Hydrogen Deposition on Pt(111) during Electrochemical Hydrogen

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Hydrogen Deposition on Pt (111) During Electrochemical Hydrogen Evolution from First-Principles Multi-adsorption-site Study Teck Leong Tan, Lin-Lin Wang, Duane D. Johnson, and Kewu Bai J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp405760z • Publication Date (Web): 01 Oct 2013 Downloaded from http://pubs.acs.org on October 11, 2013

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The Journal of Physical Chemistry

Hydrogen

Deposition

on

Pt

(111)

During

Electrochemical Hydrogen Evolution from FirstPrinciples Multi-adsorption-site Study Teck L. Tan*,, Lin-Lin Wang§, Duane D. Johnson§,¶, Kewu Bai AUTHOR ADDRESS: Institute of High Performance Computing, Agency for Science, Technology and Research, Singapore 138632, Singapore. §The Ames Laboratory, U.S. Department of Energy, 315 TASF, Iowa State University, Ames, IA 50011-3020, USA; ¶

Departments of Materials Science and Engineering, and Chemical and Biological Engineering, Iowa State University, Ames, IA 50011, USA

KEYWORDS: first-principles, cluster expansion, adsorption isotherm, hydrogen evolution reaction, catalysis, Pt, electrochemistry

ABSTRACT: We study the simultaneous adsorption of H* on Pt (111) for multiple, interacting adsorption sites (i.e., fcc, atop and hcp) and, over a wide range of electrode potential, examine the equilibrium site coverage during the hydrogen evolution reaction (HER) and oxidation reaction (HOR). We use a first-principles-based cluster expansion (CE) and Monte Carlo simulations. We predict the adsorption isotherm and cyclic voltammogram for −0.9 V < U < 0.5 V versus the standard hydrogen potential. Although strongly adsorbed H*fcc are the majority

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specie for U > 0, we show that traces of weakly adsorbed H*atop and H*hcp are present and they are expected to be active in the HER. For U < 0, we predict that H*atop takes over as the majority specie c.a. U = −0.4 V where a simultaneous decrease in H*fcc occurs – contradicting the general assumption that H*fcc remains the majority specie, even at very negative potential. We identify the favorable HER operating potentials by mapping out the coverage of the kinetically active specie H*atop.

INTRODUCTION With the world pushing for clean-energy sources and a hydrogen-based economy,1 chemical reactions involving hydrogen are increasingly being researched on. Hydrogen (H) evolution and oxidation in electrochemical environment are two of such reactions critical for hydrogen fuel cell applications,2,3 where Pt is commonly used as the electrocatalyst. Pt however is expensive and strategies to reduce cost via nano-sizing4–10 and/or alloying,6,11–13 while maintaining high catalytic activity, are actively explored. This has led to a renewed interest to fundamentally understand3,6,14 why Pt is an efficient electrocatalyst for the hydrogen evolution reaction (HER) and its reverse, the hydrogen oxidation reaction (HOR). Experiments have been carried out to characterize both polycrystalline15–17 and well-defined crystalline Pt surfaces,2,18–21 with the more recent works showing that the activity of HER varies with crystallographic orientation. Depending on the electrode potential, H* are classified as either those from underpotential deposition (UPD, at positive potential) or from overpotential deposition (OPD, at negative potential).20 For Pt, questions regarding the role of UPD H* remain open: Do they merely serve as spectators for the HER/HOR or are they the intermediates for the reactions?19 And if UPD H* are indeed spectators, then what are the H* species that are responsible for the HER/HOR? Are these active species the same as those from OPD? The answer to these questions requires


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knowledge of (i) the accessible states of H* during UPD/OPD and (ii) the HER/HOR kinetics at these states. For metallic face-centered cubic (FCC) (111) surfaces, the energetically favorable adsorbed states usually include H adsorbed on the fcc, hcp and atop sites, H*fcc, H*hcp and H*atop respectively. For Pt (111), it is believed that the UPD H* consist of H*fcc and do not participate in the HER/HOR,2,18,19 although recent spectroscopies of polycrystalline Pt show that H*atop are also evident at potentials slightly above zero;15,17 OPD H* are typically believed to consist of H*atop, besides H*fcc2 Due to the small size of H atom, it is however very difficult to probe atomic level details of the surfaces under electrochemical conditions. As such, density functional theory (DFT) calculations would provide useful information to fill these knowledge gaps at the atomic level. For Pt (111), more recent work6,22–25 has shown that the (non zero-point corrected) adsorption energies increases from H*fcc (most stable) to H*atop to H*hcp, although earlier calculations showed that H*atop is slightly more stable than H*fcc.26 As such, to a first approximation, H*fcc are expected to decorate Pt (111) up to 1 monolayer (ML) and H*atop would only be present above 1 ML. Based on these assumptions, mean-field based adsorption isotherms and theoretical voltammograms have been calculated and give reasonable predictions versus experiment.3,7,27 Moreover, simple pairwise Monte Carlo (MC) with only fcc adsorption sites have been done too.27 However, mean-field methods and fcc-only MC simulation are inadequate to address the numerous configurational possibilities of H*. Mean-field analysis are based on a small set of H* configurations created with much guess work, while an fcc-only MC simulation fails to predict coverage at other adsorption sites and its use is thus restricted to a limited potential range (U > 0 only). In view of this, we construct a cluster expansion (CE) Hamiltonian28 involving multiple


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adsorption sites, namely fcc, hcp and atop sites, using more than a hundred H* configuration energies calculated from DFT. The CE method has largely been utilized in alloy studies,6,29–37 although it had been applied to adsorption studies too.38–41 Via a groundstate search using the CE, we predict H* configuration groundstates on Pt (111) from low to high coverages. Via a multi-adsorption-site MC simulation, we show that at positive potentials (U > 0), although H*fcc is the majority species, traces of H*atop and H*hcp are also present. This discovery has important implications to the kinetics at U > 0, as it has recently been shown

42

that a small amount of

weakly adsorbed H*atop is sufficient to contribute significantly to the HER (due to the low kinetic barrier). At negative U, our simulation shows that the coverage of H*fcc remains at 1 ML up to U = −0.4 V, beyond which, H*atop becomes the majority species, while the coverage of H*fcc decreases to 2/3 ML. This is unlike mean-field based calculations, where H*fcc is assumed to remain at 1 ML for U < −0.3 V.3,43 This discovery implies that H*atop (rather than H*fcc) should play a more critical role in electrochemistry at both low and high coverages. Importantly, our work helps to identify the relevant H* configurations during HER/HOR under electrochemical conditions, thereby allowing researchers to study the amount of kinetically active species that are present over a wide potential range.

METHODOLOGY We used the Vienna ab-initio simulation package (VASP)44,45 within a Projected Augmented Wave (PAW) basis46 to obtain the DFT adsorption energies, based on the generalized-gradient approximation (GGA) using the revised PBE functional,47 where the adsorption energies of small molecules were shown to be closer to experimental values47 compared to the more commonly used PW9148 and PBE49 functionals. Plane-wave cutoffs were set at 460 eV. The Pt (111) surface


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is modeled as a 4-layer slab with a 5-layer inter-slab vacuum in the z-direction, where atomic relaxations (to within 0.01 eV/Å per atom) are allowed for only the top two layers while the bottom two layers are fixed at the FCC bulk lattice constant of 3.99 Å obtained from PW91 calculations. H atoms are adsorbed only on the relaxed surface layer at the fcc, hcp and/or atop sites. We note that adsorption at bridge sites are unstable at low coverage and would only be important for coverage beyond 2 ML. As energies of different unit cells of H configurations are compared, a dense Γ-centered k-point mesh with at least 67 k-points per Å-1 is used. Calculations are spin-polarized for our adsorption studies, although the magnetic moments are found to be small (below 0.08 µB per atom) and are negligible at high H coverage. To compare the relative stabilities of the H configurations on Pt (111) surface, we can define the adsorption energy as

ads Pt-mH Pt

H2 / /

(1)

H2 / eV/H .

(2)

or ads Pt-mH Pt

Here, !" and H2 are the energies of the bare Pt slab and the H2 molecule. Pt-mH is the (configuration dependent) energy of the Pt slab adsorbed with m H atoms and N is the total number of adsorption sites. It is mathematically more convenient to use the first expression in the CE methodology. The energies are evaluated via DFT. The fraction of adsorption sites occupied by H is given by #$ /N. It is useful to define the H coverage, θ, in terms of ML, which, for our case is,

& 3#$ ML .

(3)


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Previous work on H adsorption frequently utilized 3 or 4-layer Pt slabs with selected layers fixed at the bulk Pt lattice parameter of 3.99 Å (PW91 or PBE)7,43 or 4.02 Å (revised PBE).27,50 Going from a 4-layer to a 12-layer slab model (Table S2 of Supporting information), the magnitude of Eads increases by 0.01, 0.02 and 0.03 eV/H for H adsorbed on fcc, hcp and atop sites, respectively. These results are consistent with previous findings of < 0.1 eV/H difference between 4-layer and 8-layer slabs.50 Although previous studies used a lattice parameter of 4.02 Å for bulk Pt for revised PBE functional, the VASP optimal lattice parameter is between 3.99 Å and 4.00 Å (Figure S2). A change from 3.99 Å to 4.00 Å (Table S3) increases the magnitude of Eads by less than 0.01 eV/H; this value is smaller than energy changes induced by slab thickness. As noted below, uncertainty in Eads from slab thickness does not affect our major findings. In fact, revised PBE calculations using 3-layer slab models had yielded predictions that agree with HER experiments.3,13,27,50

Cluster Expansion Method In the CE method, the energy of each H configuration, σ , is expanded in terms of cluster (cl) correlation functions, *cl σ ∏0∈cl /0 . The CE Hamiltonian is written as:

2 3 ∑cl 5cl 6cl 3 .

(4)

σ is a vector of 7/8 , / , … , /; < denoting the occupation of each H configuration, where /0 takes the value of 1 if adsorption site k is occupied by a H atom and 0 otherwise (unoccupied). =cl is called the effective cluster interaction (ECI). In practice, all but a finite number of ECI are close to zero; thus, a properly truncated CE Hamiltonian will predict energies accurately. Because ECI


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of symmetry equivalent clusters have the same value, only symmetry distinct ECI in the truncated CE are evaluated, requiring only a finite set of DFT configuration energies as the learning set. ECI may be classified using two indices n and f,35 where n is the number of sites in the cluster and f distinguishes symmetry distinct clusters (Table S1 of the Supporting Information). For example, V1,1 and V1,2 would refer to the single-point interactions at the atop and hcp site respectively; V2,1 would refer to the first set of symmetry distinct nearest neighbor pair interactions. The search for low-energy H configurations is conducted iteratively using a database of ~500,000 H configurations generated from unit cells with N = 3i adsorption sites with i from 1 to 7. An initial CE is constructed using configurations from the smaller unit cells (N = 3, 6, 9 and 12) as the learning set. The CE is used to rapidly evaluate the energies of the 500,000 H configurations with the groundstates identified. Any newly predicted groundstates not in the learning set are confirmed by DFT calculations and the energies are included into the learning set. Subsequent CEs are thus constructed using sets with a higher proportion of low-energy configurations. The above process is repeated until no new groundstates are predicted. A CE is constructed for >? @ads . We use the Thermodynamic Toolkit (TTK)35,36 for constructing our CE and groundstate search. Among the three possible adsorption sites, fcc, hcp and atop on the Pt (111) surface, TTK creates a list of all symmetry-unique clusters that are ranked according to a physical hierarchy; clusters involving fewer sites and shorter spatial extent are physically more important (i.e., 2-body or pair interactions are more significant than 3-body or triplet etc., and shorter range pairs are more important than longer ranged pairs). Truncated CE is constructed from DFT energies of relaxed H configurations via structural inversion. Clusters in a truncated CE are selected from a large pool of clusters. Only CE that are locally


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complete are considered.51 A CE basis is locally complete if it obeys all completeness relations within a truncated finite set of atomic sites and this is ensured only when each cluster in the truncated CE has all its subclusters included, e.g., if a nearest neighbor (NN) triplet is included, all NN pairs and single-site clusters of the triplet has to be included. The predictive capability of the truncated CE is evaluated via the leave-one-out cross-validation (CV1).35,36 We initially select clusters from a pool of 50 pairs and 40 triplets only, however the CV1 of truncated CE do not go below 11 meV/site; the inclusion of 6 quadruplets is needed to obtain a CV1 of 6 meV/site. We note that some very compact quadruplet ECI could not be evaluated because H-configurations containing such clusters are unstable. An optimal CE (obeying local completeness) with the lowest CV1 error is selected. The final ECI of the iterative groundstate search (see Table S1) gives least-square and CV1 errors of 2.0 meV/site and 5.5 meV/site respectively. Monte Carlo (MC) simulations (using the ECI) are then performed, using a 24 by 24 box (N = 3×242), to assess the H coverage on Pt (111) versus electrode potential U with respect to the standard hydrogen electrode.

RESULTS AND DISCUSSION Groundstates and Optimal CE Figure 1 shows the DFT-evaluated ads for 137 H configurations, corrected for zero point energies (ZPE), for coverages up to 2.33 ML from the learning set of the optimal CE. At dilute coverages, adsorption on fcc site is the most stable and ads fcc B ads atop B ads hcp. For θ ≤ 1, we further find that the groundstates consist of configurations with H*fcc only; configurations involving H*hcp have high energies in general and those involving H*atop are somewhat in the middle. For 1< θ ≤ 2, only fcc and atop sites are occupied in the groundstates;


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low-energy states involve the H*fcc and H*atop only or the H*hcp and H*atop only. Configurations involving both H*fcc and H*hcp are energetically unfavorable due to the strong repulsive interaction. We note that, for θ ≈ 2, low-energy configurations involving H*bridge are stable and a more general CE (with bridge sites) is needed for θ > 2. The configurations of the predicted groundstates are shown in Figure 2. The groundstate hull is constructed by joining the groundstates over all θ. It is energetically favorable for states above the hull to segregate into adjacent groundstates. The corrected adsorption energy decreases monotonically along the hull until θ = 1, beyond which the adsorption energy increases with θ. This marked change in the slope of the groundstate hull corresponds to the onset of H adsorption at atop site. The groundstate at θ = 1 is the p(1×1) structure that is often observed in H adsorption experiments.2,52 Generally, it is difficult to observe directly the H configurations in experiment; thus, our simulation details the possible stable configurations over a large range of H coverage. For groundstates with θ < 1, H occupies only fcc sites. To avoid H-H repulsion, adsorbed H atoms are often assumed to be as far apart as possible, however, our groundstates in Figure 2 show otherwise. For instance, our study shows that the common p(2×2) and p(2×1) structures (where the number of NN fcc sites are minimized) have slightly higher energies than our predicted groundstates. The groundstate at θ = 0.25 is 8 meV/H (0.7 meV per site) lower than p(2×2) and the one at θ = 0.5 is 6 meV/H (1 meV/site) lower than p(2×1). We qualify that these energy differences are quite small and maybe within the error bars of our slab model. We also note that the use of thicker slab layers would lower the adsorption energy difference between fcc and atop sites by ~0.02eV/H, however, adsorption energy of fcc site remains lower (more stable) than that of atop sites when ZPE is taken into account (see Table S2).


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Previous calculations often assumed that fcc sites for θ > 1 remained fully occupied while the H*atop concentration increases with θ, i.e., fcc H are the majority species. On the contrary, our multi-site CE results show that H*atop are the majority species in the groundstates for θ > 1.

Figure 1: Eads + ∆EZPE versus H coverage on Pt (111) for various fcc, hcp and atop H configurations. Eads is evaluated via Eq. (1) and ∆EZPE is given in Table 1 for H at different adsorption sites. Different H distributions are marked according to the legend provided. Groundstates are marked in circles and forms the groundstate hull (red line); groundstates with θ ≤ 1 ML consist of H adsorbing on fcc sites only while H are found distributed on both fcc and atop sites for 1 0, which have important implications for the kinetics of the HER.42 H*atop has also been detected at U > 0 in polycrystalline Pt via infrared adsorption spectroscopy.17 The coverage trends can be explained in the following: At U > 0.5 V, concentration of H* is small at all sites and there is little H*- H* repulsion. As U decreases, coverage of H*fcc grows much more rapidly than H*hcp and H*atop, since adsorption of H*fcc is more energetically favorable. With the H*fcc coverage approaching 0.4 at U = 0.1 V, the probability of strong repulsion with H*hcp and H*atop becomes appreciable. Subsequently, the coverages of H*hcp and H*atop decrease with decreasing U and vanish at c.a. −0.2 V. At more negative U (less than −0.3 V), the reaction energy gain in adsorbing an extra H (see Eq. ∆G ∆GQ H IR ,

( 8 )) overcomes the repulsion (between adjacent H*atop and H*fcc) and the

coverage of H*atop increases. For our simulations, the coverage is constant at θ = 1 ML for −0.4 < U < −0.2, corresponding to the p(1×1) groundstate (see Figure 2). For θ > 1, DFT calculations have shown that H would next adsorb onto atop sites. Mean-field theory calculations3,43 showed that the onset of atop site occupation occurs at c.a. −0.3 V, with fcc sites still being fully occupied. In contrast, our MC simulation, shows that the onset of increase in H*atop occupation occurs c.a. −0.4 V, with a simultaneous decrease in fcc site coverage, consistent with our discovery that H*atop is the majority specie in the groundstates for θ > 1. The atop site coverage increases with decreasing U, until a state is reached at c.a. −0.7 V, where the occupation of the atop and fcc sites are 1 and 2/3 respectively, corresponding to the groundstate at θ = 5/3 (see Figure 2). H*hcp is the minority specie in our studied range of U; at dilute coverages, the adsorption energy is c.a. 0.05 eV higher than that of fcc and for θ > 1, the presence of H*fcc strongly repulses (ECI is 0.15 eV in set MCfull) the occupation of hcp site.


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Lastly, the use of thicker slab models increases the magnitude of adsorption energies by 0.01 to 0.03 eV/H and increases the relative stability of atop sites by ~0.02 eV/H with respect to fcc sites (see Table S2). Thus we expect that the overall adsorption coverage at each U would increase marginally and the relative coverage of atop sites to be higher when thicker slabs are used to model the HER.

Figure 3: Adsorption isotherms for the full CE (left) and the fcc-site-only CE (right) under standard conditions. Left: Contributions to the total coverage (black curve) from adsorbed H*fcc, H*atop and H*hcp are given by dashed (red), dotted (blue) and dot-dashed (orange) lines, respectively. Inset: Coverage of H*atop and H*hcp magnified. Right: Adsorption isotherms for sets MC1, MC2 and MC3 (see

Table 2) are shown as dashed (green), dot-dashed (red) and solid (blue) lines, respectively. Without pair repulsion, full coverage is achieved at U = 0. Inclusion of NN pair repulsion lowers the H coverage.


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For comparison, we also show the adsorption isotherms for CEs that consider fcc sites only (see

Table 2). With only the ECIs among fcc sites included, set MC1 recovers the Langmuir isotherm and at U = 0, θ = 1. Including NN-fcc pair ECI (repulsive) decreases the coverage. The pair ECIs in sets MC2 and MC3 are obtained from previous literature27 and via a fit to fcc-only configurations in our set respectively. The stronger repulsive ECI in set MC3 results in a lower coverage than MC2 for all U. We note that the adsorption isotherm for the MC3 agrees very well with the MCfull for θ < 1. This implies that equilibrium coverage for U > −0.3 V can be modeled accurately without considering the trace amounts of H*hcp and H*atop present.

Theoretical Cyclic Voltammetry The adsorption isotherms in Figure 3 are next used to estimate the cyclic voltammetry27 curves from experiment, where the current for the hydrogen electrode is obtained by cycling the voltage between two values. The measured current may be expressed as

cd

cd cf cg

j b ce b cf cg ce .

Here,

cg ce

( 10 )

is the linear sweep rate and Q is the charge transferred, assumed to be one electron per

adsorbed H (see Volmer’s reaction). Hence, the relation between charge transferred per unit area of Pt (111) surface and coverage is given by Q iQ &, where iQ is 241 µC/cm2,27 given by e times the (experimental) Pt (111) surface density, and corresponds to 1 ML of H* coverage. Using a sweep rate of

cg ce

cf

= 50mV/s and deriving cg from Figure 3, we plot the positive part of


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the calculated voltammetry in Figure 4 (the full curve is symmetric about j = 0). For –0.3 0), these weakly adsorbed species, in particular H*atop, are expected to desorb more easily and would contribute significantly to the HER.42 Furthermore, a significant proportion of these H*atop have adjacent H*fcc too (Figure 5). To illustrate the effect of minority species, the coverage of H*atop at U = 0 is 0.006 ML but its inclusion increases the exchange current (see Supporting Information) from 1.0 x 10-6 A cm-2 to 1.1 x 10-3A cm-2, bringing the prediction closer to the experiment value of 4.5 x 10-4 A cm-2.18

∗ ∗ ∗ Figure 5: P Huvv |Hx"yz in solid (black) and the coverage of fcc sites, P8 Huvv , in dashed (red)

versus U. The fcc and atop sites are adjacent to each other (see cluster (n=2, f=2) in Figure S1).


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CONCLUSION We explored configurations of H* adsorbed on Pt (111) for coverages up to 2 ML and identify low-energy ones using a cluster expansion (CE) constructed from DFT adsorption energies that include multiple, interacting fcc, hcp and atop sites. Single-point effective cluster interactions (ECI) in the CE reproduce the adsorption energies at the dilute limit and the multi-body ECI capture the interactions (mostly repulsive) between neighboring H*. Adding zero-point and vibrational corrections to the ECI, and assuming that the Volmer’s reaction is in quasiequilibrium, the multi-adsorption-site CE is utilized in the Monte Carlo simulation to assess the equilibrium H coverage on Pt (111) for a wide range of voltages, −0.9 < U < 0.5 versus the standard hydrogen electrode. For U > −0.4 V, we found that H*fcc is the majority species as is commonly known in literature, although we show that traces of H*hcp and H*atop are also present. These weakly adsorbed species are expected to contribute significantly to the HER as a result of their lower activation barriers for the Tafel’s and Heyrovsky’s reactions (compared to H*fcc). For U < −0.4 V, the overall H* coverage increases beyond 1 ML but with H*atop now becoming the majority specie – in contradiction to previous mean-field studies which assumed that H*fcc is the majority specie at all voltages. The abundance of H*atop together with its low activation barrier should make Pt (111) a good HER electrocatalyst at high coverages (U < −0.4 V). Importantly, for catalyst design, we can identify adsorption species for HER catalysts, predict the conditions when active adsorption species are in abundance, and identify the optimal operating conditions, e.g., temperature and voltage.

ASSOCIATED CONTENT


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Supporting Information. Table and figure showing effective cluster interactions. Plot of Pt total energy versus lattice constant. Tables showing the effects of slab thickness and lattice constant on adsorption energies. Section and table showing exchange current estimations. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * Address correspondence to [email protected]. Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources TLT and KWB acknowledge internal funding from Institute of High Performance Computing. DDJ and LLW efforts at Iowa State were supported by the U.S. Department of Energy (DOE), Office of Basic Energy Sciences, Division of Chemical Science, Geosciences and Bioscience under contract DEFG02-03ER15476. Ames Laboratory is operated for DOE by Iowa State University under Contract No. DE-AC02-07CH11358.

ACKNOWLEDGMENT TLT acknowledges the use of supercomputers in A-STAR Computational Resource Centre (ACRC). ABBREVIATIONS DFT, density functional theory; ECI, effective cluster interaction; CE, cluster expansion; HER, hydrogen evolution reaction; HOR, hydrogen oxidation reaction.


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Hydrogen Deposition on Pt(111) during Electrochemical Hydrogen

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