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Proton-Transfer-Driven Water Exchange Mechanism in the Na Solvation Shell Matti Hellström, and Jörg Behler J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b01490 • Publication Date (Web): 04 Apr 2017 Downloaded from http://pubs.acs.org on April 5, 2017

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The Journal of Physical Chemistry

Proton-Transfer-Driven Water Exchange Mechanism in the Na+ Solvation Shell Matti Hellström† and Jörg Behler∗,†,‡ Lehrstuhl f¨ ur Theoretische Chemie, Ruhr-Universit¨ at Bochum, 44780 Bochum, Germany, and Institut f¨ ur Physikalische Chemie, Georg-August-Universit¨ at Göttingen, Tammannstraße 6, 37077 G¨ ottingen, Germany E-mail: [email protected]

∗

To whom correspondence should be addressed Lehrstuhl f¨ ur Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany ‡ Institut f¨ ur Physikalische Chemie, Georg-August-Universität G¨ ottingen, Tammannstraße 6, 37077 G¨ ottingen, Germany †

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Abstract Ligand exchange plays an important role for organic and inorganic chemical reactions. We demonstrate the existence of a novel water exchange mechanism, the “proton transfer pathway” (PTP), around Na+ (aq) in basic (high pH) solution, using reactive molecular dynamics simulations employing a high-dimensional neural network potential. An aqua ligand in the first solvation (hydration) shell around a sodium ion is only very weakly acidic, but if a hydroxide ion is present in the second solvation shell, thermal fluctuations can cause the aqua ligand to transfer a proton to the neighboring OH– , resulting in a transient direct-contact ion pair, Na+ −OH– , which is only weakly bound and easily dissociates. The extent to which water exchange events follow the PTP is pH-dependent: in dilute NaOH(aq) solutions, only very few exchanges do, whereas in saturated NaOH(aq) solutions up to a third of water self-exchange events are induced by proton transfer. The principles and results outlined here are expected to be relevant for chemical synthesis involving bases and alkali metal cations.

Introduction The solvation structure and solvation dynamics around ions in water and in other solvents play important roles in biochemistry, 1–3 electrochemistry, 4 and geochemistry, 5–7 especially during chemical reactions where the solvation shell may experience strong distortions or even break and reform. One of the simplest dynamical events in the solvation shell is water selfexchange around a metal cation in aqueous solution. 8,9 Depending on the chemical element and oxidation state of the cation, the rate of water exchange can span tens of orders of magnitude. Water exchange around alkali metal cations like Na+ , which is the focus of the present work, is quite fast; in fact, it is so fast that the standard nuclear magnetic resonance experimental techniques used to measure exchange rates give quite unreliable results. 8 However, estimating the exchange rate is possible using molecular dynamics (MD) simulations, which have given estimates of the mean residence time for an aqua ligand around Na+ to be between 10-40 ps. 10–14 Exchange mechanisms are frequently classified as associative, dissociative, or interchange, depending on whether the incoming ligand enters the solvation shell before, after, or at the same time as, the leaving ligand leaves the solvation shell. 15 MD simulations have suggested that the exchange around Na+ (aq) is mostly associative, 12,16,17 but there are also other ways to classify ligand exchange mechanisms. For example, the pentaamminechloridocobalt(III) coordination complex, [CoCl(NH3 )5 ]2+ , can exchange its chlorido ligand for a hydroxido ligand via the “Sn1CB” mechanism, where the Cl– leaves as a result of an outside hydroxide ion deprotonating one of the ammine ligands. 18 After a few more reaction steps, the end result is a [Co(NH3 )5 OH]2+ complex, where OH– has substituted the Cl– . In such a mechanism, the deprotonation of one ligand promotes the exchange of another ligand. A similar phenomenon can be seen for many aqua complexes; for example, the rate of exchange of aqua ligands in [Al(OH)(OH2 )5 ]2+ is greater by a factor of 104 as compared to [Al(OH2 )6 ]3+ , 19 which makes the deprotonation of one of the aqua ligands the rate-limiting step for water exchange in [Al(OH2 )6 ]3+ complexes. 20 OH– ligands can thus have a labilizing effect on the OH2 ligands around the same cation. 2


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In the present work, we will show that the deprotonation of an OH2 ligand around Na (aq), resulting in an OH– ligand, influences the water exchange rate, but in a very different way as compared to the previous AlIII example. We show that around Na+ , the OH– ligand itself is more labile than the OH2 ligands. In dilute sodium hydroxide solutions, direct-contact Na+ −OH– ion pairs are very rare, 21–24 although at very high concentrations, for example near the room-temperature solubility limit of 19 mol L−1 , MD simulations have indicated that Na+ on average coordinates to between 1 and 2 OH– ions in the first solvation shell (FSS). 23,25 At low concentrations, Na+ does not manage to “trap” the OH– in the FSS. However, MD simulations have suggested that OH– ions in dilute NaOH(aq) solutions are frequently found in the second solvation shell (SSS) around the Na+ . 26–28 Hydroxide ions can participate in proton-transfer (PT) events with neighboring water molecules, i.e., HOα H · · · Oβ H− −−→ HOα− · · · HOβ H, (1) +

where the superscripts α and β are used to distinguish between different O atoms. This feature of OH– ions is responsible for their high diffusion coefficients in water. 29 At low concentration, such PT events have been shown to be coupled to specific hydrogen-bonding motifs around the OH– ion; 30 OH– normally accepts four hydrogen bonds from surrounding water molecules, but thermal fluctuations occasionally cause one of the hydrogen bonds to break, so that only three hydrogen bonds remain. This less common hydrogen-bonding environment is associated with a higher rate of PT. Recently, we showed that at higher concentrations, hydrogen-bond fluctuations also around the H2 O molecules significantly influence the PT rate. 28 If the OH– is in the SSS around Na+ , it might happen that the proton-donating original H2 O molecule is an aqua ligand around Na+ . Such a PT reaction would result in a directcontact Na+ −OH– ion pair: + β α − −− Na+ −Oα HH · · · Oβ H− ↽ −⇀ − Na −O H · · · HO H.

(2)

Such direct-contact ion pairs rarely form at low concentrations of NaOH(aq), because the PT barrier is greater for OH2 molecules that are coordinated to Na+ than for those that are “free” in the solution. 28 However, as we mentioned above, at very high concentrations, it is not uncommon to find OH– coordinated to Na+ . The direct-contact ion pair can decompose in one of two ways: (i) proton-transfer, where the hydroxido ligand becomes an aqua ligand by accepting a proton from a neighboring water molecule, i.e., the backward equation 2, or (ii) diffusion, where the OH– leaves the FSS without participating in PT, giving room for some OH2 to take its place in the FSS. We will show that Na+ −OH– bonds are shorter-lived than Na+ −OH2 bonds, i.e., that OH– more readily leaves the FSS than OH2 does (OH– is more labile than OH2 ). This turns out to be the key ingredient for a novel water self exchange mechanism, the “proton transfer pathway”, that we present in this Article for Na+ in basic aqueous solution. With increasing concentration of NaOH(aq), diffusion of hydroxide away from the Na+ turns out to play an increasingly important role for water exchange. That is, a significant fraction of water exchange events take place by the formation of a transient/intermediate direct-

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+

Na −OH2 (FSS) aqua direct kleave

aqua kdeprot , −H+ hydrox kprot , + H+

hydrox proton transfer pathway kleave

Na+ · · ·OH– (SSS)

Na+ · · ·OH2 (SSS) a The

Na+ −OH– (FSS)

“direct” and “proton transfer pathway” labels refer only to original OH2 ligands (bold) entering the SSS. For original OH– ligands, the two labels would change places.

Scheme 1: Possible reaction pathways for an aqua ligand in the first solvation shell [FSS; simple dash (−)] around Na+ to enter the second solvation shell [SSS; three dots (· · ·)], together with the corresponding effective rate constants.a depend on the NaOH concentration. The formed Na+ −OH– can then reform Na+ −OH2 hydrox hydrox , or dissociate with a rate constant kleave . In the latter case, the with a rate constant kprot original OH2 ligand has left the FSS via the proton transfer pathway. hydrox hydrox aqua aqua , for different , kprot , and kleave , kdeprot The challenge is to find the rate constants kleave concentrations of NaOH(aq). To this end, we employ a high-dimensional neural network potential 31–34 that we specifically developed to run molecular dynamics (MD) simulations of NaOH(aq) solutions with dispersion-corrected density functional theory quality over the entire NaOH room-temperature solubility range. 25,28 The potential is computationally inexpensive, and allows for proton-transfer events between H2 O and OH– . We have previously validated it 25,28 against x-ray and neutron diffraction data for NaOH solutions, 21–23 as well as results from other molecular dynamics simulations, 23,26,27,35,36 and used it to show, for example, that there is great variation in the structure and coordination numbers for Na+ ions in NaOH solutions of different concentrations. 25 In MD studies on ligand exchange reactions around metal cations, it is often necessary to impose some kind of constraint on the exchanging ligands, for example their distances to the central ion, so as to sample the entire free-energy landscape. 37 However, because both ligand-exchange events around Na+ and PT events involving OH– are quite frequent in NaOH(aq) solutions, we can run completely unbiased molecular dynamics simulations and let the system dynamics evolve naturally. From N V T simulations at 300 K (with about 1100–1500 atoms depending on the concentration) we extracted 20 different starting points per concentration separated by at least 100 ps, and continued from those starting points (positions and velocities) for 1 ns in the N V E ensemble, thus sampling the average dynamics for solutions at constant volume and temperature (300 K). The volumes (densities) had been pre-equilibrated in the N P T ensemble (at 1 bar, 300 K); see also our previous works. 25,28 We use mole fractions xNaOH to identify the concentrations of solutions, i.e., xNaOH =

NNaOH , NNaOH + NH2 O

(3)

where NNaOH and NH2 O are the numbers of NaOH and H2 O formula units in the periodically repeated simulation box. The room-temperature solubility of NaOH in water is about xNaOH = 0.33, i.e., there are two formula units H2 O for every formula unit NaOH. Here, we characterize the reactions in Scheme 1 for xNaOH = 0.016, 0.049, 0.085, 0.143, 0.185, 0.255, 5




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the FSS, intermediate, and SSS regions marked with different colors. We consider OH2 and OH– to be in the FSS if the distance Na−O < 2.7 ˚ A, and in the SSS if the distance is between ˚ ˚ 3.6 A and 5.0 A (the upper bound for the SSS has no impact on the results presented in this paper). The two smaller distance criterions were chosen because they encompass the first minimum in the Na−O radial distribution function with a margin of at least 0.2 ˚ A for all the studied concentrations of NaOH(aq). As shown in the snapshot in Figure 2, at xNaOH = 0.016, a typical Na+ is surrounded by 5 OH2 in the FSS, 1 OH2 in the TS region, and 13 H2 O + 1 OH– in the SSS. Similarly, for PT reactions, we also calculate SSP time correlation functions, where “stable” water molecules have two H within 1.1 ˚ A of the central O, and “stable” hydroxide ions ˚ have only one H within 1.4 A of the O. We calculate four different “basic” time correlation functions for each xNaOH : the ligandexchange and proton-transfer functions when the ligand is a stable OH2 in the FSS at t0 , and the same functions when the ligand is a stable OH– in the FSS at t0 . We only apply the conditions at the time origin; thus for the ligand-exchange function, the ligand can participate in an arbitrary number of PT events before entering the SSS, and for the protontransfer function, the ligand may leave and reenter the FSS an arbitrary number of times before participating in PT. This introduces some errors in the calculated reaction rates, that we attempt to correct for (see below). We limit the discussion to molecules that at t0 are in the FSS of only a single Na+ ion. In highly concentrated solutions, some fraction of OH2 molecules and OH– ions bridge two or more Na+ ions, 25 but we do not consider the kinetics of such bridging ligands here, as there may be other, more complicated, mechanisms for these structures.

Results and Discussion Figure 3 shows the calculated SSP time correlation functions for the PT reactions and ligandexchange reactions at xNaOH = 0.085. In Figure 3a, the ligand is a “stable” OH2 at t0 . At this concentration, clearly, the time it takes to deprotonate OH2 is much longer than the time it takes to leave the Na+ . Therefore, many of the OH2 will have already left the Na+ before the PT event takes place. To calculate the rate of deprotonation while the ligand aqua ), we therefore consider a third time correlation function, that is still bound to Na+ (kdeprot decays for OH2 in the FSS that either deprotonates or enters the SSS (thick blue line). This allows us to extract a better estimate of the time scale of the slower of the two possible −1 −1 −1 . In Figure 3a, the “raw” lifetime calculated for the − Rτfast ≈ τeither reactions, kslow = τslow ∞ slower reaction (i.e., PT) is τraw = 0 C(t) dt, while the “modified” (better) one is calculated aqua −1 −1 −1 −1 . ) . The effective rate constant kdeprot = τmod − τfast as τmod = (τeither Using this approach, the time scale associated with PT from H2 O to OH– in the FSS increases from the “raw” estimate of 40 ps to 54 ps. The modified τ is greater, because the barrier for PT is greater when the H2 O is in the FSS of Na+ than when it is free in the solution, 28 and the raw estimate included some H2 O that had left the SSS and then participated in the PT with a lower “free-in-solution”-PT-barrier. For OH– (Figure 3b), both the PT reaction and the ligand exchange event are faster than the corresponding reactions for H2 O (Figure 3a). However, the relative timescales involved 7




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Table 1: Calculated effective rate constants k (in ps−1 ) at 300 K and at different mole fractions xNaOH of NaOH(aq) for aqua and hydroxido ligands in the first FSS solvation shell (FSS) around a single Na+ ion, together with the fraction ξOH − of – a OH ligands in the FSS. FSS xNaOH ξOH − 0.016 0.0018(1) 0.049 0.0066(2) 0.085 0.0155(5) 0.143 0.046(1) 0.185 0.086(1) 0.255 0.197(2) 0.333 0.368(4) a The uncertainties are calculated over

aqua aqua kleave kdeprot 0.100(3) 0.006(1) 0.092(4) 0.013(2) 0.081(3) 0.019(2) 0.066(3) 0.024(1) 0.051(3) 0.026(1) 0.034(2) 0.031(1) 0.019(2) 0.032(2) 20 independent N V E

hydrox hydrox kprot kleave 1.34(10) 0.29(6) 0.94(4) 0.24(2) 0.64(2) 0.22(1) 0.35(2) 0.157(6) 0.22(1) 0.111(7) 0.123(7) 0.066(4) 0.070(6) 0.034(3) trajectories as 2.09×(standard error).

OH– in the solution that can accept the proton. Here, we reiterate that the rate constant aqua kdeprot includes the effect of OH– concentration, and thus describes the overall rate, per OH2 ligand in the FSS, of the reaction. Scheme 1 gives rise to a set of coupled kinetic equations that can be solved analytically for different initial conditions (see the Supporting Information for the full derivation of these solutions). For example, by setting the initial population of Na+ −OH2 to 1, and the population of the other species to 0, the populations of Na+ ···OH2 and Na+ ···OH– as t → ∞ then correspond to the fractions of original OH2 in the FSS that have left via the direct and proton-transfer pathways, respectively. Figure 4a shows the fate of an initial OH2 in the FSS as a function of time at xNaOH aqua = 0.081 ps−1 ≫ = 0.085, based on the calculated rate constants in Table 1. Because kleave aqua = 0.019 ps−1 , most aqua ligands will simply enter the SSS (pink dashed line) withkdeprot out participating in PT. Even for the few that do participate in PT events, most of the formed hydroxido ligands will quickly participate in another PT event and reform the origihydrox hydrox = 0.22 ps−1 , At this nal aqua ligand rather than leaving, since kprot = 0.64 ps−1 ≫ kleave concentration, only five percent (orange dashed line) of original aqua ligands leave as OH– . We also consider the fate of hydroxido ligands, and we denote the fraction of such ligands FSS FSS FSS FSS FSS FSS FSS refer to in the FSS as ξOH = NOH − , i.e., ξOH− − /[NOH− + NOH ]. Here, NOH− and NOH 2 2 – the number of “stable” OH and OH2 (as defined for the SSP time correlation functions) FSS in the FSS. ξOH − is very small at low concentrations (Table 1), which makes exchange FSS events via the proton transfer pathway unlikely, but ξOH − increases rapidly with increasing concentration and the proton transfer pathway may therefore play a more important role FSS at higher concentrations. At xNaOH = 0.085, ξOH − = 0.016, which means that only 1.6% of ligands that can be described as either stable OH– or stable OH2 are OH– , and that the rest, 98.4%, are OH2 . As shown in Figure 4b, the OH– ligand will likely participate in a PT event, which can be seen as a signficant peak in the Na+ −OH2 population at about t = 4 ps (purple line), and the OH2 can then either leave as OH2 or as OH– as discussed above. Because PT is so fast for OH– in the FSS, only 29% of ligands that are OH– leave as hydrox OH– , despite the fact that breaking the Na+ −OH– bond is much easier (kleave = 0.22 ps−1 ) aqua than breaking the Na+ −OH2 bond (kleave = 0.081 ps−1 ) that results from PT. Figure 4c 9




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participate in PT (the population of Na+ −OH– approaches 0.2 at about t = 15 ps in Figure 4d), and, consequently, that more of the initial OH2 ligands leave as OH– . In fact, 35%, or about one third, of OH2 ligands follow the proton transfer pathway and leave as OH– . For ligands that are initially OH– , most (56%) will also leave as OH– , unlike the case at xNaOH = 0.085 where 71% of OH– ligands left as OH2 because of the fast PT reaction. The weighted averages in Figure 4f reveal that in a saturated solution, about 57% of ligands leave as OH2 , and the rest as OH– . Figure 4d–e also show the total population of ligands leaving (dashed black line, which is the sum of the Na+ · · · OH2 and Na+ · · · OH– populations), together with the population of ligands that would have left had only the “direct”, and no PT, pathway been available hydrox aqua ·t) ·t) for original OH2 in Figure 4d, and 1−exp(−kleave (dashed green line; i.e., 1−exp(−kleave for original OH– in Figure 4e). As a result of the PT pathway, the total rate of water exchange increases (because the black dashed line is above the green dashed line in Figure 4d), whereas the total rate of hydroxido exchange decreases, where the rate of “exchange” refers only to breaking the Na+ −O bond through diffusion, i.e., the rate at which an O atom in the FSS enters the SSS. In Figure 5, we divide all exchange events into four categories: H2 O leaving as H2 O (pink solid bar), OH– leaving as H2 O (pink striped bar), H2 O leaving as OH– (orange striped bar), and OH– leaving as OH– (orange solid bar). Of course, there can be an arbitrary number of PT events before a ligand exchange. Therefore, for a ligand leaving as, for example, H2 O, we use the relative time periods that the ligand spent as OH– and as H2 O to weight the contribution to either of the “OH– leaving as H2 O” and “H2 O leaving as H2 O” categories. Interestingly, for all xNaOH , the number of ligands leaving as H2 O (sum of pink solid and FSS striped bars) is smaller than the average fraction of H2 O ligands (1 − ξOH − , black line and points). This means that the PT mechanism gives a net increase in the rate of H2 O ligands leaving (as already shown for xNaOH = 0.333 in Figure 4d); in contrast, it gives the corresponding net decrease for OH– ligands leaving. FSS At all concentrations, most ligands are OH2 (ξOH − < 0.5, Table 1). At low concentration, most of the OH2 ligands also leave as OH2 (solid pink in Figure 5), because the probability aqua is small, Table 1). However, with increasing concentration, more for PT is very low (kdeprot and more of the OH2 ligands leave as OH– (brown striped bar); indeed, at the highest xNaOH = 0.333, the number of OH2 that leave as OH– is about half of those that leave as OH2 , i.e., about one third of water exchange events take place via the proton-transfer pathway. The OH– ligands, on the other hand, are, independently of the concentration, roughly equally likely to leave as OH– (orange solid bar) as they are to leave as OH2 (pink dashed bar). In some ways, one can consider the OH– ions to “catalyze” water self-exchange, since they provide an alternative reaction mechanism, the proton-transfer pathway, which increases the total rate of water exchange. However, even in the saturated solution, the majority of OH2 ligands still follow the “direct” pathway, possibly because there are not enough OH– ions in the solution (as compared to the number of OH2 ligands).

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The two kinds of pathways (proton-transfer and direct) in the present article differ from the more common distinction between associative, dissociative, and interchange mechanisms. To what relative extent the direct and proton-transfer pathways proceed via associative, dissociative, and interchange mechanisms, remains an open question, as does whether there are substantial differences for ligands that bridge multiple Na+ ions as compared to those that only coordinate to a single Na+ ion. The present work illustrates how the presence of hydroxide ions, i.e., a high pH value, influences the rate of water exchange around one of the most common ions in water, Na+ (aq).

Acknowledgement This work was supported by the Cluster of Excellence RESOLV (EXC 1069) funded by the Deutsche Forschungsgemeinschaft, the DFG Heisenberg fellowship Be3264/6-1, and the DFG Heisenberg professorship Be3264/11-1.

Supporting Information Available Derivation of the solutions to the kinetic equations arising from Scheme 1, tabulated data for Figure 5, and snapshots (cartesian coordinates) for all xNaOH . This material is available free of charge via the Internet at http://pubs.acs.org/.

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