Coupling Surface Coverage and Electrostatic Effects on the Interfacial Adlayer–Water Structure of Hydrogenated Single-Crystal Platinum Electrodes

: Atomically ﬂ at, single-crystal solid − liquid interfaces attract considerable interest through their electrochemical relevance and well-de ﬁ ned structure facilitating controlled atomistic characterization. Yet, crucial details especially regarding the nanoscale adlayer − water dynamics remain uncertain. Here, the in ﬂ uence of adsorbate coverage on the interfacial structure and solvent relaxation on hydrogenated Pt(111) is examined by extensive density functional molecular dynamics simulations. Pronounced water dynamics is observed with increasing hydrogen coverage, for which an interpretation based on displacement of speci ﬁ cally co-adsorbed water and strong screening of the electrostatic interaction across the interface is proposed. However, the magnitude of the solvent ﬂ uctuations is argued to be partly overestimated by the employed RPBE-D3 exchange-correlation functional, which impedes water chemisorption and charge transfer to sparsely hydrogenated platinum. This manifests as overestimated equilibrium electrode potentials compared to experimental adsorption isotherms, which are conversely well reproduced by static calculations invoking the computational hydrogen electrode formalism. By coupling the interfacial structure with electrostatic properties, our work underscores the profound importance of functional choice as well as the persisting value and comparable precision of carefully employed static approximations in electrochemical simulations.


INTRODUCTION
−4 For a complementary picture, experiments are frequently augmented with density functional theory (DFT) simulations with interpretive and, ideally, predictive power, facilitating the rational theory-driven development of electrode materials. 5Compared to classical molecular dynamics (MD) relying on empirical force fields, the theoretical rigor of DFT-based methods comes with a high computational cost, which often leads to researchers opting for static models and approximations, such as the widely employed computational hydrogen electrode (CHE) scheme. 6,7Nevertheless, considering the highly dynamic nature of electrode− electrolyte interfaces, a proper sampling of finite-temperature fluctuations may be required, 8,9 as recently demonstrated in the context of dynamic transition path simulations highlighting the decisive effect of solvent reorganization and entropic contributions on activation and reaction free energies. 10nsequently, ab initio molecular dynamics (AIMD) simulations of metal−water interfaces have been performed extensively, and in light of the latest research, the early notion of a frozen bilayer structure 11 of interfacial water has been largely abandoned. 5,12Indeed, simulations performed on the platinum−water interface, 2,13−21 as well as other close-packed metal electrodes, 4,16−18 suggest a substantial degree of disorder.Notably, most of the extensive AIMD simulations have been conducted in the absence of adsorbates, except for a few key studies concentrating on the hydrogen, 14,19,21 hydroxyl, 22,23 and CO-covered 24 Pt(111) surfaces.Regarding the hydrogenated platinum electrodes, the simulations model mainly the high-coverage limit, thus leaving room for further refinement.Resolving surface coverage effects on the interfacial adlayer−water structure and solvent relaxation dynamics on hydrogenated single-crystal platinum in more detail is indeed greatly desired considering the relevance of the hydrogencovered electrode at HER and HOR operating conditions as well as from a fundamental perspective.Specifically, within proton exchange membrane fuel cells (PEMFC), hydrogen oxidation constitutes the anodic half-cell reaction in which molecular hydrogen dissociates either chemically or electrochemically via the (1) Tafel or (2)  Heyrovskýreactions, respectively, to form adsorbed hydrogen intermediates H ad on the electrocatalyst surface. 25Protons are subsequently liberated to the solvent phase in a further oxidation step denoting the Volmer reaction (3).
The formation of adsorbed hydrogen at the electrode surface is therefore a key step in the HOR, the rate of which depends critically on the applied electrode potential that also dictates the steady-state hydrogen coverage formed. 26,27When modeling the HOR or conversely the HER, it is thus important to account for the hydrogen coverage and the electrostatic potential at the interface to appropriately capture the complex features of the electrified adlayer−solvent environment, including the adsorbate site distribution, the adlayer dynamics, and the fluctuating water structure.Although the development of novel hybrid materials for hydrogen electrocatalysis is receiving tremendous attention, 28−30 accurate simulations of well-defined model systems, such as close-packed platinum, are nevertheless desired and highly relevant for the establishment of a rigorous theoretical picture of interfacial hydrogen electrochemistry.Low-index platinum is indeed one of the most thoroughly characterized electrode materials, 1 and the large body of available experimental reference data 26,27,31−35 enable careful benchmarking of the computational results in order to pinpoint the necessary level of theory for obtaining physically meaningful predictions.
To address this challenge, we report extensive DFTMD simulations of explicitly solvated, hydrogenated Pt(111) interfaces including the coverages 0, 1/3, 2/3, and 1 ML with particular focus on the interfacial structure, dynamics, and electrostatics.Structural features are comprehensively characterized based on density and angular distributions, while the dynamic properties are elucidated by analyzing orientational and hydrogen bonding autocorrelations.Importantly, a connection between the structure and electrostatics is established by examining internal electric fields and coupling the adsorbate coverage with equilibrium electrode potentials.Comparing the sampled dynamic coverage vs. potential data with experimental measurements and statically derived Frumkin adsorption isotherms enables a direct assessment of the accuracy of the CHE formalism, frequently employed in fast, descriptor-oriented electrocatalyst screening.Regarding the latter, special emphasis is placed on the exchangecorrelation functional dependence, which is benchmarked at both generalized gradient approximation (GGA) and hybrid Hartree−Fock−DFT levels.

COMPUTATIONAL DETAILS
All DFT calculations were performed using the CP2K/ Quickstep electronic structure and molecular dynamics software package. 36,37The hybrid Gaussian and plane wave (GPW) method 38 was used with auxiliary plane wave basis cutoffs of 550 and 400 Ry for static and dynamic calculations, respectively.The 5s, 5p, 5d, and 6s electrons of platinum, 2s and 2p electrons of oxygen, and the 1s electron of hydrogen were considered as valence states and expanded in molecularly optimized double-ζ plus polarization quality Gaussian basis sets (MOLOPT-SR-DZVP). 39−42 For the DFTMD simulations, the revised Perdew−Burke−Ernzerhof (RPBE) 43 density functional approximation (DFA) was applied as recommended by Groß et al. 15 To assess the exchange-correlation functional performance, the PBE 44 and hybrid HSE06 45 functionals were also employed in the case of static single-point calculations and geometry optimizations.In all calculations, dispersion corrections were applied using the DFT-D3 scheme of Grimme et al. 46 with accordingly chosen functional-dependent scaling factors.The dispersion interaction between platinum− platinum pairs was, however, excluded due to the known incorrect screening within the metal. 15,47−50 A matrix diagonalization scheme was used for solving the Kohn−Sham equations, and Fermi−Dirac smearing was applied using an electronic temperature of 1000 K. Convergence criteria of 2.7 × 10 −5 eV and 2.3 × 10 −2 eV Å −1 were used for energy and forces, respectively.
All static calculations were repeated also for the Pt(100) and Pt(110)-(1×2) facets for comparison.Platinum slabs consisting of 144 atoms were constructed using a (6×6×4) supercell for the Pt(111) and Pt(100) electrodes, while a (4×6×6) supercell was used for Pt(110)-(1×2).An optimized (PBE) lattice constant of 3.98 Å was employed, which agrees well with previous experimental measurements (3.92 Å) and accurate full-potential (linearized) augmented plane wave and local orbital (FP-(L)APW+lo) calculations (3.985 Å). 51 For the dynamic simulations, a 20 Å water film (160 water molecules) was added above the Pt(111) surface.A 20 Å vacuum layer was additionally employed in all simulations to decouple periodic images in the direction of the surface normal as well as to extract the value of the electrostatic potential in the vacuum needed for aligning the electronic levels in accordance with the conventional approach for evaluating absolute electrode potentials from first-principles simulations. 52As the value of the vacuum potential depends on the surface potential at the water−vacuum boundary, which in turn is determined by the corresponding net interfacial dipole, the boundary was kept unconstrained to obtain an unbiased estimate of the surface potential drop.Nevertheless, due to the strong cohesive interaction, no evaporation of water molecules was observed in any of the simulated trajectories.
Born−Oppenheimer molecular dynamics simulations were conducted within the canonical (NVT) ensemble at a target temperature of 300 K maintained by a CSVR thermostat. 53ach system was equilibrated for a minimum of 20 ps followed by a production run of 40 ps.Following Groß et al., 14,15,19 a time step of 1.0 fs was employed, and the lowest Pt layer was frozen to mimic bulk behavior.The unconventionally large time step was used to ensure an efficient sampling of the phase space while compensating for the slow convergence of the calculations due to charge sloshing.To this end, energy conservation was monitored closely and confirmed to exhibit acceptable drift (max.3 × 10 −5 eV/atom/ps).A surface dipole correction 54 was applied to account for the artificial electric fields formed across the studied asymmetric systems.he electrochemical interface is divided into a compact and diffuse layer, of which the former contains the inner and outer contact layers (ICL, OCL), defined by the layers of specifically and non-specifically adsorbed species, respectively.We note in passing that the specified interfacial partitions have a close correspondence with the inner and outer Helmholtz planes (IHP, OHP) of adsorbed ions within the Gouy−Chapman− Stern model, but since no charged ions were explicitly considered in this study, we refrain from using this nomenclature in order to avoid potential misconceptions.We emphasize that the lack of ions in our simulations is an assumption, and the results might potentially differ at high ionic strengths.For example, the addition of excess protons to the solvent phase would be screened by a net negative charge on the metallic electrode, given that the system is kept neutrally charged as a whole.This would evidently shift the Fermi level of the metal, thus altering the electrode potential and the water structure accordingly.However, since no explicit charging or ions were considered, our systems reflect dilute solid−liquid interfaces at potentials of zero total charge, i.e., the potential at which the free charge σ on the metal is balanced by the charge eθ associated with the adsorbed hydrogen, q = σ − eθ = 0. 32 The laterally averaged water density profiles across each studied interface are illustrated in Figure 1c, highlighting distinct structural features.Namely, while the hydrogenated interfaces exhibit an onset of increased water density beyond 3 Å from the platinum surface, a prominent peak slightly above 2 Å is observed for the clean surface.This peak arises from spontaneous water chemisorption at the Pt(111) top sites, as visualized in Figure 1b, facilitated by the comparably strong platinum−water interaction at the non-hydrogenated interface.The resulting "bilayer" structure has been reported before 17,20,21 but should not be confused with the icelike bilayer structure of interfacial water at ultrahigh vacuum conditions.
Importantly, the double-peak structure including the height of the first OCL peak with respect to the bulk density is for all systems significantly less pronounced than in studies employing the PBE-D3 generalized gradient approximation. 17Indeed, the applied RPBE-D3 functional yields a weaker platinum− water interaction and a softer water structure at room temperature, which is used by Groß et al. 15 as a motivation for its pertinence.A drawback, however, is the observed slightly underestimated average bulk water density of 0.90 g cm −3 .Regarding the density at the OCL (3−5 Å), two closely spaced peaks are observed for all systems with the fully saturated platinum surface exhibiting the most pronounced water density peak.As elaborated later in section 3.2, the first OCL peak corresponds to a mixed H-down O-down structure, while for the second, a predominant H-up composition is identified.
The adlayer dynamics is analyzed via the hydrogen number density profiles in Figure 1d together with the adatom rootmean-square displacements (RMSD).Although all hydrogen atoms are initially placed in face-centered cubic (fcc) adsorption sites, predicted as most preferential by static calculations (Table S2), upon equilibration, an increasing occupation of top sites is observed as the coverage is incremented, with virtually all hydrogens preferring the top The Journal of Physical Chemistry C site on the saturated surface.This spontaneous transition is driven by a minimization of lateral repulsion as well as entropic forces, emphasizing the importance of considering dynamic surface coverage and explicit finite-temperature effects when modeling adsorbate-covered interfaces.The preferential occupation of top sites on the more saturated surfaces is interesting as this species is proposed as the HER active intermediate opposed to hydrogen at deep fcc sites, 31,56,57 suggesting coverage-driven activation.Also, as shown in the inset of Figure 1d, hydrogen adatoms appear very mobile at the 1/3 ML covered interface while increasing the coverage results in more stationary adlayers, corroborating experimental measurements. 33In the limit of surface saturation, adatom site hopping is strongly suppressed.
We would like to remark, however, that the applied time step could result in some uncertainties regarding dynamic quantities such as the RMSD, but as the observed differences between the surfaces are relatively pronounced, the apparent mobility trend is likely to be qualitatively correct.The results are also plausible in the sense that an increased coverage gradually impedes adatom diffusion due to increasing interatomic repulsions.Finally, in the case of hydrogen bound to platinum, the fastest degrees of freedom are also significantly slower than for hydrogen bound to oxygen (Table S1), thus in principle allowing a larger time step without loss of accuracy.
3.2.Water Orientational Distribution.While the density profiles in Figure 1c,d reveal important details regarding the distribution of adatoms and water on the studied interfaces, it is essential to elucidate the water orientations for a more refined picture.Hence, we resolve the distributions of angles formed by the OH and dipole vectors with the surface normal vector as a function of the surface separation (Figure 2a−h).The OH and dipole distributions on the non-hydrogenated interface illustrate clearly the presence of specifically adsorbed water.That both angular distributions show pronounced populations around 70°closest to the surface indicates nearly planar water adsorption with hydrogens symmetrically tilted slightly away from the surface (O-down configuration).This orientation of chemisorbed water is well known 16,17,21,58 and ascribed to the coupling of the metal d-band with the 1b 1 orbital of water, yielding a relatively immobile adsorbed state.The chemisorbed water is further observed to hydrogen-bond strongly with molecules at the OCL, which are subsequently dragged toward the surface and momentarily constrained in an orientation with both hydrogens pointing away from the surface.Farther from the surface, at distances slightly less than 4 Å, water molecules with one hydrogen strongly coordinated toward the surface (H-down orientation) are observed, and increasing the separation further reveals a gradual rotation to the H-up configuration.At this point around 5 Å, the distributions are, however, relatively broad, indicating a largely isotropic, i.e., disordered, water structure.
For the hydrogenated surfaces, an incremental repelling of the interfacial water boundary is observed with increasing hydrogen coverage, up to 1 Å in the limit of full saturation as reported previously. 14On the 1/3 ML covered surface, a minor population of specifically adsorbing water molecules is still observed, albeit with a less planar orientation.This population also includes species momentarily bonding with hydrogen adatoms although no hydrogen desorption was observed to occur.We note that spontaneous hydrogen desorption on the fully hydrogenated Pt(111) has been previously reported, 19 and the fact that this was not evidenced herein may indicate a more appropriate equilibration.On the other hand, although being highly facile on platinum electrodes, hydrogen adsorption and desorption are still activated processes with non-negligible reaction barriers.The desorption reaction is consequently a rare event, the occurrence of which is not guaranteed during a finite DFTMD simulation.Thus, it may be just a mere coincidence that this process was not observed in our simulations.
In contrast to the clean and 1/3 ML covered surfaces, on the more saturated interfaces, negligible water is observed at the ICL, highlighting the competitive character of water and hydrogen chemisorption on platinum.At the OCL, the water orientations appear qualitatively similar on all interfaces although careful inspection of the dipole distributions slightly The Journal of Physical Chemistry C below 4 Å reveals an increasing population with angles around 50°as the hydrogen coverage is incremented.Considering that the OH distributions remain, however, rather indistinguishable, this species is identified as O-down water with OH angles coinciding with the H-down orientation.The coexistence of Odown water is understood by the emerging adlayer−water interaction via the oxygen lone pairs, thus providing a novel coverage-dependent extension to the previously proposed model for water at clean metal surfaces. 17Notably, the orientational distribution influences also the interfacial density, with an increased abundance of O-down species yielding a denser interfacial structure as discussed previously in section 3.1.
3.3.Solvent Relaxation Dynamics.The reported results suggest a somewhat ordered structure of interfacial water at the ICL and a more isotropic one at the OCL.Still, the presented distributions convey limited information on the solvent relaxation dynamics, i.e. how rapidly the water molecules are fluctuating.To this end, we calculate the OH orientational and hydrogen bonding autocorrelation functions (ACF) for water molecules within 5 Å of the respective surfaces (Figures 3a and   3b).Given an initial OH orientation u (t), the autocorrelation at a later time t + τ is defined by eq 4 where P 2 (x) is the second-order Legendre polynomial. 59The hydrogen bonding ACF is on the other hand expressed as eq 5, where h ij (t) = 1 or 0 depending on whether an acceptor i and donor j are hydrogen-bonded or not.
Both ACFs are characterized by rapid initial decays with time constants on the order of a few tens of femtoseconds arising from the nearly free, short timescale rotation (libration) of water molecules.What is more informative, however, are the long-time orientational relaxation constants 3.1 ps, 1.8 ps, 1.6 ps and 1.6 ps for the 0, 1/3, 2/3 and 1 ML covered electrodes, respectively, and the corresponding hydrogen bond lifetimes 1.5 ps, 0.8 ps, 0.5 ps and 0.7 ps.Evidently, the interfacial solvent fluctuations are most sluggish at the non-hydrogenated surface, which is rationalized by the relatively stationary nature of chemisorbed water and its tendency to immobilize neighboring molecules, as also discussed elsewhere. 21Further support for this notion is given by the lifetimes of chemisorbed water (Figure S1), which is roughly 20 ps at the clean platinum electrode, while on the partially hydrogenated surfaces only brief specific adsorption occurs with residence times on the order of 10-100 fs.
A close inspection of the ACFs in Figure 3a,b and the reported relaxation time constants reveals that the 2/3 ML covered electrode appears to exhibit the fastest relaxation dynamics.Although it is not certain whether this difference is statistically significant, this hydrogen saturation could be tentatively considered to represent a coverage approximately corresponding to the potential of maximum entropy of Pt( 111). 32At this potential, the interfacial structure fluctuates substantially, and the water molecules exhibit no preferential net orientation.While certainly a possibility, we emphasize that the preceding discussion is speculative in our case, and additional simulations are required before any further conclusions may be drawn.
It is noteworthy that for bulk water, the OH orientational and hydrogen bonding autocorrelations are found to decrease with characteristic times of 2.1 and 0.6 ps (Figure S2), indicating that water at the clean platinum electrode is more structured (less mobile) than bulk water, while water at the hydrogenated surfaces is roughly as dynamic.The computed values for water within the bulk phase also corroborate previous experimental and computational results, 59−62 thus providing a further indication that our estimated dynamic properties are at least semi-quantitative with an accuracy on the order of a few hundred femtoseconds despite the applied time step (see also the Supporting Information).These results deepen our understanding of solvent relaxation dynamics on hydrogenated platinum and warrant a reinterpretation of previous results suggesting coverage-induced structuring. 14mportantly, the observed soft water structure agrees qualitatively with recent studies proposing feasible interfacial water reorganization to be essential for promoting HER through facilitated ion transfer across the EDL. 35.4.Electrostatics and Adsorption.The adlayer−water structure at electrified interfaces is effectively governed by internal electric fields induced by nanoscale charge separation. 63Hence, we analyze the plane averaged electric field at the studied interfaces compared to a platinum slab in vacuum (Figure 4a).Significant field oscillations are observed within the slab, while the variations at the interface are more subtle.To quantify this adsorption and solvation-induced perturbation, the intrinsic vacuum contribution is subtracted from the field across the respective electrochemical interfaces (Figure 4b).Closest to the metal, a reduced electron spillover is observed as a decrease in the electric field directed toward the surface, the magnitude of which depends on the hydrogen coverage as well as the platinum−water interaction strength The Journal of Physical Chemistry C due to pronounced water chemisorption resulting in increased charge transfer to the metal. 16he interfacial field around the hydrogen adlayer is expectedly found to be oriented toward the slightly positively charged adatoms as evidenced by the dipolar peaks of a similar magnitude above and below the average adlayer position.However, at the clean platinum−water interface, the peak at 2 Å is negative, in line with chemisorbed water exhibiting an Odown configuration, i.e., a dipole moment directed away from the surface.Interestingly and most importantly, on all surfaces, a nearly identical negative electric field perturbation is revealed at distances associated with the OCL.Although this may seem counterintuitive considering the predominant H-down species exhibiting a dipole pointing toward the surface, a sensible conclusion is reached upon recalling the proposed notable coexistence of O-down water, the contribution of which appears enough to dominate over the H-down dipole-induced perturbation.Nevertheless, the similar magnitude on all surfaces suggests small coverage dependence of the water orientations at the OCL, indicating strong screening of the electrostatic interaction across the interface.Yet, the fully saturated interface stands out slightly due to the emerging adlayer−water interaction via the oxygen lone pairs.
The interrelation between surface saturation and electrostatics is finally investigated by gauging the coverage vs. electrode potential dependency.As a reference, potentialdependent Frumkin adsorption isotherms are presented derived from conventional adsorption energy calculations employing three different DFAs and invoking the static CHE formalism. 6,7,64Herein, the proton and electron electrochemical potentials (μH + + μẽ − ) are deconvoluted in terms of the free energy of molecular hydrogen (G H 2 ) and implicitly corrected for the proton activity (a H + ) and electrode potential vs. the standard hydrogen electrode (U SHE ) using eq 6 In other words, given an effective equilibrium of electrons and solvated protons at the reference electrode with gaseous molecular hydrogen at standard conditions, the need for explicit computation of solvation energies is circumvented, and the only requirement to obtain the appropriate chemical potential reference for the hydrogen adsorption calculations is to evaluate the free energy of H 2 in vacuum.Assuming unit proton activity and fast diffusion and adsorption kinetics so that the reaction remains at quasi-equilibrium, the coverageand potential-dependent adsorption free energy ΔG(θ, U) is then described by eq 7 including the Frumkin lateral interaction term (γθ) and the configurational entropy. 31,33,64Solving for U SHE yields the potential vs. coverage relation to be fitted to calculated differential adsorption free energies (Figure S4).Extracting finally the average electrode potentials from the DFTMD simulations by referencing the platinum Fermi energy (μ) to the vacuum level beyond the solvent phase (ψ S ) using eq 8 52 eU e where Φ SHE = 4.44 eV 65 yields the results in Figure 5 where sampling has been performed every 100 fs by RPBE-D3 and PBE-D3 single-point calculations to assess the functional dependence (see also Figure S7).
Compared to experimental isotherms, 27,31,33 the static CHE scheme with the RPBE-D3 functional underestimates adsorption potentials by ca. 100 mV, while an equal overestimation is observed using PBE-D3 and an even larger one with the hybrid HSE06-D3.The inferior performance of the hybrid stems from its inability to describe the delocalized electronic structure of metallic platinum, an effect arising from reduced error cancellation upon inclusion of exact Hartree− Fock exchange.Notably, the observed functional dependence persists also when considering the Pt(100) and Pt(110)-(1×2) surfaces (Figure S5).The surprising accuracy of the CHE scheme with GGA-level functionals is in part fortuitous and in  The Journal of Physical Chemistry C part due to the comparably weak adlayer−water interaction discussed here and elsewhere. 14Consequently, the most important factor governing the adsorption potential of hydrogen appears to be the strength of the platinum− hydrogen interaction, which is negligibly affected by the presence of water.The validity of the quasi-equilibrium assumption is on the other hand understood by considering the experimentally observed rapid kinetics of hydrogen adsorption on platinum.This finding is non-trivial and deems explicit solvent effects to be of less importance when considering the energetics of hydrogen chemisorption on single-crystal platinum although the influence of solvation and dynamics is expected to remain significant when considering non-equilibrium processes, such as ion transfer across the solid−liquid interface. 10e remark that a comparison of computational results with experimental reference data is generally complicated by the fact that experimental observables are most often macroscopic averages of diverse atomistic phenomena that cannot be readily distinguished.In the present case, the comparison is, however, justified considering the well-defined structure and thermodynamic stability of the close-packed Pt(111) surface, as well as the reliability of the carefully selected reference studies in which the electrode materials are prepared meticulously to eliminate the effects of surface heterogeneities. 27,31,33As no concomitant anion adsorption is either reported, we expect the experimental responses to correspond to hydrogen adsorption solely, thus facilitating a reliable comparison.This is further backed by the excellent mutual correspondence of the reference data, as illustrated in Figure 5.
The most interesting part is, however, the compatibility between the static vacuum-phase data and the fully explicit DFTMD results.While a qualitatively reasonable agreement is found due to the above discussed minor effect of solvation, the DFTMD equilibrium potentials of the partially hydrogenated surfaces are clearly overestimated, especially at the 1/3 ML covered surface.In view of the timescale limitations of DFTMD, a naive rationalization is simply that the simulations are poorly converged although monitoring the cumulative average potential (Figure S7) suggests an error of this magnitude to be unlikely.Instead, we propose that the overestimated electrode potentials arise from the decreased platinum−water interaction predicted by the RPBE-D3 functional, impeding water chemisorption and charge transfer to the metal.Indeed, charge transfer due to O-down water adsorption has been estimated to lower the platinum work function by 0.3eV, 58 a shift qualitatively illustrated in Figure 5. RPBE-D3 is thus argued to inadequately describe water coadsorption on sparsely hydrogenated platinum where the balance between the chemisorbed species appears particularly delicate, critically influencing electrostatic properties.However, the less complex limiting cases of clean and fully saturated surfaces, as well as bulk water, are satisfactorily reproduced with the potential of zero free charge (θ = 0) obtained as 0.5 ± 0.1 V, in line with previous methodologically consistent results. 15,19,66 CONCLUSIONS In conclusion, extensive DFTMD simulations were performed to characterize the influence of surface coverage on the dynamic adlayer−water structure and interfacial electrostatics of hydrogenated single-crystal platinum electrodes.By comprehensively sampling varying hydrogen saturations, we provide a novel coverage-dependent extension to previously proposed models for water at clean metal surfaces where increasing the hydrogen coverage significantly promotes solvent fluctuations via displacement of chemisorbed water and electric field screening.Importantly, our work underscores the paramount importance of functional choice and delicate influence of specific water coadsorption on electrode potentials and interfacial solvent relaxation.Careful assessment of the exchange-correlation functional performance reveals that RPBE-D3 impedes specific water coadsorption and charge transfer to sparsely hydrogenated platinum, critically affecting electrostatic properties.This manifests as overestimated equilibrium electrode potentials compared to experimental isotherms, which are conversely surprisingly well reproduced by static calculations invoking the CHE formalism.Consequently, we stress the persisting value and comparable precision of carefully employed static approximations.Our research provides refined theoretical insights into the role of varying surface coverage on dynamic solid−liquid interfaces and reveals methodological implications essential to further the accurate modeling of realistic electrochemical systems.

The
Journal of Physical Chemistry C 3. RESULTS AND DISCUSSION 3.1.Interfacial Density. Figure 1a,b illustrates the modeled platinum−water interface, and a side-view of the system highlighting the electrochemical double-layer (EDL) structure in analogy with the Gouy−Chapman−Stern model.

Figure 1 .
Figure 1.(a,b) Examined electrochemical interface with 1/3 ML hydrogen coverage as an example.In a and b, gray, white, and red spheres correspond to platinum, hydrogen, and oxygen atoms, respectively, while the blue frame marks the simulation cell boundaries.In b, specifically adsorbed water at the inner contact layer is illustrated by a ball-and-stick representation, while for loosely bound water at the outer contact layer, a stick representation is used.Water molecules within the diffuse layer are rendered transparent.(c) Laterally averaged water density profiles and (d) hydrogen adatom number densities for the studied systems.The inset in d shows the hydrogen adatom root-mean-square displacements.The legend in c refers also to d, including the inset.

Figure 2 .
Figure 2. Distribution of the dipole (top row) and OH (bottom row) angles as measured from the surface normal vector for (a,e) 0 ML, (b,f) 1/3 ML, (c,g) 2/3 ML, and (d,h) 1 ML covered interfaces.Gaussian smoothing has been applied.

Figure 3 .
Figure 3. (a) OH orientation and (b) hydrogen bonding ACFs for the investigated systems.A hydrogen bond is defined for acceptor− hydrogen distances less than 3 Å and acceptor−hydrogen−donor angles greater than 120°.Triexponential functions have been fitted to the raw data indicated by the dots.The legend in a refers to both panels.

Figure 4 .
Figure 4. (a) Laterally averaged electric fields across the studied systems and a clean platinum−vacuum slab.The inset shows a magnification of the interfacial field.(b) Adsorption and solvationinduced perturbation of the electric field, ⟨E(r, θ) − E(r, vac)⟩.Negative values indicate a field pointing away from the surface.The legend in a refers to both panels.

Figure 5 .
Figure 5. Frumkin adsorption isotherms for the Pt(111) surface derived using the static CHE scheme and three different DFAs.Also, the dynamic coverage vs. electrode potential data sampled every 100 fs by single-point calculations using PBE-D3 and RPBE-D3 is plotted.Error bars correspond to 95% confidence intervals.Experimental reference data (open ring, 27 cross, 31 and box 33 ) are shown for comparison.The arrow indicates qualitatively the expected potential shift upon water chemisorption.