newly formed products of the proton transfer reaction. To characterize the solvation of the newly formed H2O molecule, Figure 7B plots the average distance between HA and its nearest neighboring oxygen atom, RHA···O = |rHA − rOA2|. The nonequilibrium relaxation of RHA···O(τ) displays biexponential relaxation that mirrors the rise of hA(τ). The initial decay of RHA···O(τ) suggests that water molecules initially repulsed by the negative charge of the ion begin the solvation process by rapidly filling in the previously empty space about the molecule, but it takes tens of picoseconds for the newly formed water molecule to be incorporated into a bulk-like environment. It is noteworthy that the slower decay time scale of the solvation energy is comparable to the slower decay time

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CONCLUSIONS Our simulations of an MS-EVB model for aqueous hydroxide indicate that a description of the structural diffusion of the hydroxide ion is best served by both accounting for the dynamics of the local hydrogen bonding environment that govern the solvation of the reactants and products, as well as a collective electric field coordinate that represents fluctuations that guide the motion of protons through fleeting Zundel-like configurations. This picture is strikingly similar to that given previously for water autoionization.6 Although collective coordinates are less concrete in their atomistic detail, electric fields have long been recognized as the dominant forces in aqueous solvation dynamics and hydrogen-bond mediated proton transfer. Their critical role in determining O−H stretch vibrational frequencies also indicates that time-resolved infrared spectroscopy should prove to be a direct view into proton transfer in water.

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ASSOCIATED CONTENT

S Supporting Information *

Free energy surface and hA(τ) calculated with two different constraints. This information is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Present Address §

Department of Chemistry, University of Texas at Austin, Austin, TX 78712. 8067



Article

Notes

(21) Asthagiri, D.; Pratt, L. R.; Kress, J. D.; Gomez, M. A. Hydration and Mobility of OH−(Aq). Proc. Natl. Acad. Sci. U. S. A. 2004, 101, 7229−7233. (22) Ohmine, I.; Saito, S. Water Dynamics: Fluctuation, Relaxation, and Chemical Reactions in Hydrogen Bond Network Rearrangement. Acc. Chem. Res. 1999, 32, 741−749. (23) Roberts, S. T.; Ramasesha, K.; Tokmakoff, A. Structural Rearrangements in Water Viewed through Two-Dimensional Infrared Spectroscopy. Acc. Chem. Res. 2009, 42, 1239−1249. (24) Ufimtsev, I. S.; Kalinichev, A. G.; Martinez, T. J.; Kirkpatrick, R. J. A Multistate Empirical Valence Bond Model for Solvation and Transport Simulations of OH− in Aqueous Solutions. Phys. Chem. Chem. Phys. 2009, 11, 9420−9430. (25) Schmitt, U. W.; Voth, G. A. The Computer Simulation of Proton Transport in Water. J. Chem. Phys. 1999, 111 (111), 9361− 9381. (26) Day, T. J. F.; Soudackov, A. V.; Cuma, M.; Schmitt, U. W.; Voth, G. A. A Second Generation Multistate Empirical Valence Bond Model for Proton Transport in Aqueous Systems. J. Chem. Phys. 2002, 117 (12), 5839−5849. (27) Wu, Y.; Chen, H.; Wang, F.; Paesani, F.; Voth, G. A. An Improved Multistate Empirical Valence Bond Model for Aqueous Proton Solvation and Transport. J. Phys. Chem. B. 2008, 112, 467−482. (28) Voth, G. A. Computer Simulation of Proton Solvation and Transport in Aqueous and Biomolecular Systems. Acc. Chem. Res. 2006, 39, 143−150. (29) Vuilleumier, R.; Borgis, D. Quantum Dynamics of an Excess Proton in Water Using an Extended Empirical Valence-Bond Hamiltonian. J. Phys. Chem. B 1998, 102, 4261−4264. (30) Wick, C. D.; Dang, L. X. Investigating Hydroxide Anion Interfacial Activity by Classical and Multistate Empirical Valence Bond Molecular Dyanmics Simulations. J. Phys. Chem. A 2009, 113, 6356− 6364. (31) Roberts, S. T.; Petersen, P. B.; Ramasesha, K.; Tokmakoff, A.; Ufimtsev, I. S.; Martinez, T. J. Observation of a Zundel-Like Transition State During Proton Transfer in Aqueous Hydroxide Solutions. Proc. Natl. Acad. Sci. U. S. A. 2009, 106 (36), 15154−15159. (32) Roberts, S. T.; Ramasesha, K.; Petersen, P. B.; Mandal, A.; Tokmakoff, A. Proton Transfer in Concentrated Aqueous Hydroxides Visualized Using Ultrafast Infrared Spectroscopy. J. Phys. Chem. A 2011, 115, 3957−3972. (33) Eaves, J. D.; Tokmakoff, A.; Geissler, P. Electric Field Fluctuations Drive Vibrational Dephasing in Water. J. Phys. Chem. A 2005, 109, 9424−9436. (34) Corcelli, S. A.; Lawrence, C. P.; Skinner, J. L. Combined Electronic Structure/Molecular Dynamics Approach for Ultrafast Infrared Spectroscopy of Dilute HOD in Liquid H2O and D2O. J. Chem. Phys. 2004, 120, 8107−8117. (35) Rey, R.; Moller, K. B.; Hynes, J. T. Ultrafast Vibrational Population Dynamics of Water and Related Systems: A Theoretical Perspective. Chem. Rev. 2004, 104, 1915−1928. (36) Smith, J. D.; Cappa, C. D.; Wilson, K. R.; Cohen, R. C.; Geissler, P. L.; Saykally, R. J. Unified Description of Temperature-Dependent Hydrogen-Bond Rearrangements in Liquid Water. Proc. Natl. Acad. Sci. U. S. A. 2005, 102, 14171−14174. (37) Mitev, P. D.; Bopp, P. A.; Petreska, J.; Coutinho, K.; Argen, H.; Pejov, L.; Hermansson, K. Different Structures Give Similar Vibrational Spectra: The Case of OH− in Aqueous Solution. J. Chem. Phys. 2013, 138, 064503. (38) Ufimtsev, I. S.; Kalinichev, A. G.; Martinez, T. J.; Kirkpatrick, R. J. A Charged Ring Model for Classical OH−(Aq) Simulations. Chem. Phys. Lett. 2007, 442, 128−133. (39) Price, E. A.; Robertson, W. H.; Diken, E. G.; Weddle, G. H.; Johnson, M. A. Argon Predissociation Infrared Spectroscopy of the Hydroxide-Water Complex (OH−.H2O). Chem. Phys. Lett. 2002, 366, 412−416. (40) Paesani, F.; Xantheas, S. S.; Voth, G. A. Infrared Spectroscopy and Hydrogen-Bond Dynamics of Liquid Water from Centroid

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge Ivan S. Ufimtsev and Todd J. Martinez for providing us with the MS-EVB simulation trajectories and for insightful discussions. This work was funded by the U.S. Department of Energy (DE-FG0299ER14988).

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