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Ultrafast Proton Transport between a Hydroxy Acid and a Nitrogen Base along Solvent Bridges Governed by Hydroxide/Methoxide Transfer Mechanism

Aqueous proton transport plays a key role in acid-base neutralization, and energy transport through biological membranes and hydrogen fuel cells. Extensive experimental and theoretical studies have resulted in a highly detailed elucidation of one of the underlying microscopic mechanisms for aqueous excess proton transport, known as the von Grotthuss mechanism, involving different hydrated proton configurations with associated high fluxional structural dynamics. Hydroxide transport, with approximately two-fold lower bulk diffusion rates than those of excess protons, has received much less attention. We present femtosecond UV/IR pump-probe experiments and ab initio molecular dynamics simulations of different proton transport pathways of the bifunctional photoacid 7-hydroxyquinoline (7HQ) in water-methanol mixtures. For 7HQ solvent-dependent photoacidity, free energy-reactivity correlation behaviour and QM/MM trajectories point to a dominant OH-/CH3O- transport pathway, for all water-methanol mixing ratios investigated. This provides conclusive evidence for the hydrolysis/methanolysis acid-base neutralization pathway formulated by Manfred Eigen half a century ago.


Main
Aqueous acid-base neutralization involves a proton exchange with strong involvement of water solvent molecules. The current understanding of proton exchange between Brønsted acids and Brønsted bases originated from seminal studies by Eigen 1 and Weller 2 more than half a century ago. The general kinetic scheme has been described in Eigen's review of the field 3 . According to the scheme, the proton transfer converting the acid-base reactant pair into its conjugate acid-conjugate base product pair is considered to follow either concerted or sequential pathways (Figure 1a). In the sequential (proton hopping) case two possible directions for proton transport can in principle occur: either a forward excess proton transfer from acid via intermediate hydrated protons to the accepting base (protolysis pathway), or an inverse proton defect transport (hydrolysis pathway) where the base extracts a proton from the solvent, generating hydrated hydroxide anions, that ultimately react with the acid 4 , 5 . A third pathway involves a direct proton exchange between acid and base, with an underlying concerted proton transfer mechanism. Which proton transfer pathway prevails depends on relative reaction rates of the individual proton transfer steps. The relevance of proton transport in cases as diverse as hydrogen fuel cells and biochemical environments, including transmembrane protein channels [6][7][8][9] , necessitates a further exploration of the underlying proton transport mechanisms for conditions clearly distinct from those of bulk water, i.e., for lower polarity solvent media and possible crucial roles of hydrophobic alkyl-and hydrophilic alcohol-functionalities.
Experimental and theoretical results point to a water-mediated proton transfer mechanism on ultrafast time scales between aromatic alcohols and carboxylate bases [10][11][12][13][14][15] . A limited number of intermediate water molecules connecting these acid and base molecules facilitate the protolysis pathway through a hydrogen-bonded "water bridge" or "water wire". These findings can be compared to theoretical studies on proton transport in bulk water, where the transport mechanism of the excess proton has been intensively explored [16][17][18] . It has been found that different conformations of hydrated protons play a key role in the sequential von Grotthuss-type proton hopping mechanism, with Eigen-type (hydronium, H 3 O + ) or Zundel-type (H 5 O 2 + ) hydrated protons often found to occur at distinct phases of the elementary proton hopping events [19][20][21][22] . Hydroxide (OH -) transport has only been considered in a small number of ab initio molecular dynamics studies [23][24][25] , where for OHtransport in bulk water two different hydrated forms of OHhave been found. These studies found OH -transfer to occur by either 4-or 5-fold hydrated configurations, with OHdonating one and accepting 3 or 4 hydrogen bonds to first solvation shell water molecules, respectively.
In this report we present results of a joint experimental and theoretical study of proton transfer between a proton donating OH-group of an acid and a proton accepting aromatic Nmoiety of a base. To avoid a possible variation of the distance between the acid and base, thus maintaining a well-defined number of solvent molecules forming the solvent bridge, we use a so-called bifunctional photoacid 26 , 7-hydroxyquinoline (7HQ) [27][28][29][30][31][32] (Figure 1b). This bifunctional compound has both the photoacid properties of 2-naphthol and the photobase properties of quinoline. Excitation to the first electronically excited state results in a pK ajump from 8.67 to around 0.4 for the OH-group and from 5.64 to around 11.1 for the N side (see Table 1). As a result, both the acidity of the OH-group and the basicity of the N-group strongly increase, initiating a net proton transfer from the neutral (N*) to the zwitterionic (Z*) form with a time constant of ~ 37 ps in water 28 and 170 ps in methanol 29 . In a previous study we have characterized 7HQ dissolved in deuterated methanol (CD 3 OD) 33 , and found the IR-active fingerprint patterns of N*, Z*, and intermediates A* or C* that are expected to occur when the reaction proceeds through a forward or an inverse proton transfer pathway, respectively (Figure 1c), where, however, the results have not been sufficient to draw definite conclusions on the dominant reaction pathway.
In this work we follow the conversion of N*  Z* in real time for different watermethanol mixtures, further exploring the N*  Z* conversion kinetics with ultrafast UV/IR pump-probe spectroscopy. We characterize the reaction rates as a function of X H 2 O :X CH 3 OH molar fraction ratio, and look for possible presence of transient species. To substantiate the observed reaction rates we derive the differences in acidity of reactants and products and possible intermediates through the respective pK a /pK a *-values using well-established free energy-reactivity correlations 12,[34][35][36][37] . We conclude that for ensemble averaged population kinetics upon photoexcitation of 7HQ, the proton transfer follows general rules for acidities when going from methanol to water. To further substantiate our findings that the proton transfer pathway through a sequential hydroxide/methoxide transport occurs for all X H 2 O :X CH 3 OH molar fraction ratios we use QM/MM molecular dynamics simulations applied to the S 1 -state of 7HQ using time-dependent density functional theory (TD-DFT) calculations. We infer that the primary events of proton transfer for 7HQ involves a proton abstraction from the nearest solvent molecule to the quinoline N-side. Our combined experimental and theoretical results demonstrate that the hydrolysis/methanolysis pathway of acid-base neutralization through a water/methanol bridge consisting of three solvent molecules is the dominant pathway. Our results on the 7HQ model system have not only direct relevance for proton transport in water-rich solutions, but also for less polar water poor media, that are ubiquitous in the important cases of proton transport channels in transmembrane proteins or ion exchange regions within hydrogen fuel cells.

Results and Discussion
We have measured the transient response of the vibrational marker modes of 7HQ in the IRactive fingerprint spectral region between 1400 and 1550 cm -1 . In a previous publication 33 we have reported on the distinct vibrational patterns for the different charged species N*, C*, A* and Z*, dissolved in neat CD 3 OD. We have used deuterated methanol as a solvent, to facilitate a direct access to the most important vibrational marker modes in this spectral region, which for normal methanol CH 3 OH would be inaccessible under our experimental conditions. We have concluded that the deuteron transfer process occurs from N*  Z* with a 330 ps time constant. Figure 2a shows our transient IR-absorption spectra, with basic features similar for all water-methanol mixtures studied, i.e. for the X D 2 O :X CD 3 OD molar ratio ranging from 0.0:1.0 to 0.7:0.3. Indeed, we identify the N* marker mode located at 1475 cm -1 , and the Z* marker mode at 1440 cm -1 , to let us observe a profound increase in overall conversion rates from N*  Z* with increasing water content (Figure 2b). For all watermethanol solvent mixtures the time scale of the decay of N* population is equal to the rise of Z* population. We have not observed significant spectral features indicative of transient population build-up of either the C* or A* species upon increased molar fraction of water. From these results we conclude that the underlying proton transport mechanisms for 7HQ in water-methanol mixtures must be similar to those in neat methanol, up to the highest water molar fraction investigated here. An in-depth kinetic analysis of the transient IR spectra can be found in the SI. We summarize our findings of this kinetic analysis in Table S1, and compare the obtained time constant values with those previously reported. 7HQ in principle can exhibit acid-base reactivity as an aromatic alcohol (through its 2naphthol functionality) and as a protonated nitrogen base (through its quinolinium functionality). Free energy-reactivity correlations connect acid-base reaction rates with pK avalues 38,39 . Empirical data have been gathered on the solvent dependence of the reactivity of acids and bases [40][41][42] . A determination of pK a *-values of 7HQ as a function of solvent mixture composition should thus reveal which reaction pathway (proton transport via pathway I, or inverse proton transport via pathway II) dominates. We use free energyreactivity correlation curves -well-established in photoacid research 12, 34-39, 43, 44 -to determine the overall pK a *-values governing the proton transfer dynamics in water, in methanol, and in water-methanol mixtures. For details we refer to the Supplemental Information. Figure 3 depicts our findings on 7HQ dissolved in neat CD 3 OD as well as the X D 2 O :X CD 3 OD solvent mixtures using our femtosecond UV/IR pump-probe measurements, for the overall N*  Z* proton transfer reaction, as well as for the C*  Z* and A*  Z* steps in neat CD 3 OD. For comparison we also have added previously reported results by other research groups obtained with time-correlated single-photon counting (TCSPC) measurements 28,29 . It follows that the measurements performed in H 2 O, in CH 3 OH and in CD 3 OD all follow the same free energy-reactivity correlation, provided that the N*  Z* reaction underlies a change in value of pK a = pK a (donor) -pK a (protonated acceptor), by increasing about 1.2 -1.3 units when going from H 2 O to CH 3 OH (or, equivalently, from D 2 O to CD 3 OD) as solvent. This result strongly points to the quinoline unit dominating the overall proton transfer dynamics for the N*  Z* conversion, as for the naphthol unit a shift of 3 -5 units is expected [40][41][42] . Hence we conclude that our experimental results are indicative of a proton transport mechanism via the N*  C*  Z* pathway II, i.e. an inverse proton transfer mechanism by hydroxide/methoxide transfer. An additional increase in magnitude of 0.3 -0.5 units for pK a = pK a (donor) -pK a (protonated acceptor) occurs when one changes CH 3 OH with CD 3 OD 34 . As we do not observe any irregularities in the free energy-reactivity correlation for 7HQ in the water-methanol mixtures, we derive that at the level of our ensemble-averaged observations of the proton/deuteron transfer reaction dynamics, no preference can be concluded for proton transfer via either water or methanol. To investigate further the underlying microscopic mechanisms of proton transport between donating and accepting groups of 7HQ in water-methanol mixtures, we have performed equilibrium molecular dynamics (MD) simulations to investigate the microscopic solvation of 7HQ, adiabatic MD calculations using a TD-DFT molecular mechanics (MM) approach to identify the propensity of particular ultrafast protonation events of 7HQ in the S 1 -state, and AIMD simulations to obtain key insight into the proton transport along a solvent bridge, following the initial proton transfer between 7HQ and the solvent.
Microsolvation around 7HQ, in particular along the solvent bridge connecting the OH and N moieties, appears to show a bias to a larger number of water molecules than the statistical value given the X H 2 O :X CH 3 OH molar fractions used, even though the actual numbers depend on using either ab initio MD or classical MD routines to determine this. For the X H 2 O :X CH 3 OH mixtures investigated here, 0.5:0.5 and 0.7:0.3, the dominant configurations involve two or three water molecules, with ones consistent of methanol only playing a minor role. From our simulations we deduce that solvent bridges with full hydrogen bonds ("solvent wires") are only a minor part (7 -17 %) for the X H 2 O :X CH 3 OH = 0.5:0.5 and 0.7:0.3 molar fraction ratios. Hence the most typical solvent bridge configurations involve two to three water molecules with partially broken hydrogen bonds. Further details are provided in the SI.
To investigate the mechanism of N* to Z* conversion, we carried out first principles adiabatic MD simulations of the fully solvated 7HQ in the first electronically excited state, employing TD-DFT. The main focus was on whether the reaction proceeds concertedly via a solvent wire or sequentially in a von-Grotthuss-type hopping mechanism. In the case of a sequential reaction, there are two further possibilities, namely H 3 O + /MeOH 2 + or OH -/CH 3 Otransport. For this reason, we prepared the system in two initial conditions that were based on AIMD snapshots of N in the ground state: (I.) C* with a hydrogen bonded OH -/CH 3 Oat the nitrogen site, and (II.) A* with an H 3 O + molecule hydrogen bonded to the A*-Osite (cf. Figure 4). Moreover, to allow for the possibility of a concerted reaction, all of the selected initial configurations exhibited a solvent wire which connected the photobasic and photoacidic sites of 7HQ. The system was propagated adiabatically on the excited state potential energy surface for the duration of about 1 ps, whilst the migration of the excess charge was followed. This approach allows us to assess the temporal stability of C* and A* protonation states inside a realistic solvent environment and helps to address the question which of the possible reaction pathways is the most likely.
The simulations reveal that for most trajectories with C* as the initial state, no back transfer of the proton to the adjacent negatively charged solvent ion was observed. In contrast, the proton was transferred back to the basic 7HQ oxygen atom already within the first 200 fs for trajectories if the initial state was A*. For one of the A* trajectories, we observed the transient formation of C* which was formed after back-protonation of the 7HQ hydroxyl group. Hence, an anionic charge transfer through the solvent, i.e. based on OHand CH 3 Oions, is favoured, whereas the cationic variant, featuring H 3 O + or CH 3 OH 2 + species, is clearly disfavoured. Although our MD simulations yield a consistent picture with our experimental results, we emphasize here that significantly longer MD simulations are necessary to unequivocally assess whether there exists a pathway for a concerted transfer, or not.
To follow the picosecond dynamics of the negative solvent ion (OH -/CH 3 O -) beyond the ultrafast time scales accessible by the TD-DFT MD simulations, we carried out further AIMD simulations employing the revPBE0 hybrid functional and D3 dispersion corrections. To elucidate the underlying transfer mechanism, the hydrogen bonding configurations of the reacting species at various times during the transfer were analyzed. The left panel of Figure  5 shows the average number of hydrogen bonds for the proton-donating solvent molecule (Figure 5a) and the solvent ion (Figure 5b), respectively. Note, it was not distinguished whether the solvent ion was methoxide or hydroxide. It can be seen that due to the lower density in the case of the X H 2 O :X CH 3 OH = 0.5:0.5 mixture, the number of accepting hydrogen bonds is reduced by about 0.2. However, when the proton is symmetrically shared between the two solvent molecules, i.e. for structures close to the transition state, the number of hydrogen bonds is the same for both water-methanol ratios. Therefore, the simulations strongly support that the same underlying transfer mechanism exists in both cases. During the transfer, the number of accepted hydrogen bonds at the donor molecule increases to its ideal number 2. On the other hand, the number of accepting hydrogen bonds at the solvent ion drops on average to 2.9 at the transition state. This has important consequences. In the case of the X H 2 O :X CH 3 OH = 0.5:0.5 solution, larger changes of the hydrogen bonding network are required at the donor molecule because the number of accepting hydrogen bonds is less due to the lower density. The situation is reversed for the X H 2 O :X CH 3 OH = 0.7:0.3 mixtures. Here, the changes of the hydrogen bonding configuration are most pronounced at the solvent ion. This is because at higher water concentrations there is an increasing number of hyper-coordinated methanolate or hydroxide ions, i.e. structures that accept 4 hydrogen bonds. Consequently, the coordination number difference between solvent ions in their minimum free energy and their transition state configuration also increases. Therefore, our simulations reveal that two mechanistically counteracting effects are occurring when altering the water-methanol ratio. Notably, the changes in hydrogen bonding are larger in the case of the X H 2 O :X CH 3 OH = 0.5:0.5 solutions that may be one reason for the lower conductivities in this case.
Our results are in line with what one would expect from the presolvation concept proposed by Tuckerman et al. 23,24 . However, these studies pointed out that in the dynamical hypercoordination mechanism of hydroxide ion migration in water a donating hydrogen bond of the hydroxide ion plays an important role. To investigate this for our water-methanol mixtures, we computed the average number of donating hydrogen bonds of the hydroxide ion for different stages of the reaction. Note, methoxide lacks the possibility to donate a hydrogen bond. The results are shown in the right panel of Figure 5. It can be seen that with increasing water concentration the average number of hydrogen bonds increases drastically. The relative frequency more than doubles when going from X H 2 O :X CH 3 OH = 0.5:0.5 to 0.7:0.3 molar fractions. Moreover, it increases significantly for structures that share the proton symmetrically (low -values), but the relative frequencies of a donating hydrogen bond are still low for both ratios. Hence, the donating hydrogen bond of the hydroxide ion only plays a minor role in the case of the investigated concentration ratios, and, therefore, is not a necessary condition for the charge transfer in water-methanol mixtures at the concentrations investigated here.

Conclusions
We have shown that for proton exchange between the proton-donating naphthol OH-group and the proton-accepting quinoline N-moiety of the bifunctional photoacid 7HQ, linked together by a water/methanol solvent bridge, occurs by a sequential hydroxide/methoxide transport mechanism taking place on ensemble-averaged time scales of tens to hundreds of picoseconds. The observation that charge migration along a preformed solvent bridge at the hydrophobic 7HQ-solvent interface proceeds in a step-wise manner has direct implications for the understanding of charge migration along other hydrophobic interfaces, such as in proton channels, where there is still an ongoing debate whether concerted proton transfer is the reason for the high efficiencies of biological proton channels. Free energy-reactivity correlations show that for all X H 2 O :X CH 3 OH mixing ratios bulk acidities (pK a -values) follow general trends in solvent polarities, strongly advocating for further studies of the applicability of such correlations between acidities and reaction time scales for proton transport near apolar regions, as well as polar or ionic functionalities within transmembrane proteins and hydrogen fuel cells. Finally our combined experimental and theoretical study shows the equal importance of the hydrolysis/methanolysis as possible alternative pathway to the more intensively studied protolysis pathway for acid-base neutralization in protic solvents as originally formulated by Eigen.       Steady-state absorption and fluorescence spectra were recorded on a Perkin Elmer spectrometer and a JOBIN YVON Horiba Fluorolog, respectively. The concentration of samples was 10 -5 M guaranteeing an optical density below 0.5 at the band maximum in a 1 cm quartz cuvette.

Supplementary Information
In Figure S1 we show the absorption and fluorescence spectra of 7HQ in water/methanol mixtures. The gradual shift in equilibrium constants upon increased water fraction leads to a pronounced change in relative population of N and Z, and N* and Z*, in the S 0 -and S 1states, respectively.  To avoid any possible sample damage during the pump-probe measurement, the solution was constantly flowing in the CaF 2 windowed cell of 50 um thickness by means of a peristaltic pump. FT-IR spectra were measured before and after each pump-probe measurement to ensure that there was no sample structure change upon excitation or over time.

Principal Component Analysis of 7HQ UV/IR Pump-Probe Data
One of the most reliable ways to extract detailed kinetics information from transient spectrally-resolved pump-probe measurements is to carry out principal component analysis (PCA) of the experimental data 2, 3 . This method relies on the so-called "bi-linear assumption", which requires that the experimental data can be represented as a sum of (possibly overlapping) transients with time-independent spectral fingerprints.
Mathematically PCA relies on the method of singular value decomposition (SVD), which represents the data matrix M as a product:    Figure S1a.
The feature at zero delay corresponds to the solvent response, typically observed in ultrafast UV/IR pump-probe spectroscopy, due to an interplay of cross phase modulation by the nonlinear refractive index and transient absorption features due to free carrier generation by multiphoton absorption in the solvent and flow cell windows. These features peak around "zero" delay and have fully decayed within a time scale of a few picoseconds.
In the following we only analyze the data matrices starting from point #200 (delay of about 1 ps) and thus exclude this artifact. The delay-independent bleach component results from contributions of the neutral N form of 7HQ in the electronic ground state. Figure S3 shows the singular values (diagonal entries of the matrix S) for the measurement in Figure S2a (7HQ in neat CD 3 OD) in decreasing order. Three first singular values are clearly larger than the rest indicating that the data matrix in Figure S2a contains three significant components. Figure S4 shows these three components as false colour maps in panels (a)-(c). Figure S4d shows the sum of these components. Comparing it with the data matrix reproduced in Figure S4e one can see that the three main components capture all essential dynamics in the recorded transient spectra. Figure S4f shows the residuals. Note that the maximum value on the colour bar constitutes only about 5% of the maximum value in the data matrix. The residuals show two weak components around the wavenumbers 1460 cm -1 and 1490 cm -1 , with spectra shifting towards larger wavenumbers at longer time delays. These features correspond to a spectral diffusion and, as mentioned above, cannot be captured using the principal component analysis. Therefore in the following we neglect these weak features.
As described in Ref. 4 Table S1.    Table 1). The reason why the intermediate C* species, expected to occur for the hydrolysis/methanolysis pathway II, cannot be extracted from the PCA-SVD analysis, likely lies in the fact that the C* → Z* rate is about two times faster than the decay rate of N*, for both neat methanol and neat water (see Table 1

Free Energy-Reactivity Analysis
To understand our observations we first discuss the reactivity of acids and bases as a function of solvent medium. Typically acidities in the condensed phase are quantified with Photoacid research has matured to a general understanding that the photoacidity effect results from an increase of acidity upon electronic excitation, i.e. pK a * = pK a (S 1 ) decreases by following the BEBO-model. In the free-energy relationship: where k r is the first-order rate constant and (k * ) -1 is the frequency factor of this type of reaction, R is the gas constant and T the absolute temperature. The effective activation energy of the proton transfer reaction, ∆G a , has been estimated using the Marcus BEBO equation 19 : Here ∆G o # is the solvent-dependent activation energy of the charge-exchange reaction when the total free energy change ∆G o : in the proton-transfer reaction is equal to zero.
Free energy-reactivity correlations can be used to derive an unknown pK a -value of one of the acids/conjugate acids of bases in the acid-base neutralization reactions, as has been demonstrated for carbonic acid 13 . In this report we have applied these now wellestablished free energy-reactivity correlation relationships to conclude that the proton transfer hydrolysis/methanolysis pathway II dominates for 7HQ in water-methanol solvent mixtures. Figure 3 shows the free energy-reactivity correlations for the N*, C* and A* forms    we are able to assess the reactivity of N* as a deuteron acceptor (when ∆pK a = pK a (D 2 O or CD 3 OD) -pK a (C*) ), or of N* as deuteron donor (when ∆pK a = pK a (N*) -pK a (D 3 O + or CD 3 OD 2 + ) ), see Table S2.   This procedure resulted in densities of 0.833 g/ml and 0.915 g/ml for 50% and 30 % methanol, respectively, which are close to the respective experimental densities of methanol water mixtures at 25 °C of (~0.88 g/ml and ~0.92 g/ml) 28 . For each mole fraction, we sampled five configurations at evenly spaced intervals from the last 5 ns of the simulations. In a second step, ab initio molecular dynamics (AIMD) simulations were run using these 10 configurations as starting points. After around 10 ps of simulation in the NVT ensemble at 350 K using a Nosé-Hoover chain thermostat [29][30][31] , we switched to the NVE ensemble, where the systems were propagated for another 30 ps. For the AIMD simulations, we used the GPW scheme 32 as implemented in the CP2K software package 33 .
The BLYP functional 34,35 with a TZVP valence basis set 36 , Goedecker potentials 37 , and a 350 Ry plane-wave cutoff was employed. With the increase in temperature we aim to balance overstructuring effects, found in simulations at lower temperatures 38,39 . For the very same reason, we used DFT-D2 dispersion corrections 40 . The simulation temperature of 350 K corresponds to a physical temperature of 300−320 K. For the ground-state simulations, we used restricted Kohn−Sham density functional theory (DFT) and a time step of 1 fs. All protons in the system were given the mass of deuterium to allow us to use a 1 fs time step. The goal of our simulations was to trace the charge migration through the solvent in proximity to the 7HQ chromophore and to elucidate the role of the hydrogen-bonding network of the solvent on the charge migration mechanism. For this, the definition of the asymmetry parameter δ for proton location along a hydrogen between donating and accepting sites is shown in Figure S7. Here, 7HQ was modeled by classical force field potentials, where we reparametrized the 7HQ partial charges with a restrained electrostatic potential fit, using the S 1 electron density as a reference. This treatment implicitly assumes successful acid-base dissociation, i.e. no back-donation to the solvent occurs after the protonation of the nitrogen site. After a short equilibration phase, the charge migration was simulated for 10 ps starting from five different initial conditions.

MD Simulation of 7HQ in the First Excited State
The MD trajectories reveal that the negative charge, i.e. CH 3 Oor OH -, migrates through the solution with participation of both methanol and water molecules.   Figure S7: Definition of the asymmetry parameter δ for proton location along a hydrogen between donating and accepting sites, as used to determine the average number of donating hydrogen bonds along the solvent bridge as a function of δ (see Figure 5, right panel).

Microsolvation around 7HQ
The local distribution of water and methanol molecules in direct proximity of the 7HQ chromophore differs significantly from the homogeneous distribution. As a consequence,  Although this site-unspecific microsolvation is not expected to significantly affect the migration of solvent ions in proximity to the chromophore, 7HQ is able to accept and donate hydrogen bonds at its photoacidic and photobasic moieties, which might alter the solvation structure more site specifically. Most importantly, the well-defined separation of these groups allows for the formation of stable hydrogen bonded chains of solvent molecules. It has been previously shown by us that 'solvent wires' which are comprised of three water molecules are particularly stable over several tens of picoseconds 56 . Hence, these configurations might serve as a potential channel for a sub-picosecond tautomerization reaction. In this case, the system would be in a resting state until a solvent wire forms at which point the tautomerization reaction would take place on a sub-picosecond time scale, involving the concurrent transfer of all protons within the wire 57 . For this reason, information regarding to what extent these wires are already present in the ground state might provide important clues about whether this ultrafast mechanism might play a role at all in the case of more complex solutions than neat water, such as the current methanol water mixtures. To this end, we analyzed ab initio and classical MD trajectories of N and investigated the presence of three-membered solvent wires. As shown in Table S4, wires are formed in 7 % of the simulation time in the case of the classical MD simulations, and 9 -17 % in the case of the AIMD simulations. The discrepancy between the two simulation approaches is likely due to imperfect sampling in the case of the ab initio simulations as converged statistics require simulations in the nanosecond regime. Besides the existence of solvent wires, it is compelling to ask whether these configurations are preferably composed of a specific solvent type, i.e., either water or methanol, or whether the distribution of methanol versus water molecules reflects the overall bulk mixing ratio.
To answer this, we computed the distribution of water and methanol molecules within the wire, shown in Figure S8b, and compared it to the distribution one would expect by merely counting the various possibilities to form wires of a specific type. As becomes apparent, there is a clear preference for water molecules over methanol molecules to be in the solvent wire than one would expect from plain statistics: Most of the wires consist either of two or three water molecules, whereas wires containing two or three methanol play only a minor role. Apart from the solvation structure in vicinity to the chromophore, the charge migration crucially depends on the hydrogen-bonding network between solvent molecules.
One obvious difference between water and methanol is that the latter has one hydrogen bonding donor site less. Therefore, the resulting network will exhibit fewer branches the more methanol molecules are present in the solution. Moreover, the higher the number of methanol molecules relative to water molecules becomes, the lower the density will be (cf. ρ(H 2 O) = 0.997 g/ml; ρ(MeOH) = 0.791 g/ml at T = 298 K and p=1 atm.).
For a comparison of the density differences for the two mixing ratios, see the RDFs between water and methanol oxygen atoms and all solvent oxygen atoms, respectively, in Figure S9. It can be seen that only the first solvation shell differs, whereas the remaining part of the RDF is almost identical for the two mixing ratios. The number of particles in the first solvation shell, as measured from r = 0 Å until the first minimum, is 3.