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Spectroscopic snapshots of the proton-transfer mechanism in water

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Science  02 Dec 2016:
Vol. 354, Issue 6316, pp. 1131-1135
DOI: 10.1126/science.aaf8425

Frame-by-frame view of acidic transport

Protons in acidic solution constantly hop from one water molecule to the next. In between the hopping, controversy lingers over the extent to which the proton either sticks largely to one water molecule in an Eigen motif or bridges two of them in a Zundel motif. It has been hard to probe this question directly because the distinguishing vibrational bands in bulk aqueous acid spectra are so broad. Wolke et al. studied deuterated prototypical Eigen clusters, D+(D2O)4, bound to an increasingly basic series of hydrogen bond acceptors (see the Perspective by Xantheas). These clusters displayed sharp bands in their vibrational spectra, highlighting a steadily evolving distortion toward a Zundel-like motif and pointing the way toward further investigations.

Science, this issue p. 1131; see also p. 1101

Abstract

The Grotthuss mechanism explains the anomalously high proton mobility in water as a sequence of proton transfers along a hydrogen-bonded (H-bonded) network. However, the vibrational spectroscopic signatures of this process are masked by the diffuse nature of the key bands in bulk water. Here we report how the much simpler vibrational spectra of cold, composition-selected heavy water clusters, D+(D2O)n, can be exploited to capture clear markers that encode the collective reaction coordinate along the proton-transfer event. By complexing the solvated hydronium “Eigen” cluster [D3O+(D2O)3] with increasingly strong H-bond acceptor molecules (D2, N2, CO, and D2O), we are able to track the frequency of every O-D stretch vibration in the complex as the transferring hydron is incrementally pulled from the central hydronium to a neighboring water molecule.

The translocation of positive charge through water is widely understood to occur through intermolecular transfer of a proton between oxygen atoms linked by a strong ionic hydrogen bond (1, 2). This transport requires thermal fluctuations in the water H-bond network and occurs in a cooperative fashion such that H-bonds distant from the center of charge control the barrier for proton transfer (35). Many models of this process have been advanced, ranging from molecular-level pictures emphasizing the key role of the second solvation shell (3) to more holistic treatments where the entire medium is treated as a supermolecule in an electronic structure calculation (4, 610). At the heart of this discussion is the relative importance of the two limiting forms of proton accommodation in water: the charge-delocalized, tricoordinated hydronium ion [H3O+(∙∙∙OH2)3 (or Eigen form)] (11) and the more charge-localized configuration where the proton is located at the midpoint of two closely separated oxygen atoms [H2O∙∙∙H+∙∙∙OH2 (or Zundel form)] (12). The extremely diffuse vibrational signature of the aqueous proton (1113) is a clear manifestation of the wide-ranging intramolecular distortions intrinsic to its molecular speciation, but this breadth also precludes unambiguous structural characterization of the proton defect by analysis of these bands.

Recently, Thämer et al. (5) reported ultrafast two-dimensional (2D) vibrational spectra of an aqueous 4 M HCl solution, which they interpreted to indicate a surprisingly large population of Zundel-type configurations. The ultrafast transients associated with the H5O2+ Zundel motif were subsequently explored by Dahms et al. (14) in a scheme where this species was isolated in a room temperature solution of HClO4 in acetonitrile. An important aspect of that study was the analysis of the ultrafast spectral diffusion displayed by the excess proton absorptions. In particular, Dahms et al. emphasized how the local electric field fluctuations in the liquid drive large structural changes in the embedded H5O2+ moiety due to the contribution of the bridging proton to its polarizability. This, in turn, leads to the diffuse character of the vibrational spectra of weak acids, an idea first introduced by Zundel in 1972 (13).

The interpretation of the ultrafast infrared (IR) spectroscopy results rests on understanding how the local distortions in the charge accommodation motif are manifested in the vibrational frequencies associated with the displacement of the transferring proton parallel to the O-O axis, as well as the bending modes of the donor and acceptor water molecules. Analyses of the spectra displayed by H+(H2O)n clusters at low temperature and over a wide spectral range have played an important role in providing this information (1519). A long-standing goal for the cluster work is to capture specific configurations along the pathway for proton transfer as locally stable structures and then identify the spectral signatures of all key protons involved in the transfer event. Arrangements that are transient in the bulk are often metastable or even global minima in clusters (17, 20, 21). Our strategy exploits the fact that H-bond acceptors attach preferentially to the OH groups of one of the three solvent water molecules that bind to the H3O+ core ion in the Eigen form of the n = 4 cluster, denoted E4. The scheme in Fig. 1 illustrates how, by complexing molecules with increasingly larger proton affinities (represented as “A”; A = H2, N2, CO, and H2O) to the E4 scaffold, we can follow the concerted distortions of the hydronium core and of the solvent water molecules as one of the hydronium protons is incrementally pulled closer to the solvated water molecule. From this perspective, the critical configuration for proton transfer corresponds to a cluster in which the proton is trapped at the midpoint between the donor and acceptor oxygen atoms. These measurements are carried out on cold (~20 K), size-selected protonated water clusters using cryogenic ion trap photofragmentation mass spectrometry. The multiple photon action spectrum of the bare D+ (D2O)4 cluster was obtained using the instrument at Yale, along with the linear action spectra of the solvated clusters, D+ (D2O)4-A (with A = D2 and N2). Spectra of the A = CO and D2O clusters were obtained on a similar instrument in Leipzig. Schematic diagrams of these instruments are included in fig. S1.

Fig. 1 Schematic of the proton-relay mechanism.

The symmetric H9O4+ Eigen ion is distorted upon the addition of proton acceptors A and A′ (A = H2, N2, CO, H2O; A′ = H2O) to one of the water molecules. Formation of these complexes induces the attraction of a proton in the H3O+ core toward the solvated H2O molecule and reduces the corresponding O-O distance, ROO.

Until very recently, the use of cluster vibrational spectroscopy to reveal the spectral reporters of the collective proton-transfer reaction coordinate has been hampered by the strongly anharmonic potentials that govern this process. As a result, cold-cluster vibrational spectra often display broad features that mask the small splittings expected to occur at the start of the proton-transfer path. Moreover, the observed patterns routinely display more bands than are expected for the fundamentals of a particular structural isomer. Such extra bands in the spectra of the crucial n = 4 and 5 clusters have been attributed, alternatively, to anharmonic features arising from a single isomer (19, 22, 23) or to overlapping bands from two isomers identified using a classical ab initio molecular dynamics approach (24). For n = 4, one of these isomers corresponds to the Eigen-based structure (E4), which was originally proposed (25). The other corresponds to a more open arrangement with an equally shared proton between central water molecules, as occurs in the Zundel ion, and is hereafter denoted Z4.

The difficulty in disentangling the roles of isomers and anharmonic effects can be traced to the fact that these systems are floppy and may not be reliably treated with the commonly applied theoretical and computational tools for predicting vibrational spectra. For example, calculating the simple band pattern displayed by the H5O2+ cluster required combining very accurate potential energy and dipole surfaces over a large configuration space with a full (15D) quantum mechanical treatment of the nuclear motion (26). Such demanding methods have not yet been extended to larger cluster sizes due to their extreme computational overhead. As such, this work is being carried out in a regime where experiment leads theory, and our approach here is to combine analysis of empirical trends with several theoretical approaches to provide compelling assignments for the structures in play and the OH stretching fundamentals associated with them.

Implementation of the scheme outlined in Fig. 1 requires reliable isolation of the Eigen form of the n = 4 cluster, a structure that has been invoked since the earliest reports of the H+(H2O)4 vibrational spectrum by Okumura et al. (25). The D2-tagged spectrum, H+(H2O)4-D2, is presented in Fig. 2C. (19) This assignment has recently been challenged by Kulig and Agmon (24), however, on the basis of cluster spectra calculated using classical molecular dynamics methods. The role of isomers in the n = 4 spectra was clarified by the recent determination [using an isomer-selective, IR-IR hole-burning technique] (19) that the H+(H2O)4 spectrum (Fig. 2C), reproduced in many laboratories (17, 18, 23, 25), is homogeneous. Application of vibrational perturbation theory (VPT2) (27), using the harmonic approximation for the unperturbed normal modes and frequencies to the E4 structure, provides compelling assignments for several of the key features in question (Fig. 2A), but it does not account for the doubling of the peaks a8,9 and a10,11. As a result, it is presently unclear whether the diffuse features (a10 and a11) above the intramolecular HOH bend are due to fundamentals of the H3O+ bend (22) or combination bands involving lower-frequency modes (19), and their assignments are still uncertain. Of most concern for our study, however, is the observation of the predicted splitting in OH stretching features [ionic H-bonded OHs labeled IHB1 (blue) and IHB2 (red) in Fig. 2A], calculated (at both the harmonic and VPT2 levels) to signal the initial distortion of the embedded H3O+ ion in the E4 structure by the action of the weakly bound D2 molecule. The three OH stretches in the hydronium are calculated to evolve into two distinct features that split apart as a proton is transferred; therefore, these features are denoted IHB1 and IHB2. This predicted splitting is completely obscured in the experimental H+(H2O)4-D2 spectrum, however, by broadening that is not anticipated at these levels of theory, the origin of which is not presently known.

Fig. 2 Comparison of the experimental and calculated vibrational spectra of the H+(H2O)4-D2 and D+(D2O)4-D2 clusters.

(A) Calculated anharmonic (VPT2) and (B) harmonic spectra of H+(H2O)4-D2, compared with the experimental vibrational predissociation spectrum in (C). (D) Experimental spectrum of D+(D2O)4-D2 compared with (E) its calculated anharmonic (VPT2) and (F) harmonic spectra. Calculations were performed at the MP2/aug-cc-pVDZ level, with the harmonic frequencies scaled by 0.9538 and the VPT2 frequencies left unscaled. Bands indicated by IH(D)B1 (blue) and IH(D)B2 (red) refer to symmetric and antisymmetric OH(D) stretches of the core D3O+ ion, which are slightly perturbed by complexation with D2. Band labels (a1 to a12, b1 to b12) aid referencing in the text and in table S1. a.u., arbitrary units.

A useful empirical tool in the assignment of anharmonic spectra involving hydrogen bonds is to follow the evolution of the band pattern with H/D substitution (18, 28). Fundamentals primarily involving displacements of the hydrogen atoms are expected (at the harmonic level) to appear lower in energy by a factor of ~1.36 derived from the reduced mass change of the OH(D) system, and this scaling relation is closely followed by nonbonded OH stretching and HOH intramolecular bending fundamentals in many systems (29). Figure 2D presents the D2-tagged n = 4 spectrum [D+(D2O)4-D2] with the energy axis scaled by 1.36. An unexpected dividend of this scheme is that some of the bands in the H+(H2O)4-D2 spectrum, whose assignments have been in question (a8-11 in Fig. 2C), are suppressed relative to bend fundamentals (a12 and b12) in the D+(D2O)4-D2 spectrum. Such selective suppression is anticipated for features that arise from coupling between the high-frequency OH stretches and soft modes of the scaffold (23). The persistent bands in the D+(D2O)4-D2 spectrum are close to features in the scaled H+(H2O)4-D2 spectrum, thus revealing that these transitions primarily involve displacements of the hydrons. Moreover, the pattern of sharp bands in the D+(D2O)4-D2 spectrum can be readily assigned to OD stretching and bending fundamentals expected for the Eigen structure E4, as indicated by comparison with the calculated VPT2 spectrum in Fig. 2E and table S1. The prominent sharp feature (b9) not assigned to a fundamental has been analyzed in detail for the H3O+-Y3 series (Y = Ar, N2, CH4) and traced to a very strong enhancement of the transition moment of the H3O+ bending mode (not evident in Fig. 2D) upon rotation of the hydronium moiety about its symmetry axis within the tricoordinated solvent cage (22).

The fact that the fundamentals in the D+(D2O)4-D2 spectrum are close to strong absorptions in the scaled H+(H2O)4-D2 spectrum also provides compelling evidence that the Eigen structure is adopted by both isotopologues (E4H and E4D). A comparison of the predictions obtained by application of VPT2 to both isotopologues is included in table S1, which includes assignments of the transitions in the calculated (VPT2) spectra for E4H-D2 and E4D-D2. The underlying causes for the extra features and broadening in the E4H-D2 spectrum are of great interest but cannot be resolved with currently available theoretical tools. Consequently, we now focus on the simpler perdeutero isotopologues to identify the spectroscopic markers of intracluster proton transfer.

Key features that were obscured by broadening in the E4H-D2 spectrum sharpen notably in that of E4D-D2. As a result, the subtle splittings (IHB1 and IHB2) predicted to signal symmetry breaking of the hydronium core in the D2-tagged E4 structure are clearly revealed in bands b5,6 and b7. In the C3 symmetric E4D structure, two OD stretching fundamentals of the hydronium ion are predicted to be separated by only 38 cm−1 at the harmonic level. The lower-energy transition corresponds to the nondegenerate, symmetric OD stretch, whereas the higher-energy feature is due to the doubly-degenerate antisymmetric OD stretch. This near-degeneracy of the three OD stretches in the bare E4D species is quickly broken as a central hydron is displaced away from D3O+, causing one of the OD stretch vibrations of the D3O+ to become localized on this OD group and to be displaced energetically below the nearly degenerate symmetric and antisymmetric stretching bands associated with the –OD2 moiety. For reference, we recorded the infrared multiple photon dissociation (IRMPD) spectrum of E4D (at a temperature of ~20 K) over the limited range afforded by that technique, with the spectrum displayed in Fig. 3A. A single feature is observed close to the centroid of the IDB1,2 doublet in E4D-D2.

Fig. 3 Vibrational predissociation spectra of D+(D2O)4-A clusters.

These spectra reveal the local frequencies of all five OD oscillators involved in the transfer of a deuteron from one water molecule to another upon addition of incrementally stronger H-bonding molecules, A (see Fig. 1), to one of the water molecules in the primary hydration shell around the hydronium ion. (A) IRMPD spectrum of the bare ion. (B to D) Spectra of A = D2, N2, and CO. (E) D2-tagged spectrum for A = D2O [i.e., D+(D2O)5-D2]. (F) H2-tagged spectrum of the Zundel isomer of the H+(H2O)6 cluster, with the structure indicated in the inset (21), scaled by 1/1.36 to estimate the locations of key bands in the heavy isotopologue with this geometry. The arrow indicates the position of the bridging proton stretch in the D5O2+ Zundel ion (28). This scaling is required because the D+(D2O)6-D2 cluster does not occur in this structure, as is evident by its vibrational spectrum (fig. S5). Band colors are correlated with atoms in the structure insets that are most associated with these transitions (red represents the transferred proton, dark green the OD group attached to the exterior acceptor, light green the other OD group in this DOD unit, and blue the –OD2 motif that will reform a neutral water molecule after the transfer is complete).

The experimental results for a series of H-bond acceptors (A and A′ in Fig. 1) are presented in Fig. 3. For clarity, we color code the features traced primarily to the motion of the active hydrons engaged in the transfer process (red and blue for the hydronium, light and dark green for the relay or AD water molecule). The calculated harmonic and VPT2 spectra are presented in figs. S2 to S4, along with assignments of the calculated (VPT2) spectra in tables S2 to S4. The collective spectral response to complexation with increasingly basic (and, hence, more strongly H-bonded) molecules can be qualitatively understood as the spectral manifestation of partial charge accumulation on one of the central hydrons as it is pulled closer to the AD water molecule. Thus, when D2 is replaced by N2 and CO (with gas-phase basicities of 424, 495, and 594 kJ/mol, respectively) in the second shell, the highest-energy OD stretches are now clearly split apart such that two bands (b1 and b3) remain unaffected, whereas new bands [light green (b2) and dark green (b4)] appear lower in energy (Fig. 3, C and D). At the same time, the doublet associated with the hydronium ion [red (b7) and blue (b5,6)] splits farther apart (Δν = 213 cm−1 for CO) in such a fashion that b7 red-shifts to a greater extent than b5,6 shifts to the blue. The CO stretching band is also evident in Fig. 3D and occurs 39 cm−1 above the stretch of the isolated CO molecule (2143 cm−1), reflecting its response to the formation of the H-bond from a water molecule in the primary hydration shell.

The evolution of the Embedded Image and Embedded Image bands (b3,4 and b1,2) upon complexation warrants comment. Although the first H-bond acceptor molecule, A, is calculated to attach to only one of the OD groups, both ODasym and ODsym bands (b2 and b4) shift to the red relative to the two fundamentals (b1 and b3) associated with the spectator water molecules. This effect results from the relatively strong (~60 cm−1) coupling between the two OD oscillators, which maintain their collective character so long as the perturbation of one of the OD groups upon accepting the H-bond is small relative to their intrinsic coupling. The phenomenon is accurately recovered at the harmonic and VPT2 levels, and a detailed analysis of the tag-induced decoupling is presented in the supplementary text (section SIV, part C) and fig. S7.

Formally, replacement of the more weakly perturbing molecules with a water molecule generates the Eigen-based form of the protonated water pentamer, E5, which is the traditionally accepted structure of this cluster (16, 17, 30, 31). As in the situation regarding the assignments of the H+(H2O)4 spectrum discussed above, the band pattern displayed by the H+(H2O)5 cluster has recently come into question (24). The resolution of this issue and assignment of the fundamentals in the D+(D2O)5-D2 spectrum exclusively to the E5D isomer follows the same protocol described above for the n = 4 system and is presented in a separate publication (23). Figure S4 shows both VPT2 and more computationally demanding vibrational self-consistent field results on both n = 5 isotopologues to address the location and fine structure associated with the key IDB2 fundamental, which presents the greatest challenge for theory. The assignments of the OD stretches in the E5D-D2 spectrum are collected in table S4 and are color-coded in Fig. 3E to highlight the key bands, which fall in line with the overall trend set by the weaker perturbers (Fig. 3, A to D). Because the bands associated with the hydrons most involved in the transfer (red and dark green) are increasingly red-shifted, the H-bond donor band (b4, dark green) approaches the blue-shifted –OD2 bands (b5,6, blue) due to the increasingly distorted hydronium core. The symmetric (b6) and antisymmetric (b5) OD stretches of the –OD2 group are now clearly split apart as a result of the lower symmetry of the E5 scaffold, a feature that is accurately recovered in the VPT2 calculations (fig. S4).

The observation that the n = 5 cluster is approaching the tipping point for transfer of the bridging proton to the adjacent water molecule is related to the fact that the addition of one more water molecule to form the H+(H2O)6 cluster results in the formation of at least two isomers, one with a Zundel arrangement (Z6) and the other best described as a distorted Eigen accommodation motif (E6) (20, 21). Their spectra have been isolated through the application of isomer-specific IR-IR double-resonance spectroscopy (21), and a particularly important structure in this regard is that in which the proton is stabilized at the midpoint between the oxygen atoms of a proton-bound water dimer while the remaining four water molecules form the first hydration shell around a H5O2+ Zundel core (16). The spectrum of the D2-tagged n = 6 perdeutero cluster, included in fig. S5, does not clearly reflect either of the structures found in the light, H2-tagged isotopologue (21), likely emphasizing the role of nuclear quantum effects when different arrangements are close in energy (23).

To estimate the band locations in the n = 6 perdeutero cluster with the Zundel core, we return to the isotopic scaling approach exploited earlier in our assignments of the E4 and E5 structures. Figure 3F presents the similarly scaled (1/1.36) spectrum for the Zundel form of the H+(H2O)6 cluster (Z6H, isolated by double resonance) (21) to gauge how this arrangement would be encoded in the D+(D2O)6 spectrum. The measured location of the bridging deuteron stretch in the isolated D5O2+ ion is indicated by the arrow at the left of Fig. 3F, which, falling only 62 cm−1 below the location obtained by scaling in Z6D (15, 28), indicates that the errors introduced by this procedure are small compared with the overall shifts in the bands. The comparison over the entire spectral region can be found in fig. S6.

The band positions in the Z6D spectrum (Fig. 3F) generated by scaling are readily understood as a continuation of the trend displayed by the series shown above in Fig. 3, B to E. The parallel stretch of the shared deuteron is estimated by the scaling procedure to occur at ~750 cm−1 (red), whereas the four H-bonded OD stretches of the water molecules in the first solvation shell around the Zundel core (light green, dark green, and blue) now appear as a single broadened feature at 2321 cm−1, labeled “ADD” in Fig. 3F. In effect, the Z6 structure can be viewed as a pair of coupled Eigen ions, each with a maximal splitting between the three OD oscillators.

The observation of clear spectroscopic signatures that encode progress along the proton-transfer reaction provides an opportunity to quantify the relationship between a hydron’s stretching frequency and the environment in which the hydron is located. A useful index to describe the extent of proton transfer is the shortest distance between two oxygen atoms that surround the hydron defect, ROO in Fig. 1, which ranges from 2.57 to 2.41 Å in the transition from the Eigen to the Zundel accommodation motifs. The experimental (and, for n = 6, estimated by scaling from Z6H) band positions of the five most active OD groups for six ROO values calculated for the various complexes are presented in Fig. 4. The points along this curve correspond to the centroids of the key bands in Fig. 3 (given in table S5). These are colored to highlight the D atom between the nearest oxygen atoms (red), the remaining –OD2 group on the Eigen core (blue), the OD group bound to A (dark green), and the free OD stretch in that water molecule (light green). Specifically, the three closely spaced OD stretching bands in the Eigen cation (red and blue at ROO ~ 2.57 Å) quickly split apart such that the one corresponding to the transferred deuteron falls in frequency in accordance with the usual correlation with the distance between the heavy atoms (3234). The most important result of this work is therefore the determination of the parametric dependence of the four other OD stretches on ROO, which encodes the collective response of the surrounding H-bonding network throughout the course of the hydron transfer. Overall, attachment of an H-bond acceptor (A) to an OD group on a water molecule in the primary hydration shell of hydronium acts to break the near degeneracy of the three OD groups, whereas the newly formed H-bond decouples the two OD oscillators on the AD water molecule. This effect can be driven to the point that the deuteron is equally shared with addition of two water molecules to yield an ADD arrangement for the deuteron acceptor, at which point the stretches of the outer four OD groups are quasi-degenerate and most widely separated from the very low frequency of the deuteron trapped at the midpoint.

Fig. 4 Experimentally observed frequencies of the five OD stretches associated with the transfer of the hydron are plotted against the computed O-O distance between the acceptor and donor waters (MP2/aug-cc-pVDZ) for the series of D+(D2O)4-A complexes.

Red, transferring proton (IDB2); blue, OD stretch of the donating water (IDB1); dark green, OD of the water molecule bound to the H-bond acceptor, A; light green, free OD of the accepting water. The trends for the five OD stretches are fit to exponentials to guide the eye. The centroid frequencies and computed O-O distances are given in table S5.

The key to understanding the large solvatochromic response of the excess proton lies in the nature of the Zundel ion, Z2. In Zundel’s model for the breadth of the hydrated proton spectrum (13), the potential that governs the parallel vibration of the excess proton is strongly perturbed by the electric field of the solvent surrounding the H5O2+ moiety. This effect arises because of the very large mechanical contribution to the polarizability due to field-induced displacement of the central proton (12). Because this potential is softest for Z2, low-energy displacements of the shared proton lead to large changes in the effective dipole moment, as evidenced by the very intense vibrational fundamental associated with this mode (15, 28). Dahms et al. (14) have very recently revisited this calculation using modern quantum chemical methods in the context of understanding the ultrafast relaxation of the Zundel ion. The spectroscopic behavior of the cold-cluster model systems now allows a more quantitative exploration of this proton polarizability model. In fig. S8, we illustrate how the effect of H-bond acceptors on the potential-energy curve for the bridging proton can be recovered by considering the electric field they impart to an isolated H5O2+.

It is clear from the distance dependence of the OD stretching frequency in Fig. 4 that there is a continuum in the spectral response of the system to hydron transfer that covers the entire infrared spectral region. A particularly important aspect of this work is the determination of the correlations between the hydron stretching absorptions across a very large spectral range, with the lower range due to the transferring hydron and the upper range due to the flanking OD groups. The geometries represented in a spectroscopic measurement in bulk water will therefore reflect the convolution between the population of ROO values and the oscillator strengths for the bands correlated with this distance. Such information should be accessible with two-color 2D IR methods and could affect the present interpretation of correlated transients based on intramolecular HOH bending and excess proton stretching assignments (5). In the extrapolation of cluster behavior to the liquid, however, the ROO values operative in solution are likely to be substantially different from those in small gas-phase clusters. This effect was recently emphasized in our work on the surface-embedded D3O+, where the OD stretches manifest a red shift of ~300 cm−1 as the cluster size increased from n = 4 to 21 (18, 19). The extension of the cluster studies to follow how symmetry breaking is manifested in larger networks is thus a challenging but important direction for future work.

Supplementary Materials

www.sciencemag.org/content/354/6316/1131/suppl/DC1

Materials and Methods

Supplementary Text

Figs. S1 to S9

Tables S1 to S5

References (3543)

References and Notes

Acknowledgments: M.A.J. and K.D.J. acknowledge financial support from the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Numbers DE-FG02-06ER15800 and DE-FG02-06ER15066. K.D.J. acknowledges the use of resources in the University of Pittsburgh's Center for Simulation and Modeling. A.B.M. thanks the U.S. NSF (grant CHE-1619660) and the Ohio Supercomputing Center for resources on the Oakley Cluster. M.R.F. and K.R.A. acknowledge financial support from Collaborative Research Center 1109 of the German Research Foundation (Deutsche Forschungsgemeinschaft). Additional data supporting the conclusions are available in supplementary materials.
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