Water Adlayers on Noble Metal Surfaces: Insights from Energy Decomposition Analysis Paul Clabaut,1 Ruben Staub,1 Joachim Galiana,1 Elise Antonetti,1 and Stephan N

Water Layers On Noble Metals Water Adlayers on Noble Metal Surfaces: Insights from Energy Decomposition Analysis Paul Clabaut,1 Ruben Staub,1 Joachim Galiana,1 Elise Antonetti,1 and Stephan N. Steinmann1 Univ Lyon, Ecole Normale Supérieure de Lyon, CNRS Université Lyon 1, Laboratoire de Chimie UMR 5182, 46 allée d’Italie, F-69364, LYON, France (Dated: 7 May 2020) Water molecules adsorbed on noble metal surfaces are of fundamental interest in surface science, heterogeneous catalysis and as a model for the metal/water interface. Herein, we analyse 27 water structures adsorbed on five noble metal surfaces (Cu, Ag, Au, Pd, Pt) via density functional theory and energy decomposition analysis based on the block localized wave function technique. The structures, ranging from the monomers to ice adlayers, reveal that the charge-transfer from water to the surface is nearly independent from the charge-transfer between the water molecules, while√ the√ polarization energies are cooperative. Dense water-water networks with small surface dipoles, such as the 39 × 39 unit cell (experimentally observed on Pt(111) ) are favored compared to the highly ordered and popular Hup and Hdown phases. The second main result of our study is that the many-body interactions, which stabilize the water assemblies on the metal surfaces, are dominated by the polarization energies, with the charge-transfer scaling with the polarization energies. Hence, if an empirical model could be found that reproduces the polarization energies, the charge-transfer could be predicted as well, opening exciting perspectives for force field development.

I. INTRODUCTION charge-transfer, which encompasses electron sharing. This energy decomposition not only provides deep insight into the Ice-like water layers over noble metal surfaces are widely bonding, but also allows to gain information for force field 37 studied, both experimentally and theoretically.1–4 Due to development: The charge-transfer (chemisorption) is the term the sparsity of the characterization of the metal/water inter- that is the most difficult to reproduce, as it is intrinsically a face, they are sometimes considered model systems for the many-body term with no generally applicable analytical ex- solid/liquid interface,5–9 even though the validity of this ex- pression known for it. The polarization is, on the other hand, a trapolation is far from obvious.10,11 Furthermore, the ice ad- better understood many-body term, which can be modelled via layers are regularly used to model the metal/liquid interface in induced dipoles, themselves modelled according to different (electro-)catalysis.12–16 The alternatives for approximate treate- techniques. BLW, which includes polarization at the DFT level, ments of the solvent are implicit solvents,17 which do not com- also defines the limit of which precision can be expected from pete with adsorbates for surface sites,18 microsolvation19,20 a polarizable force field in the absence of error cancellations which solvates adsorbates only locally, and ab initio molecular between different interaction energy components. dynamics, which is computationally very expensive21. To achieve this detailed insight, the remaining of the work is structured as follows: After describing the computational The most commonly reported and applied√ ice adlayers√ over closed-packed noble-metal surfaces are the 3 × 3 Hup and details, we analyse the stability of the various ice-layers on Hdown models, going back to the seminal STM work of Doering the five investigated metal surfaces. Next, we perform an on Ru.1 However, larger unit cells have been observed for EDA for the ice-layers, but also for 23 smaller (monomer to Pt(111)2 and explained in terms of more disordered ice-like heptamer) clusters. According to these computations, the polar- layers featuring ring-structures of various sizes.3 ization interaction is strongly correlated to the charge-transfer energy, so that the total interaction can be estimated based on Previous theoretical studies have focused on the bonding 38 mechanism of individual monomers on metal surfaces22,23 or the (linear-scaling ) BLW energy. Furthermore, we quantify on the possibility of water dissociation.24 Herein, we focus on the cooperativity between water–water and water-metal polar- non-dissociated water layers, fully covering the noble metal ization interactions and evidence a competition between the surfaces. The purpose of this study is, on the one hand, to water–water and water–metal charge-transfer interactions. elucidate the relative stability of these ice-like structures on five noble metal surfaces (Cu, Pd, Ag, Pt, Au) and, on the other II. METHODS hand, to identify the driving force of their formation via energy decomposition analysis. We rely on dispersion corrected DFT to achieve a balanced description between water–water and We start by defining the total adsorption energy of a given water–metal interactions.25,26 system: Energy decomposition analysis (EDA) is a powerful tool ∆Eads = ESCF − E opt − n · EW opt + ∆EBSSE (1) which is mostly applied in molecular chemistry,27–29 but also sur f 30 31–33 increasingly in condensed phase and at surfaces. In par- where ESCF is the standard KS-SCF energy of the full system, ticular, we have recently extended the block localized wave Esur f opt and EW opt are the corresponding energies of the freely function (BLW) technique34–36 to metallic surfaces.33 The optimized surface and water molecule, respectively. n is the BLW based EDA now allows to decompose the adsorption number of water molecules in a given system. Since the BLW energy into four terms: deformation, frozen, polarization and is only defined in a localized basis set, we have to correct for the Water Layers On Noble Metals 2 basis set superposition error (BSSE), which we do according covers electrostatic interaction and Pauli repulsion27 as well 39 41 to the counterpoise procedure of Boys and Bernardi , giving as dispersion interactions . ∆Epol is the polarization energy rise to the (by definition positive) energy correction ∆EBSSE . which is obtained by variationally optimizing the BLW. ∆ECT As common in BLW-EDA,27,40,41 we decompose the total is, finally, the charge transfer interaction that includes the co- adsorption energy ∆Eads into: valent bond formation. Note, that the BSSE only affects the charge-transfer term, as all other terms are evaluated using the ∆Eads = ∆Ede f orm + ∆E f rozen + ∆Epol + ∆ECT (2) same fragment-decomposed basis set.

where ∆Ede f orm is the preparation or deformation energy, The following equation summarizes the scheme and different ∆E f rozen is the frozen energy term that describes the interac- terms. Further details on the computation of these terms are tion of the isolated fragment densities brought together and given in the corresponding equations as indicated:

BLW ∆Eint (Eq.6) z }| { ∆Ede f orm ∆E f rozen ∆Epol ∆ECT −∆EBSSE Eisolated −−−−−→ E f ragments −−−−→ ESFD −−−→EBLW −−−−→Ecor −−−−−→ ESCF (3) Eq. 4a Eq. 4b Eq. 4c Eq. 4d | {z } ∆Eint (Eq.5) | {z } ∆Eads(Eq.2)

38 where Eisolated = Esur f opt +n·E opt is the sum of the electronic near linear scaling with respect to the number of fragments, Wi energy of each fragment optimized separately, E f ragments = which contrasts with the cubic scaling for the computations n Esur f sys + ∑ E sys is the sum of the energy of each fragment including the charge-transfer interactions. i Wi evaluated in its final geometry. The superscript “sys” corre- For the energy decomposition analysis and its interpretation, sponds to the energy of a fragment in the geometry adopted each system is either divided into two blocks (one for the metallic surface, one for all the n water molecules together) or in the presence of the other fragment. ESFD is the total energy into n + 1 blocks. after Superposition of the Fragment Densities, EBLW is the total energy obtained by the Block Localized Wavefunction33 and Taking the frozen interaction as an example, we denote the standard decomposition: Ecor corresponds to the final energy of the complete system, corrected for the BSSE, while ESCF is the energy obtained by ∆E f rozen = ∆E f rozen(W1,...,Wn,sur f ) (7) a standard SCF computation. This leads to the following definitions for the four terms of as the situation where every water molecule Wi is treated as a the adsorption energy as decomposed in Eq. 2: separate subsystem. This contrasts with decomposition into two blocks, the surface and the adlayer: n sur f −layer [ ∆Ede f orm = Esur f sys − Esur f opt + E sys − n · EW opt (4a) ∆E f rozen = ∆E f rozen( Wi,sur f ) (8) ∑ Wi i i n where all the water molecules are treated together as a single ∆E f rozen = ESFD − Esur f ,sys − E sys (4b) ∑ Wi block and the surface is a second block. Finally, in order to i assess many-body effects, we also determine the “additive” ∆Epol = EBLW − ESFD (4c) frozen interaction: ∆ECT = ESCF − EBLW + ∆EBSSE (4d) n add ∆E f rozen = ∑∆E f rozen(Wi,sur f ) (9) Furthermore, we define the interaction energy, ∆Eint as the i adsorption energy excluding the deformation energy, i.e., where we perform n separate computations, one for each water molecule, and then sum the corresponding contributions. ∆E = ∆E + ∆E + ∆E (5) int f rozen pol CT The standard decomposition leads to the most complete in- Similarly, we define the BLW interaction energy as the interac- teraction while Eq. 8 excludes the water–water interaction tion energy that excludes the charge-transfer interaction: components and Eq. 9 is free of any many-body interactions. It is, therefore, possible to define the missing part of the inter- ∆EBLW = ∆E f rozen + ∆Epol (6) action component NonAdd add ∆E f rozen = ∆E f rozen − ∆E f rozen (10) Since ∆EBLW include all polarization contributions at the DFT level but excludes any charge-transfer, it can be understood as which represent the non-additive part of the interaction. the interaction energy of an “ideal” polarizable force field. Fur- Analogous equations to Eq. 7-10 can be written for the thermore, computationally its evaluation can be performed with polarization and charge-transfer energy. Water Layers On Noble Metals 3

III. COMPUTATIONAL DETAILS relation between the lowest surface energy of each metal and the reported experimental value. Except for Cu, the trends are The adsorbed structures were optimized with VASP nicely reproduced. Since, furthermore, the interatomic distance 5.4.142,43 using periodic boundary conditions applying the of Cu is significantly smaller compared to the other metals and re-optimized Perdew, Burke and Ernzerhofer (PBE) functional thus less compatible with the ideal H-bond length of ∼ 2.8 to make it compatible with the non-local van der Waals (vdW) Å, this might indicate that liquid water behaves differently on functional, in short optPBE-vdW44 functional. An energy cut- Cu(111) compared to the other noble metal surface. off of 400 eV is chosen for the expansion of the plane-wave basis set. The electron–ion interactions are described by the PAW formalism.45,46 The unit cells are built from bulk plat- B. Electronic Analysis inum (2.821 Å nearest neighbor distance) with four metallic layers. The out-of-plane vector of the unit cell was chosen to Before moving to the energy decomposition analysis, we be ∼ 20 Å to achieve a negligible interaction between periodic here investigate the electronic nature of the various interfaces images. Coordinate files for all discussed systems are available by computing the surface dipole moment and the workfunction in the supporting information. Φ. The workfunction is intimately connected to the electro- In CP2K,47,48 the molecular orbitals were represented by chemical potential and it has been argued that the Hup and a double-ζ Gaussian basis set with one set of polarization Hdown phases should co-exist over large potential ranges.9,10 functions, called DZVP-MOLOPT-SR-GTH for both BLW- However at that time the three other surfaces investigated here EDA and BSSE corrected SCF DFT simulations.49 A cutoff have not been assessed. of 400 Ry was used to describe the electron density. The All ice adlayers taken alone, except Hup for all metals and exchange-correlation (XC) energy was approximated with the chain-Hdown on top of Cu(111), feature a positive dipole mo- 44 optPBE-vdW functional. Like in VASP, the Brillouin zone ment, meaning that there is a positive charge accumulation on was described at the Γ-point. Goedecker, Teter and Hutter the “bottom” and a negative one on the “top” (see SI). The 50 √ (GTH) pseudo-potentials based on the PBE functional were maximum (1.4 eÅ) is obtained for 39 over Pd(111), while used to describe the interactions between the valence electrons the minimum is found for Hup over Cu(111) (-2.7 eÅ). The and the ionic cores, and the electronic smearing was approxi- water layers, when optimized on different metallic surfaces mated by a Fermi-Dirac distribution at 300 K. As discussed in (and hence, on different lattice size), undergo noticeable geom- 33 our previous publication the 18 valence electron potential is etry distortions. A specific layer, evaluated without metallic necessary for Pt to obtain similar results between CP2K and slab but in the perturbed geometry corresponding to different VASP. For Cu and Au the 11 valence electron potential is ap- metals, can exhibit a range of dipole moment up to 1.3 eÅ. This plied. For the adopted choice, Fig. S1 provides the comparison maximum is obtained for the Hup layer optimized on Au(111) between CP2K and VASP, showing an excellent agreement. (-1.4 eÅ) compared to the one from Cu(111) (-2.7 eÅ). Since In order to identify the water molecules in the ice-layers, water is adsorbed only slightly stronger on Cu than on Au(111), where the atoms are ordered by elements rather than molecule, this shows that it is mostly the lattice missmatch, and not so we have used our in-house code imecs, which is provided in much the interaction strength with the metal, that affects the the supplementary information. electronic structures via geometrical constraints significantly. Similarly, the change in workfunction upon adsorption of an ice adlayer depends significantly on the metal (larger changes IV. RESULTS AND DISCUSSION in absolute values for Pt, Pd and Cu than for Ag and Au) and on the ice layer (see Fig. 3). In particular, the workfunction A. Relative Stability of Ice-like Layers is lowered by almost 3 eV when adsorbing the Hup layer on Pt, Pd and Cu, but “only” 1.6 V on Au and Ag. Given the very We are comparing five previously reported ice-like layers reductive nature of the Hup structure,9 its stability is doubt- up (depicted in Fig. 1) on√ five metals,√ which we will denote H , ful in itself. Even though one could have expected that the Hdown, chain-Hdown, 37 and 39. The nominal coverage of Hdown layer has the opposite effect, this is not the case and the these structures is 0.67 ML for the first three,√ 0.70 and 0.72 workfunction still drops for Pt and Pd (-0.8 eV), but remains ML for the last two. Figure 2 shows that the 39 structure unchanged for Cu and increases slightly (0.2 eV) for Ag and leads to the lowest surface√ energy Γ for almost all metals, Au. This not only shows that a purely geometric analysis of the closely followed by 37. Cu(111) is the exception in the structure is not enough to retrieve the trends on the electronic sense√ that it is√ the only metal investigated herein for which structure, but also that the metal-dependant interaction plays a Γ( 37) < Γ( 39). Concomitantly, Cu(111) has the lowest major role. interatomic distance of 2.58 Å which compares to 2.80 Å for As expected based on basic physical principles,53 the surface Pd, which is the second smallest metal investigated here. dipole moments of the hydrated metal surfaces are correlated In terms√ of absolute values, the surface energy of Pt(111) with the change in workfunction (∆Φ), with an intercept of for the 37 structure is 1.73 kcal/(mol· Å2), which compares zero (see Fig. S3). In other words, a positive surface dipole to 0.46 kcal/(mol· Å2) for the adhesion of solid water at ∼ 100 moment is associated with a positive change in workfunction K51 and 3.45 kcal/(mol· Å2) for the Pt/liquid water tension.52 and vice versa. Given the generally positive dipole moments For a broader comparison to experiment, Fig. S2 shows the cor- for the isolated layers as discussed above, the dominance of Water Layers On Noble Metals 4

FIG. 1: Structures of the ice adlayers on Pt(111) together with their short-hand notation as used herein. The unit cell is indicated in green. For the small unit cells, a supercell is chosen to have comparable sizes for all systems and allow the use of the Γ point only in the DFT computations.

negative changes in Φ, and, thus, the negative dipole moments for hydrated surfaces, require additional explanations. Indeed, 0.40 Hdown the change in dipole moment upon adsorption is generally Hup up ) negative (the one exception being H on Cu(111)), with an

2 0.35 Chain-Hdown average of -0.8 eÅ and a minimum of -1.6 eÅ (chain-Hdown Å 0.30

1 37 on Pt(111)). This nicely demonstrates a “universal” interac- l

o 0.25 39 tion between water and noble metal surfaces featuring a net m

l polarization (or charge-transfer) from water to the surface, i.e., a 0.20 c

k the surface becomes more negatively charged and behaves as a (

n 0.15 i more reductive system compared to vacuum. Note, however,

m √ 0.10 √that the arrangements with the lowest surface energy ( 39 and 37) feature a ∆Φ close to zero and thus also the smallest 0.05 surface dipole moments. 0.00 In summary, both the energetic and the electronic structure Pt Pd Cu Ag Au analysis support the idea that the lowest energy arrangement√ of water on noble metal surfaces might resemble the 39 2 FIG. 2: Surface energies√ Γ in kcal/mol/Å relative to the most structure, i.e., densely packed, but containing various relative √stable ice adlayer, i.e., 39 for all metals except for Cu, where orientations of the water molecules. 37 is slightly more stable. The higher the bar, the less stable is the corresponding structure. C. Energy Decomposition Analysis

1. Water–Metal Interaction

Hdown Hup Chain-Hdown 37 39 The first, fundamental, question addressed herein is how 0.5 the interaction of water with a given metal surface depends on the arrangement of the water molecules and on the nature 0.0 of the metal surface. This question is, furthermore, of impor-

0.5 tance when aiming at the development of a second generation force field, improving over the existing ones that are fitted

) 1.0 V to monomer interaction energies, i.e., missing all many body e ( terms. Therefore, we start by analyzing the interaction of the 1.5 sur f −layer Pt preformed adlayers with the metallic surface, i.e. ∆Eint , 2.0 Pd and each of its components, defined in analogy to Eq. 8. This Cu means that the deformation energy is excluded, while the water 2.5 Ag molecules interact with each other freely, i.e., the water–water Au 3.0 charge-transfer associated with the hydrogen bonds is present at all stages of the analysis. As a consequence, the water–water CT does not directly contribute to the studied energy differ- sur f −layer FIG. 3: The change of workfunction (∆Φ) when an ice ence: the “frozen” term, ∆E f rozen , solely accounts for the adlayer is adsorbed on a (111) noble metal surface. electrostatic, steric and dispersion interaction between the ad- sur f −layer layer and the metal surface. The polarization term ∆Epol is mainly composed of the polarization of the metallic surface Water Layers On Noble Metals 5

up ) H Au 1 o 10 40

l Au

o Cuo ) m Cu 1 20

l Pto l a 5 Pt o c Au

k l ( m 0

l t Cul a n c e 0 20 k n Ptl ( o

r p e

y 40 m a l

o 5 c

f r W

y 60 L u g s B r E e 10 n 80 E

100 surf layer surf layer surf layer surf layer Eint Efrozen Epol ECT 300 250 200 150 100 50 0 Esurf layer (kcal mol 1) FIG. 4: Average (per water molecule) frozen, polarization, int charge-transfer and interaction energy for oligomer and ice FIG. 5: The interaction of the water subsystem with the metal adlayer interaction energies with metal surfaces. The error bar sur f −layer surface at the BLW level, ∆EBLW , is plotted against the gives the standard deviation among all the 27 considered sur f −layer corresponding total interaction energy, ∆E . The systems. Red dots give the specific values for the Hup layers. int oligomers (o) and adlayers (l) are given by separated√ symbols. The (l) point most left and right corresponds to 39 and Hup, respectively. and the adlayer, but also contains a response of the water–water interaction due to this polarization. Finally, the charge-transfer contribution Esur f −layer captures the charge-transfer between ∆ CT ponents and the profound difference between Hup compared the metal surface and the adlayers and its repercussions on the to the other ice adlayers, let us discuss them at the example water–water interaction. To simplify the discussion, we will of Pt(111), even though the observations and conclusions for only discuss the case of three metals: Pt, Cu and Au. Indeed, the other metal surfaces would barely differ. First, many water the corresponding values for Pd resemble Pt very closely and molecules in the ice adlayers are not adsorbed in the optimal the same is true for the couple Ag and Au. On the other hand, single molecule geometry. This contributes to a lowering of the we enrich the discussion by including oligomeric clusters on Esur f −layer the surface, in order to deduce more general trends than just repulsion (∆ f rozen ) for the ice adlayers compared to the av- up observation of the five ice adlayers. erage (4.6 vs. 8.9 kcal/mol). For H this repulsion is even only 0.6 kcal/mol, illustrating the little steric hindrance between the Fig. 4 reports average energies per water molecule for the ice-layer and the metal surface. The polarization energy is simi- interaction energy and its components. As expected based larly small for Hup (-1.6 kcal/mol) while the two Hdown adlayers on the single molecule adsorption25, the average interaction feature ∆Esur f −layer ≈ -5 kcal/mol. ∆Esur f −layer reaches even energy is largest for Pt (-9.5 kcal/mol) and smallest for Au f rozen √ f rozen √ (-6.2 kcal/mol). Note, that this is less than the single molecule ∼-8 kcal/mol for the more complex 37 and 39 structures, a adsorption (-10.6 and -7.5 kcal/mol), indicating that the net value that compares well to an average of -8.3 kcal/mol for all effect of high coverage is slightly repulsive. 27 systems considered. The situation for the charge-transfer, sur f −layer sur f −layer When moving to the components, we can first note a general ∆ECT , is close to the observations for ∆E f rozen , i.e., trend for all components to be, in absolute value, more impor- up sur f −layer H only marginally benefits from CT (∆E f rozen = −3.3 tant for Pt than for Cu, than for Au. For instance, the steric kcal/mol), while the other structures are, with -7.8 kcal/mol repulsion, at the origin of the positive sign for ∆Esur f −layer sur f −layer f rozen somewhat shy of the average ∆ECT of -10.1 kcal/mol. is highest for Pt and almost zero for Au. This can be traced These observations demonstrate that Hup behaves differently back to “geometrical” reasons, with a mean distance Au–O of compared to the other adlayers.√ However,√ most of the other ice 3.20 vs. Pt–O of 2.98 , which is a consequence of the overall adlayers, and in particular the 37 and 39 structures which stronger adsorption on Pt, which leads to shorter internuclear are the most stable ones, are closely related adsorption patterns distances. The origin of this strong difference in geometry, and that can be mimicked via oligomers. The oligomers have the sur f −layer thus steric repulsion, is mostly found in ∆ECT , which is advantage of offering access to a larger diversity. Furthermore, more than twice for Pt compared to Au (-10.1 vs -4.2 kcal/mol). since they are just molecular clusters on the surface, they can The same proportion applies to the polarization energy, but relax and accommodate more easily the various lattice con- sur f −layer sur f −layer overall, ∆Epol is less stabilizing than ∆ECT , ex- stants, in contrast with the periodic addlayers that need to be cept for Cu, where they average to -5.9 and -5.4 kcal/mol, stretched or compressed to fit into the unit cell. respectively. From the perspective of designing a force field, the most To give an illustration of the spread of the individual com- important question at this point is if the charge-transfer energy Water Layers On Noble Metals 6

respectively. This oxophilicity can explain the importance up 0 of CT over Pt(111). Strikingly, with the exception of the H , Au down down sur f −layer H and chain-H adlayers, ∆ECT can be estimated Cu sur f −layer sur f −layer

) from ∆E (see Fig. 6). The slope of ∆E vs 1 50 Pt pol CT l sur f −layer o ∆Epol only slightly depends on the metal when exclud- m

l up down down a 100 ing the “outliers”, which are H ,H and chain-H . The c k (

slope is close to unity for Pt and Au, whereas it is only 0.7 r e y

a for Cu. However, for the latter the slope rises to 0.9 when l 150 f

r excluding all ice adlayers, revealing once again the impact of T u s C

E the lattice mismatch. Hence, if an accurate prediction of the

200 surf layer surf layer metal/water polarization energy could be found via an empiri- ECT (Au) =0.938 Epol (Au) -5.153 Esurf layer(Cu) =0.654 Esurf layer(Cu) -6.219 CT pol cal force field, the corresponding charge-transfer term could Esurf layer(Pt) =0.833 Esurf layer(Pt) -13.012 CT pol be estimated without a detailed physical model. This possibil- 200 150 100 50 0 surf layer 1 ity opens encouraging perspectives for the next generation of Epol (kcal mol ) water/metal force fields. sur f −layer sur f −layer FIG. 6: Correlation of ∆ECT with ∆Epol . The empty symbols correspond to the three outlier adlayers (Hup, Hdown and chain-Hdown) which are excluded from the 2. Adsorption energy of water at noble metal surfaces correlation. Having established that the interaction energy between an ice adlayer, or just a water oligomer, and a noble metal surface between the ice-like layer and the metallic surface is indeed can be expressed in terms of the frozen energy and a scaled required. Hence, Fig. 5 reports the interaction energy of the polarization energy, we now tackle the more general question water subsystem with the metal surface when charge-transfer of the total adsorption energy on metal surface. ∆Eads, (Eq. is neglected (∆Esur f −layer) as a function of the total interaction 2) accounts for all the many-body interaction terms, i.e., the BLW water–water many-body interactions that are already present Esur f −layer energy (∆ int ). To better distinguish the behavior of the in the absence of a metal surface,54 the water–metal many- oligomers (o) and the complete ice adlayers (l), the two groups body interactions at the interface and, moreover, the change of are depicted with different symbols, but using the same color. the water–water interaction due to the presence of the metal For the oligomers (o) Fig. 5 it is evident that for Pt (green) surface. there is no relation between the BLW (polarization-only) and To settle the stage, Fig. 7 represents the same kind of analy- the total interaction energy. However, for Cu (orange) and sur f −layer Au (blue), where the role of CT is less important, there is a sis for ∆Eads, as Fig. 4 does for ∆Eint , i.e., the different good correlation between the two quantities, suggesting that interaction energy components per water molecule for each relative adsorption energies could already be estimated at the metal. The first, general, comment is that the two Figures BLW level. The BLW computations could benefit from a look quite similar, with the same increase in absolute value significant speedup due to its (near) linear scaling, dramatically of all terms when going from Au to Cu and then to Pt. The reducing the computational cost of sampling phase space at additional energy contribution, ∆Ede f orm, turns out to be of the metal/liquid interface. When considering the ice adlayers minor importance overall (<1 kcal/mol). Even for Cu(111) the (l) we first see a rough correlation for all three metals which deformation energy is not larger than for Pt, despite the more supports the suggestion that CT might not be necessary for important lattice missmatch. This can be traced back to the relative energies at the metal/liquid interface. At a closer look, relative rigidity of the water molecules compared to the softer the value for Hup point (rightmost points of the (l) series) does hydrogen bond interactions between them. Hence, while the not fit in the correlation for any of the metals. Apparently, monomer geometry do not respond much to the unit cell, it is Hup has a non-typical behavior, meaning its properties are the assembly into an adlayer that has to adapt upon adsorption. significantly different from other water arrangements on noble metal surfaces. We, therefore, advise against its use in practical On average, ∆Eads only differs by ∼2 kcal/mol per water applications as a model for the water/metal interface. molecule between Au (weakest adsorption) and Pt (strongest adsorption), even though the magnitude of the major adsorp- Even if in the absence of CT a good correlation with sur f −layer tion energy components differ by at least a factor of two. In ∆Eint can be obtained, in absolute terms it cannot be order to uncover if this similarity is only true on average or sur f −layer sur f −layer neglected: ∆Eint in the absence of CT, i.e., ∆EBLW , if it due to a more “universal” similarity of the interaction of is not even stabilizing for Pt and only mildly so for Cu and water with any of the noble metal surface, Fig. 8 reports the sur f −layer Au (see Fig. 5). This demonstrates that ∆ECT is a correlation of adsorption energies on Pt(111) and Cu(111) with significant term over all the metals and most important on the more physisorption-like adsorption on Au(111). Due to Pt. Platinum is known to be more oxophilic than Au and Cu, the large absolute difference between the adsorption energies which is also seen in the water monomer binding energy, which of oligomers (up to -90 kcal/mol) and ice adlayers (up to - is -10.6 for Pt(111) vs -8.5 and -7.5 kcal/mol for Cu and Au, 380 kcal/mol), the two families of systems are separated. The Water Layers On Noble Metals 7

3. Non-Additivity and Cooperativity of Water–Water–Metal Many-Body Interactions 15

) Au 1

l Cu

o 10 Operationally, modification of the water–water interaction

m Pt

l at the metal interface cannot be distinguished from the mod- a

c 5

k ification of the water–metal interaction due to the presence (

t of co-adsorbed water molecules. We first quantify and com- n 0 e NonAdd n pare the non-additivity of the interaction energy (∆Eint = o

p NonAdd NonAdd NonAdd 5 ∆E + ∆E + ∆E ) for oligomers on Pt(111)

m f rozen pol CT o

c and Au(111). The non-additivity (Eq. 10) measures the differ-

y 10

g ence in the interaction energy between the sum of single water r e

n molecules interacting with the surface and the assembly of all E 15 water molecules interacting with the metal surface. NonAdd Eads Edeform Efrozen Epol ECT For the oligomers, ∆Eint contributes to more than 30% to the total interaction energy. In other words, the non- additivity is significant for a quantitative understanding of the FIG. 7: Average (per water molecule) deformation, frozen, interactions at the metal/water interface. Fig. S5 demonstrates, polarization, charge-transfer and adsorption energy for NonAdd 2 however, that ∆Eint correlates very well (R = 0.93 and oligomer and ice adlayer adsorption energies with metal slope of almost unity) between the two extreme metals, Au surfaces. The error bar gives the standard deviation among all (weak adsorption) and Pt (strong adsorption), suggesting that it the 27 considered systems. NonAdd is a “universal” quantity. The components of ∆Eint do not all behave the same: The repulsive frozen terms is very weakly correlated (R2 ≈ 0.5), but noticeably smaller for Au than for oligomers (Fig. 8a) have slope close to unity and the intercept Pt (roughly one third). This is to be expected since the water reflects the stronger adsorption of a single water molecule on molecules are further away from the surface on Au than on Pt. Cu and Pt compared to Au(111). For the ice adlayers (Fig. Oppositely, the non-additive charge-transfer and polarization 8b), Cu(111) is nearly indistinguishable from Au(111). The energy are quite well correlated between Pt and Au and bring combination of the two figures clearly shows that even though about the correlation between the metals. water oligomers are more strongly bound on Cu(111) than Having established the “universal” character of the non- on Au(111), the lattice-missmatch affects the water adlayers additivity interaction, we now focus on the case of Pt(111) significantly. ∆Eads for ice adlayers on Pt(111) is, with a slope to obtain a geometric understanding of its origin. Since the of 1.24 against Au(111), stronger and indicative of additional structures are essentially two-dimensional, we do not simply stabilization on Pt(111) compared to the other noble metals determine the coordination number,55 but perform a directional compared to the oligomers. This stabilization is presumably analysis: in each structure, the H-bond (H···O distance be- due to a combination of stronger chemisorption and a well- low 2.5 Å) acceptors are identified. Then, they are classified matching metal lattice. according to the Pt–O distance (<3.0 Å for chemisorbed wa- Despite this seemingly simple distinction between adlayers ter molecules, > 3.0 Å for physisorbed molecules). The θ and oligomers when analyzing the differences between metals, and φ rotational angles, which describe the rotation of the the individual components offer a complementary insight. In water dipole moment with respect to the surface normal and Fig. 9 we trace ∆ECT as a function of ∆Epol for the three the rotation of the molecular plane around the dipole moment, metal surface. When excluding the three “exceptional” and respectively, provide natural, additional parameters (see Fig. energetically less stable ice adlayers (Hup,Hdown and chain- S4 for a graphical definition). In order to simplify the analysis, Hdown), an excellent correlation is obtained with slopes of the two-dimensional space spanned by θ and φ is divided into about 1.5 for all three metals. This slope is higher compared 9 rectangles for the physisorbed water molecules. The limits of to the near unity slope from Fig. 6, where only the interaction these rectangles are optimized to find the optimal linear model between the adlayer and the metal surface was analyzed. The reproducing the non-additivity for all 27 structures, i.e., includ- origin of the difference is two-fold: first and foremost, the ing the ice adlayers. For the chemisorbed molecules, only two water–water interaction, which is directly present in the scaling combinations are necessary (see Table S1). The root mean of Fig. 9, features a comparably stronger CT component with square error of this linear regression amounts to 1.37 kcal/mol respect to the polarization energy. Second, Fig. 9 also contains (see Fig. S6), demonstrating the good predictive power of the full cooperativity between water–water and water–metal this simple model. The advantage of the linear model is that interactions, which are quantified in more details in the next we also gain insight into geometrical arrangements that are subsection. The linear correlation of Fig. 9 means that ∆Epol responsible for the non-additivity. The corresponding energy is sufficient to retrieve the complex many-body physics of coefficients for chemisorbed molecules (see Table S1) indicate ∆ECT , even including the water–water interaction. Therefore, that the typical adsorption minimum of a single water molecule modelling the polarization energy in the absence of charge- (θ ≈ 80◦,φ ≈ 0◦, Pt–O ≈ 2.5Å) is the worst H-bond acceptor acceptor,NonAdd transfer should be enough to capture the essential features for (∆Eint = −3.0 kcal/mol), i.e., does not contribute the full adsorption energies ∆Eads. significantly to the non-additivity. This is compatible with the Water Layers On Noble Metals 8

200 Cu Cu

20 Pt Pt Au (ref) 250 Au (ref) ) ) 1 1 l l o 40 o 300 m m l l a a c c k k ( (

60 s

s 350 d d a a E E

80 Eads(Cu) =1.039 Eads(Au) -2.788 400 Eads(Cu) =1.076 Eads(Au) + 31.715

Eads(Pt) =1.084 Eads(Au) -5.550 Eads(Pt) =1.245 Eads(Au) + 38.296

100 380 360 340 320 300 280 260 240 80 70 60 50 40 30 20 10 1 1 Eads(Au) (kcal mol ) Eads(Au) (kcal mol ) (a) Oligomers (b) Ice adlayers

FIG. 8: The adsorption energy for oligomers (a) and ice adlayers (b) on Cu(111) and Pt(111) is plotted against the adsorption energy on Au(111).

0 Au

Cu ) 90 1

100 Pt l

6 o ) 80 1 m l

70 l o

7 a

60 c m

200 k l ) ( a 50 ( d c

8 d k 40 A (

n T 30 o C 300 9 N , E 20 r o t p

10 e

10 c t c n a 400 ECT(Au) =1.656 Epol(Au) -1.510 0 i

0 20 40 60 80 100 120 140 160 180 E ECT(Cu) =1.524 Epol(Cu)+ 6.819 ECT(Pt) =1.440 Epol(Pt) -1.027 ( )

300 250 200 150 100 50 0 1 Epol (kcal mol )

FIG. 9: The charge-transfer ∆ECT is correlated to ∆Epol for the adsorption energy. The empty symbols correspond to the FIG. 10: Representation of the non-additive energy three outlier adlayers (Hup,Hdown and chain-Hdown) which are contribution of physisorbed H-bond acceptors as a function of excluded from the correlation. their θ and φ characteristics. Dots indicate the observed points. The data is also available in Table S1 observation that the oxygen atom is already interacting with the metal surface via its lone-pairs. Therefore, its electrons are a potential H-bond donnor. A more in-depth study on model less available to interact with a third hydrogen atom. In con- systems would be necessary in order to deduce clearer trends trast, the typical building block of the ice-like layers, where the and adapted functional forms to reproduce these trends in an chemisorbed water molecule is tilted so that the hydrogens are empirical force field. pointing away from the surface (θ ≈ 50◦,φ ≈ 0, Pt–O ≈ 2.5Å) Now that we understand the geometrical origin of the is a better H-bond acceptor (-5.4 kcal/mol). The best H-bond non-additivity, we unravel its origin in terms of contribut- NonAdd acceptors are, however, not chemisorbed to the surface but ing components. Overall, ∆E f rozen is destabilizing while physisorbed (Pt–O> 3.0), and present all small φ values (<70◦), both the polarization and charge-transfer energies are stabi- meaning that the two hydrogens are at somewhat similar dis- lizing the adlayer and are responsible for ∼ 40% and 60% of NonAdd NonAdd tances from the surface. The very best region (-10.4 kcal/mol) ∆Eint − ∆E f rozen (i.e. the stabilizing component), respec- is found for θ > 120◦, which corresponds to two hydrogens tively and are highly correlated with each other (R2 = 0.98). pointing toward the surface, but with a lone pair of the oxygen The major exception to this trend is, again, the Hup layer for atom pointing in the direction of the surface, and thus, towards which the frozen interaction is attractive, but the polarization Water Layers On Noble Metals 9

and charge transfer provide less additional stability compared rameters of the H-bond acceptor molecule. In summary, our to the average. investigation highlights the closely related physics that governs the various noble-metal – water interaction and suggests that polarization energies should be enough to retrieve most of the 4. The synergy between water–water charge transfer and complex many-body interactions at the metal/water interface. water–metal charge transfer

syn ACKNOWLEDGMENTS The synergistic energy can be defined as ∆ECT = n NonAdd S ∆ECT − ECT ( Wi) = ∆ECT − ∑∆ECT (Wi,sur f ) − i i The authors thank the SYSPROD project and AXELERA S ECT ( Wi), which represents the CT-associated energetic Pôle de Compétitivité for financial support (PSMN Data Cen- i difference between, in one hand, the overall CT and, and in the ter). We are grateful to A. Michaelides for providing some of other hand, the sum of each individual charge transfer between the ice adlayers and to C. Michel for stimulating discussions. a single water molecule and the surface plus the charge transfer 1 within the isolated water layer. This synergy is therefore D. L. Doering and T. E. Madey, “The adsorption of water on clean and oxygen-dosed Ru(011),” Surface Science 123, 305–337 (1982). positive (destabilizing) if there is a competition between these 2A. Glebov, A. P. Graham, A. Menzel, and J. P. 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