Proton Dissociation and Delocalization under Stepwise Hydration of Zeolite HZSM ‑ 5

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INTRODUCTION
−15 A comprehensive understanding of the protonation state is crucial for gaining a deeper mechanistic understanding of these processes since access to the proton is the basis for the Brønsted acidity of the catalyst.
Despite extensive study, the protonation state of the zeolite Brønsted acid site (BAS) as a function of hydration level is not fully understood.−27 The proton affinity of the water cluster increases with size, 28−31 deprotonating the BAS above a critical hydration level.However, the number of water molecules necessary for deprotonation is not known.This has been a topic of many simulation studies, which arrived at different conclusions depending on the computational approach. 17,20 −22,24,25,32,33 The main point of debate is the adsorbed water dimer, where different studies concluded that protonated BAS, 22,34 protonated water cluster, 17 or both 20,21,24,25,33 are stable species.To date, experiments that can identify protonation states at distinct microscopic hydration levels have not yet been reported.
Infrared (IR) spectroscopy has been a valuable experimental technique for investigating the hydration behavior of zeolites since the O−H stretch vibrational frequency is sensitive to its molecular H-bonding environment.To date, most IR studies of hydrated zeolite have focused on the characterization of ≤ 1 equivalents (equiv) H 2 O/BAS, 16,35−37 where the most prominent spectroscopic feature is a broad doublet arising from the H-bonded BAS O−H stretch. 16,21,38,39Experimental studies at elevated hydration are more limited.In one approach, the hydration level was controlled by the partial pressure of water vapor in contact with the zeolite, which required calibration to a second gravimetric measurement. 16,40lternatively, the water loading was controlled by varying the temperature from 30 to 430 °C, 22 enabling accurate measurement of the hydration level at the cost of temperature effects in the IR spectra.In addition to the experimental challenge of hydration control, quantitative analysis of the protonation state is confounded by broad, overlapping IR features and the inevitable microscopic distribution of hydration states at an average water loading.Notably, a recent 1 H NMR study identified a signature of hydronium ions which appeared at average water loadings between 1.6 and 9.1 equiv H 2 O/BAS, though the protonation state of the microscopic 2-water cluster was not assigned. 23ime-resolved vibrational spectroscopy can access additional experimental information about the structure and dynamics of water and protons in zeolite.Picosecond transient absorption studies demonstrated that vibrational energy is rapidly redistributed from the high-frequency BAS O−H stretch to lower-frequency framework vibrations. 41,42−45 Among other advantages, 2D IR spectroscopy resolves spectral information as a function of both excitation and detection frequencies, enabling both selective excitation and enhanced resolution for interpreting congested spectra.
In this work, we report linear absorption and 2D IR spectra of hydrated HZSM-5 zeolite at a constant temperature over the range of 1−8 equiv H 2 O.This builds on our previous study of high-hydration HZSM-5, 43 extending the hydration range and spectral region probed by 2D IR spectroscopy.The 2D IR spectra, particularly at 1 equiv H 2 O, display peculiar features which cast doubt on the most common interpretation of the linear IR spectrum. 37,38Samples were prepared with an ex situ hydration methodology which enabled quantitative control over the hydration level at a constant temperature.Analysis of this data identified distinct signatures of protonated BAS and protonated water cluster, showing experimental evidence that the BAS is deprotonated in the presence of two or more water molecules.From this analysis, we report measured values for the heat of adsorption for the first two water molecules and a deprotonation energy of 1.6 kcal/mol.In the case of the adsorbed water dimer, we see no evidence of a stable protonated zeolite state, which is often predicted by simulations.
These results form a quantitative experimental benchmark for comparison to simulations as a function of water loading.We also report ab initio molecular dynamics (AIMD) simulations on clusters of 1−8 H 2 O molecules confined in HZSM-5 which display both protonation behavior and calculated spectral trends consistent with our experiments.To further investigate the water structure around the proton, we applied the recently developed rCEC method 46,47 to quantify the location and delocalization of the proton charge defect.This analysis revealed that the excess charge is located preferentially near the most highly coordinated water molecules and remains relatively localized between two oxygen atoms even in the largest clusters.

Sample Preparation.
A full description of the sample preparation has been reported previously, 43 and additional details are in the Supporting Information (SI).Briefly, HZSM-5( 17) zeolites (received from Johnson Matthey) were calcined in air, dehydrated on a Schlenk line with vacuum, and then rehydrated at 150 °C to a fixed level in a sealed Parr acid digestion chamber.The hydration level was measured by titration with methanol.Hydrated zeolites were suspended in a mixture of oils (Flurolube polychlorotrifluoroethylene and perfluoro(tetradecahydrophenanthrene)) which prevented exchange of water with the atmosphere.The Si:Al ratio was 17:1 for all samples, as measured by inductively coupled plasma− optical emission spectroscopy (ICP-OES).
2.2.IR Spectroscopy.IR spectra were collected with samples suspended between two 1 mm CaF 2 windows.Spectral decomposition used maximum entropy reweighting of SVD components based on the method of Widjaja and Garland. 69D IR and transient absorption spectra were collected with polarization control using a spectrometer that has been described previously. 70,71Scatter artifacts were suppressed with a combination of chopping both pump and probe beams, quasi-phase cycling 72 by oscillating the probe delay stage, and negative time subtraction, as described previously. 43Additional details describing data collection and analysis can be found in the Supporting Information.

AIMD Simulations.
The atomistic modeling of the protonated water cluster includes a BAS residing in a two-unit cell ZSM-5 zeolite framework (l a = 20.090Å, l b = 19.736Å, l c = 26.284Å), 73 an excess proton to balance the negative charge at the Aluminum T11 site, and a water molecular cluster (H 2 O) n consisted of 1, 2, 3, 4, 6, or 8 water molecules near the BAS.To capture proton shuttling within the cluster and at the interface, as well as the dynamics and statistical distributions of the protonated water cluster at each hydration level, the zeolite framework and the protonated water cluster were treated explicitly with quantum mechanical calculations at the DFT/ revPBE/DZVP (revPBE-D3) level of theory. 74The CP2K package 75 was used to carry out the AIMD simulation using the Quickstep code 76 and the hybrid Gaussian and plane waves (GPW) method 77 with the Goedecker−Teter−Hutter pseudopotential parameterized for the PBE functional. 78Grimme's D3 dispersion correction was applied to the long-range interactions using a cutoff distance of 40 Å. 79 All AIMD simulations of protonated water clusters are integrated with an MD time step of 0.5 fs at 298 K to sample configurations in the constant NVT ensemble with a Nose−Hoover thermostat and a time constant of 1 ps.For each protonated cluster, the AIMD simulation was first equilibrated for ∼4 ps prior to a production run of ∼20 ps.
The power spectra of protonated water clusters were calculated from Fourier transform of the velocity autocorrelation function of each H atom. Since the protonic excess charge is delocalized in the hydrogen-bond network, it is described by the CEC position rather than a localized atomic position.The rCEC approach 46,47 was used to assign the CEC positions in the AIMD trajectories of protonated water clusters at BAS.The rCEC analysis also provides the distribution of the excess charge in the BAS oxygen atoms and all water molecules.Further details of the AIMD methodology were reported previously, 43 and the rCEC analysis is elaborated in the Supporting Information.

RESULTS AND DISCUSSION
3.1.Controlled Hydration of Zeolites.Sample preparation was a crucial component for hydration-dependent IR spectroscopy, which required quantitative control of the adsorbed water per acid site.The methodology was based on previously published work 43 and is detailed in the SI.Here, we The Journal of Physical Chemistry C extend that methodology to a much wider hydration range than in our previous study.HZSM-5 samples were hydrated ex situ by equilibration with water vapor, then suspended in a mixture of hydrophobic index-matching oils for spectroscopic experiments.The mean hydration level of each sample, h̅ , is the ratio of adsorbed water to Al content, measured by methanol titration and ICP-OES, respectively.As a simple ratio between two directly measured quantities, this measurement of the hydration level does not require calibration to a second experiment such as thermogravimetric analysis or isothermal adsorption, which is a drawback of the more common in situ method.For measuring 2D IR spectra of water in zeolites, the greatest challenge is the significant scattered light from micronsize particles. 43,44The ex situ hydration method enables suspension in index-matching oils, which significantly reduces scatter in nonlinear IR spectroscopy. 43,45A Si/Al ratio of 17:1 was used to reach a sufficient signal/scatter ratio in nonlinear experiments.
3.2.Hydration-Dependent Infrared Spectroscopy and Spectral Decomposition.FTIR spectra of H 2 O in HZSM-5 (17) zeolites were measured as a function of hydration level from 0.5 to 8.0 equiv H 2 O per Al (Figure 1).
In Figure 1, the dehydrated zeolite spectrum was subtracted; the series without subtraction is shown in Figure S5.At low hydration, 0.5−1.0equiv H 2 O, the most prominent spectroscopic feature is a broad doublet peaked near 2500 and 2850 cm −1 .The depletion at 3610 cm −1 arises from the subtraction of the O−H stretch of dehydrated BAS, and adsorbed waterfree O−H appears at 3700 cm −1 .−39 While the character of the band can be debated, it is unambiguous that the doublet arises from the H-bonded zeolite BAS O−H stretch, as the same feature appears for a range of H-bond acceptors including molecules such as dimethyl ether and THF, which lack intramolecular O−H bonds. 16,37Therefore, in the hydrated zeolite system, this feature is a signature of protonated zeolite BAS donating a H-bond to adsorbed H 2 O.
The IR spectrum changes markedly with increasing hydration, gaining intensity across the O−H stretch frequency range.At high hydration, 4−8 equiv H 2 O, a prominent set of features arise centered at high frequencies, with a broad tail extending across the observed spectral region.On the basis of 2D IR spectroscopy, AIMD simulations, and spectral calculations, we recently assigned the features at 3220, 3400, and 3640 cm −1 to the water stretch-bend Fermi resonance (FR), H-bonded O−H stretch, and free O−H stretch, respectively. 43We assigned the broad continuum absorption as a signature of the hydrated proton, as a qualitatively similar feature is observed in the liquid 48,49 and protonated gas-phase water clusters. 50At lower frequencies, below 2100 cm −1 , water and proton features are distorted by zeolite framework vibrations (Figure S5).
While variations in the IR spectrum represent changes in the populations of water molecules in different environments and protonation states, a quantitative analysis is complicated by the broad and overlapping spectral signatures.Furthermore, due to non-Condon effects in vibrational O−H stretch spectroscopy, 51 the absorption cross section is expected to vary for water molecules in different environments.
We sought a quantitative relationship between changes in the IR spectrum and populations of water molecules in specific environments with distinct spectral signatures S n (ω) and the hydration-dependent populations in those environments C n (h̅ ).To deconvolve the overlapping features, we expressed the hydration series absorbance A(h̅ ,ω) as a linear combination of three components labeled α, β, and γ.
Component spectra and amplitudes were computed using singular value decomposition (SVD) with reweighted components subject to maximum entropy, positivity, and dissimilarity constraints (details in the SI).The resulting areanormalized component spectra are displayed in Figure 2a.
To account for differences in absorption cross sections between spectral components, the component populations were constrained to sum to the hydration level.
The relative absorption cross sections�integrated over the frequency axis�are contained in the fitted values ε n , yielding ε β /ε γ = 2.6 and ε α /ε γ = 0.96.The hydration-dependent amplitude C n (h̅ ) of component n is proportional to the population of water molecules with spectrum S n (ω) at mean hydration level h̅ , shown in Figure 2b. Figure 2c shows the populations of the three components as fractions of the total water adsorbed, C n /h̅ .Next, we assigned the components to their respective molecular environments using their spectral signatures.S α strongly resembles the spectrum at low hydration, capturing the broad doublet, water-free O−H stretch, and subtraction of the dry zeolite bridging O−H stretch.Therefore, we assigned component α to the protonated BAS donating a H-bond to adsorbed water.S γ strongly resembles the spectrum at high hydration, capturing the prominent water stretch-bend FR, water−water H-bond, and free O−H features.Therefore, we Figure 1.FTIR hydration series.FTIR spectra of HZSM-5 from 0.5 to 8.0 equiv H 2 O/Al.Spectra were normalized to the water stretchbend combination band at 5260 cm −1 (Figure S5) and scaled to the measured hydration level, then the dehydrated zeolite spectrum was subtracted.

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assigned component γ to the addition of water molecules to a water cluster.Comparing S γ to the high-hydration spectrum, intensity is missing in the broad low-frequency shoulder, which we previously assigned to the excess proton. 43This broad feature is captured by S β , which spans nearly the entire spectral range in Figure 1.
The hydration-dependent populations of the components (Figure 2b,c) are consistent with these assignments.At low hydration, C α accounts for the majority of the adsorbed water molecules, but it falls off steeply accounting for only 10% of the population by 2 equiv H 2 O.This is the expected behavior of a protonated zeolite component since the BAS becomes deprotonated at higher hydration. 21,23,25C β rises steeply from 0.5 to 2.0 equiv H 2 O, then plateaus at higher hydration.This is the expected behavior of an excess proton component, which grows as the zeolite is deprotonated and reaches a constant value once deprotonation is complete.C γ grows slowly at low hydration, then linearly with hydration above 2.0 equiv H 2 O, consistent with a component capturing the addition of water not strongly influenced by the excess proton.
Therefore, the spectral decomposition allows us to extract quantitative trends describing the changes in protonation state and water environments as a function of hydration level.However, the linear decomposition is a simplifying assumption that does not account for changes in the individual component spectra with hydration.This could be an issue if the excess proton spectrum varies dramatically between clusters of 2−8 H 2 O, as is the case in cold gas-phase protonated water clusters. 50Figure S7 shows that the reconstruction with three components has excellent agreement with the measurement, with coefficient of determination R 2 > 0.99 and without large systematic errors indicative of spectral shifts.Most likely the excess proton spectrum varies somewhat with cluster size, but the linewidth of the feature is so broad at room temperature that those shifts are relatively small and can be neglected to a good approximation.

2D IR Spectroscopy with Variable Hydration.
To further validate the spectral decomposition, we investigated the persistence of the doublet feature S α by measuring 2D IR spectra as a function of hydration.2D IR spectroscopy can more selectively probe this feature, without the use of spectral decomposition, by exciting the lower-frequency band at 2500 cm −1 where spectral overlap with other features is minimized.Therefore, the hydration trend of this 2D IR feature can be used to test the hydration trend in component α from the spectral decomposition result.
Figure 3 shows the 2D IR hydration series with excitation centered at 2500 cm −1 , measured at 100 fs waiting time.At 1 equiv H 2 O, a diagonal feature at 2500 cm −1 is observed alongside a prominent cross-peak to the higher-frequency band of the doublet at 2850 cm −1 .This is the 2D IR signature of the doublet corresponding to protonated zeolite BAS donating a H-bond.The lineshape displays homogeneous broadening, with equal diagonal and antidiagonal linewidths of 170 cm −1 FWHM in the isotropic spectrum (Figure S13).The transient absorption spectrum (Figure S14) shows the feature is shortlived with a population relaxation timescale of ≤190 fs.Using that timescale, we estimate a lifetime broadening of ∼175 cm −1 , which accounts entirely for the 2D IR linewidth.The fast population relaxation is consistent with previous suggestions that the zeolitic H-bonded O−H stretch is coupled to O−O stretching 16,38 and other low-frequency modes, providing a route for rapid nonradiative relaxation.
The predominant signature of a homogeneously rounded diagonal and cross-peak is clearly observed from 1 to 2 equiv H 2 O and appears to be present up to 4 equiv, although now overlapped with the growing excess proton continuum.By 8 equiv H 2 O, the predominant signature in the 2D IR spectrum no longer resembles the low-hydration doublet, instead displaying a more intense excited-state absorption below ω Det = 2400 cm −1 .
The 2D IR spectrum of the low hydration doublet is highly unusual due to the lack of clear, high-intensity induced The Journal of Physical Chemistry C absorption resonances.While the assignment of the doublet to the protonated BAS donating a H-bond to water is firmly rooted in experimental evidence, 16,52 the 2D IR spectrum provides further information about the nature of the vibrations giving rise to the bands.The traditional explanation for the splitting has been stretch-bend Fermi resonance, 37−40 though that assignment does not explain the missing induced absorption intensity in the 2D IR spectrum. 53In fact, model 2D IR spectra based on Fermi resonance coupling predict an intense induced absorption at an intermediate detection frequency between the two prominent features in Figure 3a, which is clearly not observed. 53Further 2D IR experiments and analysis may reveal anharmonic couplings or higher-lying vibrational states, which can provide additional constraints on this problem.For now, we treat the doublet merely as a fingerprint of the protonated BAS state.
3.4.Modified BET Model for Hydration Dependence.The spectra in Figures 1−3 are ensemble measurements at macroscopic hydration level h̅ , which is an average over the distribution of microscopic hydration numbers h = 0,1,2••• Therefore, there are two possible explanations for the presence of the protonated BAS signature α at h̅ = 2: (a) both protonated BAS and excess proton are stable species in adsorbed water dimer clusters or (b) protonated BAS is only stable in the adsorbed water monomer, but there is a substantial fraction of clusters with h = 1 at mean hydration level h̅ = 2.To distinguish between these possibilities, a model is needed which can relate the mean water adsorbed per site h̅ to the distribution of adsorbed cluster sizes {θ h }, where θ h is the fraction of sites occupied by clusters of size h.
To do so, we considered the preparation of the hydrated samples, where zeolites were equilibrated with water vapor in a sealed container at 150 °C.We modeled this equilibrium using a modified Brunauer−Emmett−Teller (BET) theory 54 described in the SI.In this model, equilibrium is reached between water adsorbed on the zeolite sites and water in the gas phase at partial pressure P Hd 2 O according to a system of equations for sequential adsorption events.

K H O ,
The adsorbed first and second water molecules at the BAS are treated with distinct equilibrium constants K 1 and K 2 , and all subsequent steps are described by K L = 1/P 0 , the equilibrium constant for liquefaction.P 0 is the saturation partial pressure, and equilibrium constants are related to heats of adsorption q h by K h = exp(q h /k B T).This treatment of K h for subsequent adsorption steps is a reasonable approximation, based on adsorption studies showing that the heat of adsorption decreases with hydration and varies gradually at hydration levels greater than 2. 55−57 The system of equations, eq 3, was solved to relate the fractional coverages θ h to the partial pressure x = P Hd 2 O /P 0 , the amount of water adsorbed in clusters of size h, N h = hθ h , and the average water cluster size h̅ = ∑ h hθ h .By treating x as an implicit variable, we expressed θ h as a function of h̅ , subject to two parameters b 1 = K 1 /K L and b 2 = K 2 /K L (see SI). Finally, the derived expressions for the distribution of adsorbed molecules in clusters of size h were related to the populations, or number of molecules, displaying spectral signatures α, β, and γ (representing protonated BAS, excess proton, and additional adsorbed water molecules, respectively).We assume that S α arises only from singly hydrated sites; therefore, C α is given by the fraction of sites with h = 1.
Since a hydrated site can either be protonated with signature S α or deprotonated with signature S β , C β is the fraction of sites hydrated by two or more molecules.
Then, in clusters of size two or more, one water molecule is accounted for by C β and the rest are accounted for by C γ .The number of subsequent water molecules is given by the total molecules adsorbed in clusters of two or more, subtracting the first molecule in those clusters.2b,c and coefficient of determination R 2 > 0.99.Using the preparation temperature of 150 °C, this corresponds to the relative heats of adsorption for the first two water molecules Δq 1 = q 1 − q L = 4.4 kcal/mol and Δq 2 = 1.6 kcal/mol.Using the heat of liquefaction 58 q L = 9.1 kcal/mol at 150 °C results in q 1 = 13.5 kcal/mol and q 2 = 10.7 kcal/mol, both falling within the range of previous measurements. 35

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Setting b 2 = 1 returns the model to the typical BET theory, where only the first adsorption has a distinct equilibrium constant.Under that assumption, the data was reasonably well fit except for the region near h̅ = 2, where the model then underestimated C β (Figure S11).Increasing b 2 > 1 accounts for an additional stabilization energy upon adsorption of the second water molecule.That energy can be attributed to the stabilization associated with proton dissociation which we estimate as Δq 2 = 1.6 kcal/mol.This measured value can provide a benchmark for evaluating the accuracy of theoretical methods for simulating deprotonation in zeolites, where the choice of density functional can have a large effect on the protonation behavior. 32his analysis shows that the hydration-dependent IR spectra of HZSM-5 can be captured quantitatively by a model which treats the proton as dissociated from the BAS when 2 or more molecules are adsorbed; the presence of a stable protonated BAS state in adsorbed water dimers is not necessary.In this framework, the persistence of the signature C α until ∼4 equiv H 2 O is accounted for by the distribution of microscopic hydration environments, which includes a fraction of singly hydrated sites at higher hydration levels.

AIMD Simulation of 1−8 H 2 O Molecules at the Brønsted Acid Site.
To understand the spectroscopic components at atomistic detail�particularly the trends near 2 equiv H 2 O�and to further investigate the evolution of the protonation state as a function of adsorbed water cluster size, AIMD simulations were performed at the revPBE-D3 level of theory with 0−8 H 2 O molecules equilibrated in HZSM-5 at 298 K.The revPBE-D3 functional has been shown to have good performance for water, including at the interface of acidic zeolite. 32,59−62 Seven independent trajectories were analyzed, revealing connections between calculated atomic positions, charge location and delocalization, and vibrational spectra.
The H-bond network is relatively simple at lower hydration numbers (1−3 H 2 O) and becomes complicated with increasing cluster size.Beyond 2 H 2 O molecules, numerous potential energy minimum structures can be located through geometry optimization at 0 K, but only a few are statistically meaningful at room temperature.The most representative configurations of adsorbed water clusters at the BAS are shown in Figure 4.
H-bond formation was observed between water molecules and one or more oxygen atoms in the BAS (the 4 nearestneighbor oxygens to Al), which we will refer to as interfacial Hbonds.H-bonding was not observed in any other framework oxygen atoms.At an equilibrated state, the hydrogen-bond configuration within the protonated water cluster was relatively stable, and at least one interfacial H-bond remained intact during each simulation.When two or more interfacial H-bonds were present, the bond with the shortest O−O was identified and the participating zeolite and water oxygens were labeled O Z and O W1 .
The distributions of O Z −O W distances are displayed as dashed lines in Figure 4a.The most probable distance from O Z to the first water oxygen is 2.5 Å when one water is present and increases with cluster size to 2.9 Å in the 8-water cluster.The second and third adsorbed water molecules form H-bonds to the first with O Z −O W distances of ∼4 Å.In larger clusters, the constrained geometry of the zeolite channels influences the Hbonding network, causing some branching into the pores and not necessarily maximizing water−water H-bonds.For example, in the representative snapshot for 6 H 2 O the only triply coordinated water molecules are coordinated to a zeolite

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oxygen, while the 8-water cluster supports triple-coordination to three other water molecules.
The charge distribution associated with the excess proton and its hydration dependence was quantified using the rCEC approach adopted from Li et al. 46 ,47 Based on the multistate empirical valence bond (MS-EVB) method developed by the Voth group, 65−67 r CEC is a collective variable which describes the location of the center of excess charge (CEC) associated with the net positive charge defect from the excess proton.In this method, the adiabatic ground state of a configuration as a function of the nuclear coordinates is expressed on a basis of diabatic states determined by the H-bonding topology.
Each diabatic state represents a localized excess charge near a single oxygen atom, defined by its center-of-charge (COC) position r COC .For a molecular cluster with h H 2 O molecules at the BAS, there are h + 4 basis states, one for each H 2 O oxygen atom plus the four zeolitic oxygen atoms bonded to Al.The squared expansion coefficient c i 2 represents the distribution of proton excess charge in the ith diabatic state.In the rCEC method, the weights of adjacent diabatic states are parameterized based on the interatomic O−H−O distances using constrained DFT calculations. 68The CEC position r CEC is then the weighted average of the COC positions.In the 8 H 2 O cluster, the proton charge is statistically located near the periphery of the cluster, shared between water molecules that are not coordinated to a zeolitic oxygen.This shifting of the excess proton position away from the deprotonated BAS at high hydration numbers was also captured in metadynamics simulations by Grifoni et al. 25 This observation could be neither verified nor disputed on the basis of FTIR spectroscopy experiments, as we did not resolve any changes in the measured excess proton IR spectrum from 6 to 8 equiv H 2 O. Spectral calculations based on the CEC time correlation function also displayed little change from 6 to 8 H 2 O, suggesting that the proton spectrum is relatively insensitive to the exact position in the cluster once the BAS is deprotonated (Figure S24).
The delocalization of the proton charge defect was quantified using the participation ratio (PR) at each hydration number.The PR, shown in Figure 4b, is a measure of the number of diabatic states that contribute effectively to the state of the excess proton. 63,64 The PR ranges from PR = 1 for a localized state to N for full delocalization over N basis states.In the absence of water, the excess charge is localized on a single O Z and the PR distribution is a delta function at unity.When water is present, the PR distribution displays a large shift from 1 H 2 O to 2 H 2 O and relatively minor changes at higher hydration.At 1 H 2 O, the excess charge is largely localized in a single state (mean value PR = 1.2 corresponds to approximately c 1 2 = 0.9 and c 2 2 = 0.1), with a tail to larger values indicating a small fraction of configurations where there is increased charge sharing with the adsorbed H 2 O molecule.For 2−8 H 2 O, the PR assumes a roughly bimodal distribution peaked near PR = 1.5 & 2. This indicates that the protonic charge is largely shared unequally between two states.Interestingly, while the number of diabatic states grows linearly with the number of water molecules, the PR does not.The PR never approaches a value of 3, indicating that most of the protonic charge remains relatively localized along a single O−H−O axis.Notably, an assignment of partial atomic charges (Figure S25) supports the conclusions of the rCEC analysis.4 where the first H 2 O molecule is Hbonded to two other water molecules, and thus has two potential partners for proton sharing.When the excess proton is not shared with O W2 , then the hydrogen atom along that axis is bound to O W1 with PMF minimum at δr = −0.5 Å, while states with asymmetric proton sharing between O W1 and O W2 account for the additional local minimum at δr = +0.3Å. Together, the results in Figure 5 show that atomic hydrogen positions follow a similar trend as the charge distribution, consistent with the assignment of a shared proton in clusters of 2−3 H 2 O molecules and proton sharing between O Z and O W in the adsorbed dimer.

Spectral Analysis.
To draw connections between hydration, molecular structure, and vibrational spectra, both harmonic normal modes and anharmonic power spectra were calculated.Harmonic spectra of optimized clusters are displayed in Figures S15−S17.While O−H stretch normal The Journal of Physical Chemistry C modes fall broadly in the expected frequency ranges, harmonic spectra are limited for describing the highly anharmonic vibrations of water and protons. 49Instead, we considered power spectra of individual hydrogen atoms in clusters of 1−3 H 2 O, which each correspond to the motions of the selected atom.Power spectra are shown in Figure 6 following the hydrogen atom numbering in Figure 4.This approach better reflects the anharmonicity of the vibrations and relates calculated frequencies to molecular environments with atomic specificity.
The power spectra in Figure 6 display either a broad proton feature spanning ca.2000−3000 cm −1 or narrow free O−H features >3500 cm −1 .The proton feature is most prominent in the spectra of H 1 (1 While power spectra show reasonable agreement with the frequencies and linewidths of experimental excess proton and free O−H features, they notably do not capture the broad doublet feature at 1 H 2 O.This may be a result of relatively large-amplitude motions of H 1 (1 H 2 O) combined with the ∼20 ps trajectory length, which is feasible for AIMD simulations.As a result, modulations in the broad H 1 feature are on the order of the noise level, which could be improved with longer simulation time.Therefore, these spectral calculations are useful for identifying hydrogen atoms that carry some protonic charge�leading to broad low-frequency spectra�but not for discriminating between bound and excess proton states.

Protonation State and H-Bonding Network.
Taken together, the trends in the AIMD simulations agree with the model of hydration-dependent protonation state that was used to capture the experimental IR spectra.The proton can be described as zeolite-bound in the presence of one H 2 O molecule and shared excess proton when two or more H 2 O molecules are present.The clear transition between these two states can be observed in the CEC position, PR, and PMF minimum between O Z and O W1 , and is consistent with trends in the power spectra of hydrogen atoms.
The AIMD simulations reveal further atomistic details and connections between the protonation state and H-bonding

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network.The PR distribution between ∼1.5 and 2 for clusters of 2−8 water molecules suggests delocalization over 2 oxygen atoms, leading to the language of a shared proton.While the water dimer is described well by this picture, the proton can be shared either between O Z and O W1 or between O W1 and O W2 , with roughly equal probability.This is distinct from larger clusters, where the proton is more prominently shared between two water molecules, as seen in the shifts in r(O Z -CEC), PMF, and hydrogen power spectra.This distinction may account for some of the debate over the description of the water dimer.
Furthermore, the simulation results suggest that the location of the excess proton is strongly influenced by the connectivity of the H-bonding network, which extends to the zeolitic oxygen atoms.The trends in H-bond connectivity and CEC location suggest that the proton charge is located preferentially near the most highly coordinated water molecules.For the small clusters present in confined HZSM-5 pores, the largest coordination number is often 3, and a triply coordinated water molecule is an important structural motif for stabilizing the proton.The adsorbed water trimer is the smallest cluster where a water molecule is triply coordinated, and also the smallest cluster where the proton is shared primarily between water molecules and not with O Z .At higher hydration, the excess proton charge defect position r CEC moves further from the deprotonated BAS only when water molecules triply coordinated to three O W become available in the water octamer.Therefore, we suggest a simple scheme for identifying the most probable proton location in adsorbed water clusters: (1) in the adsorbed water monomer, the zeolite BAS is protonated; (2) in the adsorbed water dimer the proton is shared either between O Z and O W1 or between O W1 and O W2 ; and (3) at higher hydration, the proton is shared preferentially between the most highly coordinated water molecules.

CONCLUSIONS
We have presented experimental IR spectroscopic evidence identifying the crossover point from protonated zeolite BAS to shared proton.Using a spectral decomposition, we extracted quantitative information from the hydration series of HZSM-5 zeolite prepared at controlled hydration levels.At 1 H 2 O, the proton is stabilized on the zeolite BAS.From 2 to 8 H 2 O, the proton is instead shared between two oxygen atoms, placing the critical water number at 2 H 2 O.A series of AIMD simulations with varying H 2 O numbers reproduced the experimental trends in the protonation state and IR spectrum.An analysis of excess charge position, atomic potential of mean force, and local mode power spectra further revealed that the excess protonic charge is shared asymmetrically between two oxygen atoms.The case of the water dimer is distinct because significant sharing occurs between water and the deprotonated BAS, while proton sharing in larger clusters occurs primarily between two water molecules.H-bonding connectivity is important for determining protonation state and location, as the excess proton preferentially occupies locations resembling a triply coordinated hydronium ion.Taken together, these experimental and theoretical results provide a consistent description of the protonation state of the HZSM-5 BAS and its evolution across the hydration range of 1−8 H 2 O per acid site.

Figure 2 .
Figure 2. Spectral decomposition using constrained SVD analysis.(a) Area-normalized spectral components with hydration dependence presented as (b) distribution of all H 2 O molecules among α, β, and γ environments and (c) the corresponding population fractions.The components report on water and protons in different environments.Components α and β report on the protonation state, with component α representing protonated zeolite BAS donating a Hbond and component β representing excess proton.Component γ is the signature of additional water molecules that are not strongly perturbed by the excess proton.Shaded curves in (a) are areanormalized spectra at 0.5 equiv (red) and 8.0 equiv (blue).Solid lines in (b) and (c) are the fit to a modified BET model described in the text.
a model of C n (h̅ ) with fit parameters b 1 and b 2 .Fitting that model to the data yielded b 1 = 180 and b 2 = 7 with the resulting curves plotted in Figure

Figure 3 .
Figure 3. 2D IR hydration series.(a) 2D IR hydration series of HZSM-5 at 100 fs waiting time and perpendicular polarization, excited with pulses centered at 2500 cm −1 .(b) Slices of the spectra at excitation frequency 2500 cm −1 .The relative intensities of major features do not have a strong polarization dependence, as shown in Figure S12; perpendicular (ZZYY) spectra are displayed to minimize scatter artifacts.

Figure 4 .
Figure 4. AIMD trajectory statistics of CEC position and delocalization.(a) Distribution of distances between the zeolite oxygen atom (O Z ) and center of excess charge (CEC, solid lines), overlaid with the distribution of water oxygen (O W ) atoms (dashed lines).(b) Proton charge delocalization, represented by the distribution of participation ratios (PR). 63,64Probability distributions are offset by 1 unit for clarity.(c) Expectation values of r(O Z -CEC) and PR as a function of water cluster size.Representative trajectory snapshots from AIMD simulations of 1−8 H 2 O molecules in HZSM-5 are displayed above and labeled by the number of H 2 O molecules.The CEC, which represents the excess proton charge location, is displayed in each configuration as a green dot.Hydrogen atoms in snapshots of 1−3 H 2 O molecules are numbered for reference.
the CEC position with respect to O Z , r(O Z −CEC), are displayed in Figure 4a next to the r(O Z −O W ) distributions.The distribution of r(O Z −CEC) increases modestly with the addition of the first water molecule, then increases more dramatically with the addition of the second.From 2 to 4 H 2 O molecules, the center of the r(O Z −CEC) distribution displays a much smaller positive shift, while the tails have different behavior.The distribution for 2 H 2 O has a tail to smaller distances, indicating charge sharing between O W1 and O Z .While there is little change in the CEC position from 3 to 6 H 2 O, there is an increase of about 2 Å from 6 to 8 H 2 O.

3 . 6 .
Hydrogen Atomic Positions.In addition to the charge distribution, the protonation state is related to the atomic positions of hydrogen atoms.To investigate the proton dissociation from BAS to water cluster, we consider the statistics of hydrogen atom locations along selected O−H−O axes for 1−3 H 2 O molecules.Trajectory statistics were used to calculate the potential of mean force (PMF) between O Z and the adsorbed water oxygen O W1 as a function of δr(O Z −H− O W1 ) = r(O Z −H) − r(O W1 −H), shown in Figure 5a.The PMF minimum shifts from δr = −0.5 Å at 1 H 2 O to +0.3 Å at 2 H 2 O and +0.5 Å at 3 H 2 O, showing that the most probable proton position switches from the O Z side of the axis to the O W1 side between 1 and 2 H 2 O, and moves even closer to O W1 at 3 H 2 O. Proton sharing between water molecules is visualized by the PMF along the O W1 −H−O W2 axis (Figure 5b), where O W2 is defined as the water oxygen closest to O W1 at a given trajectory snapshot.When 2 H 2 O molecules are present, the PMF across the O W1 −H−O W2 axis favors O W1 with a minimum at δr = −0.5 Å.At 3 H 2 O, the PMF retains that global minimum and gains an additional local minimum at δr = +0.3Å.The shape of this PMF is a result of water trimer configurations such as the one pictured in Figure and H 2 & H 3 (3 H 2 O).The evolution of that feature correlates well to the movement of the CEC and atomic hydrogen positions in Figures 4−5.The spectra of H 1 & H 7 in the 3 H 2 O cluster� both located along a O W −H−O Z axis�display some spectral density between ca.3000 and 3500 cm −1 , reflecting interfacial H-bond formation.Broadening of the free O−H features and growth in the H-bonded O−H region with increasing hydration agrees qualitatively with trends in the experimental IR spectrum.

Figure 5 .
Figure 5. Potential of mean force (PMF) at 298 K. (a) O Z −H−O W1 axis between the zeolite oxygen and nearest water oxygen and (b) the O W1 −H−O W2 axis between the first two water oxygen atoms.The hydrogen atom position is described by the difference between O−H distances, δr(O A −H−O B ) = r(O A −H) − r(O B −H). Shaded curves denote error bars calculated with the bootstrap method.The cartoon on the right depicts an adsorbed water dimer labeling the O−H−O axes considered in (a, b).

Figure 6 .
Figure 6.Power spectra of individual hydrogen atoms.Optimized clusters of (a) 1 H 2 O, (b) 2 H 2 O, and (c) 3 H 2 O are shown.Hydrogen atoms are labeled by number, corresponding to the labels in Figure 4. Spectra are offset for clarity; dashed lines are baselines.

AUTHOR INFORMATION Corresponding Author Andrei
Tokmakoff − Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States; orcid.org/0000-0002-2434-8744;Email: tokmakoff@uchicago.eduacknowledge funding by the Office of Basic Energy Sciences, U.S. Department of Energy (Grant No. DE-SC0014305).X.M. and G.A.V. were supported by the Office of Naval Research through Award N00014-21-1-2157, and they acknowledge the computational resources provided by the University of Chicago Research Computing Center (RCC) and the U.S. Department of Defense High Performance Computing Modernization Program.The authors acknowledge Johnson Matthey PLC for providing the zeolite samples free of charge and Halocarbon LLC for providing the PCTFE oils free of charge.■ ABBREVIATIONS 2D IR, two-dimensional infrared; AIMD, ab initio molecular dynamics; BAS, Brønsted acid site; CEC, center of excess charge; DFT, density functional theory; equiv, equivalents; FR, Fermi resonance; FTIR, Fourier transform infrared; ICP-OES, inductively coupled plasma−optical emission spectroscopy; MS-EVB, multistate empirical valence bond; PMF, potential of mean force; PR, participation ratio; SVD, singular value decomposition