Deprotonation and Cation Adsorption on the NiOOH/Water Interface: A Grand-Canonical First-Principles Investigation

Nickel-based oxides are highly active, cost effective materials for the oxygen evolution reaction in alkaline conditions. Recent experimental studies have revealed the importance of surface deprotonation and alkali metal cation adsorption on the activity of Ni oxide surfaces, in contact with aqueous alkaline electrolyte. As a first step to elucidate the role of the alkali adsorption for the activity, we performed first-principles electronic structure calculations to address the stable surface structures of β-NiOOH(0001) as a function of the operating conditions in an electrochemical environment. We present a grand-canonical approach to compute the surface Pourbaix diagram of the β-NiOOH/water interface for the processes of deprotonation and alkali metal cation adsorption. The results of this study emphasize the importance of double layer effects, including the adsorbate-induced change of surface dipole moments and the rearrangement of water molecules due to their strong interaction with the adsorbed species, for the most stable interface structure.

Oxygen Evolution; Density Functional Theory; Computational Hydrogen Electrode

Introduction
Green hydrogen will be essential as a fuel of a defossilized energy economy [1].
Compared with conventional fuels such as coal, natural gas and oil, hydrogen has the highest specific energy [2], and if used in fuel cells it constitutes a clean, efficient and sustainable technology [3]. 5 An already well-developed and cost-effective green technology for hydrogen production is alkaline water electrolysis, in which hydrogen gas is produced from the water splitting reaction under alkaline conditions [4]. In alkaline electrolyzers the anode and the cathode are immersed in highly concentrated alkaline solutions (e.g., NaOH or KOH). These electrodes are separated by a porous and 10 electrically insulating separator material, which is filled with a highly ionically conducting medium for hydroxide ions (OH − ) transport from cathode to anode.
The separator hinders H 2 and O 2 gases to crossover between the electrodes.
The electrochemical oxidation and reduction reactions take place at the anode and cathode surface, respectively. At the anode, the oxygen evolution reaction 15 (OER: 4OH − → 2H 2 O + O 2 + 4e − ) produces oxygen gas, O 2 , while at the cathode, hydrogen gas is produced via reduction of water in the hydrogen evolution reaction (HER: 4H 2 O + 4e − → 2H 2 + 4OH − ) [4]. The standard equilibrium potential of the overall water splitting reaction is 1.23 V. However, the practical operating cell voltage for hydrogen evolution lies between 1.5-2.0 V. The 20 additional voltage, also referred to as overvoltage or overpotential, must be applied to overcome the energy barriers of the OER. The overall system efficiency thus remains between 59-70 % for commercially available electrolysers [5,6]. Improvement of this efficiency and increasing the hydrogen production rate are pivotal practical goals to achieve for this technology. 25 Ni-based oxides are earth-abundant materials and recognized as promising electrocatalyst materials for alkaline electrolysers. They offer a favourable combi-nation of high electrochemical activity and stability [7,8]. Many attempts have been made to improve the electrochemical activity of Ni materials via modification of the composition and structure of the catalyst material, e.g., using doping 30 it with iron [9,10]; via novel synthetic design of nanoparticles and porous materials to increase the active surface area [11,12,13,14]; or OER enhancement through modifications in pH or the type and concentration of ionic species in the electrolyte [15,16].  [15]. 40 It was found that in highly alkaline pH, the degree of surface deprotonation increases, thereby producing negatively charged surface species (NiOO − ) that lead to an enhanced OER activity [15]. where A is Li, Na, K, Cs) on OER activity of NiOOH. The consistent activity 45 trend of Cs + > Na + > K + > Li + was found for both pure NiOOH as well as NiOOH containing iron impurities. Combining the deprotonation and alkali metal cation adsorption effects, one may speculate that the interaction of cations with negatively charged surface oxygen species (NiOO-A + ) plays an important role in stabilizing cations on the surface [16]. 50 Even more recently, the mechanism of OER based on deprotonation was investigated on the (0001) facet of NiOOH using density functional theory (DFT), which provided further support for the role of deprotonation in OER activity [17]. These calculations suggested that the deprotonation step is the potentialdetermining step with an overpotential of 0.44 V. It was discussed that this step 55 also oxidizes Ni 3+ to Ni 4+ , while not changing the oxidation state of surface oxygen atoms [17].
As a prerequisite for understanding the kinetic processes involved in the OER, the relevant local reaction conditions at the interface need to be revealed. Any mechanistic study should be preceded by the identification of the stable ab-60 sorbate structures [18]. Herein, we employ a first-principles grand-canonical approach to explore the thermodynamic stability of NiOOH/water interfaces for the processes of deprotonation and alkali metal cation adsorption under varying electrochemical conditions with respect to pH and electrode potential. We will discuss the crucial importance of double-layer effects such as the adsorbate-induced surface dipole moment as well as the explicit presence of water molecules [19,20,21,22] for the computed surface Pourbaix diagrams.

Computational Methods
Model system. The bulk structure of β-NiOOH used in our simulations is based on our previous study [23]. It is represented as a model system with a 1 × 70 2 × 1 unit cell, the stability of which compares well with the most stable bulk phases reported in the literature [24]. The material has the ABBCC oxygen stacking sequence [25], for which hydrogen atoms present in the inter-layer space create a saturated number of hydrogen bonds between the layers, in agreement with infrared spectroscopy measurements [26]. Surface structures were modelled 75 as three-layer slabs of β-NiOOH(0001) with 3 × 4 unit cells. Stoichiometric surface structures include 12 Ni atoms, 24 O atoms, as well as 12 H atoms per layer of the slab for β-NiOOH(0001). These unit cell configurations are commensurate with the addition of explicit water layers. A water coverage of 5/6 ML at NiOOH(0001), initially equilibrated with ab initio molecular dynamics 80 simulation at 140 K for 8 ps (1 fs time-step), was used [23]. The H-down configuration of water was found to be more stable on NiOOH(0001) due to formation of H-bonds between water and unsaturated surface O atoms.
The (0001) facet of NiOOH is terminated with 50% of O* and 50% OH*, as shown in Fig. 1 (a). Surface deprotonation was modelled by successive removal 85 of surface H atoms from the surface, while keeping the unit cell electroneutral at any given degree of deprotonation. Thereafter, adsorption of Li + , Na + , K + and Cs + ions on the fully deprotonated surface was considered, as shown in Fig. 1 (b). To find the most stable adsorption site for cations, all possible surface O adsorption sites on the deprotonated surface -including all atop, bridge and 90 the three-fold sites -were examined, from which the cations were found to be stabilized only on the four possible three-fold sites. Among these sites, site α, as shown in Fig. 1 (b), was found to be the most stable site for all cations, which is on top of the surface Ni atom and involves two of the deprotonated O atoms, as shown in Fig. 1 (b). The relative stability of these four sites is provided in   [27,28]. The ionic cores were represented by projector augmented waves (PAW) [29]. Kohn-Sham one-electron wave functions were expanded in a plane wave basis set with an 100 Table 1 of 5.5 eV, which was calculated by Li and Selloni [32] using linear response theory [33]. A geometry relaxation for bulk NiOOH was performed with a 12×12×8 Monkhorst-Pack k-point mesh [34] and a force threshold of 0.01 eVÅ −1 . For geometry optimizations of the slab models, we used 5 × 5 × 1 k-points, and a force threshold of 0.05 eVÅ −1 .

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Grand-canonical approach. Our goal is to explore the thermodynamic stability of the NiOOH(0001)/water system for the processes of deprotonation and cation adsorption under varying electrode potential and pH. This can be achieved by employing the combination of periodic DFT calculations and the grandcanonical approach based on the computational hydrogen electrode (CHE) [35,36,37,38]. In this approach, the change in the Gibbs free energy due to the formation of interface structure, normalized by the unit area, is given by, where, ∆G tot ads is the change in the Gibbs free energy of adsorption, µ i is the electrochemical potential of ions in the electrolyte, and n i is the number of adsorbed species i per unit cell surface area, A. In the CHE scheme, it is assumed that the electrode and the electrolyte are thermodynamic reservoirs for electrons and ions such as protons, respectively, whereas the reference system typically corresponds to the standard hydrogen electrode (SHE) [35,39]. At standard conditions (T=298 K, and P= 1 atm, and pH = 0), molecular hydrogen in the gas phase is in equilibrium with the solvated proton and the electron ( 1 2 H 2 (g) H + (aq) + e − ). Therefore, in thermodynamic equilibrium the corresponding chemical potential of hydrogen in the gas phase is equal to that of a protonelectron pair. Consequently, referring the potential to the SHE, we can avoid the calculation of the proton solvation energy in water and instead use the gas-phase energy of H 2 which can easily be calculated based on DFT: This way, the adsorption free energy is approximated by the total binding energy obtained using periodic DFT calculations, while the electrode potential U and pH enter this equilibrium expression to account for deviations from the standard conditions. The CHE is not only applicable to coupled proton-electron transfer processes but it can also be applied to any solvated ionic species [35,40,41]. For In thermodynamic equilibrium, where a A + is the thermodynamic activity of the cation A + . We assumed an activity of 0.1, which for an ideal solution correspond to a cation concentration of 0.1 M. The derivation of the Gibbs free energy of adsorption for the independent processes of deprotonation and cation adsorption is provided in the Supplementary Information (SI). For both processes of deprotonation and alkali metal cation adsorption at NiOOH(0001)/water, the total free energy is given by, where ∆G tot ads can be approximated by ∆E tot ads , which is obtained from DFT calculations, neglecting entropy and zero-point energy corrections, n H is the number of hydrogen atoms removed from the surface and n A is the number of adsorbed cations. Moreover, we have and In Eq. 5, E cohesive  and Li + adsorption. In thermal equilibrium, the most stable deprotonated surface is determined from the lowest ∆γ deprotonation at a given potential and pH.
As will be discussed, this way, the Pourbaix diagram for surface deprotonation can be constructed. with cation adsorption, and p dipole slab|water is that for the stoichiometric NiOOH (0001) surface. In both cases, the slab forms an interface with a water layer. d is the width of the double layer, i.e., the distance between electrode surface and electrolyte which lies in the range of 2.5 and 3.5Å; here, we apply the value of d=3Å consistent with the previous study [45].

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The absolute potential scale, U abs , can be shifted to the SHE scale, using the conversion U abs = U SHE + 4.44 eV, as recommended by Trasatti [46]. The potential at zero charge, U P ZC , is linearly correlated to the electrode work function in the absence of the electrolyte [47]. However, this correlation is empirical and it depends on the degree of orientation of surface water molecules as well as the electron density redistribution at the interface [48]. Mills et al. assumed U P ZC as zero in their similar investigation [45]. We consider U P ZC = Φ 0 +const. as hyperparameter, with Φ 0 = 5.3 eV as the experimentally measured work function of NiOOH [49], and evaluate a range of values from (-4.5,-3.5) eV for the constant term. This covers a range of (0.8, 1.8) V vs. SHE for U P ZC , in which NiOOH was reported to be stable in a pH range of 2 to 14 [50]. A change in the surface dipole moment relative to the stoichiometric surface due to deprotonation and cation adsorption was obtained from the direct correlation with the corresponding work function shift [51], where ε 0 and e are vacuum permittivity and elementary charge. The work function is calculated from the difference between the Fermi energy and the value of the one-electron potential in the vacuum region.

Results and Discussion
We first discuss the effect of accounting for explicit water layers as well as the 140 induced dipole on the stable surface structure of NiOOH(0001), followed by the discussion on the origin of this effect. Fig. 3(a) shows the change in the surface Gibbs free energy of adsorption, calculated in the gas phase, as a function of potential for a varying degree of deprotonation (Eq. 4) at a constant pH value of 13. At a given potential, the lowest value of ∆γ corresponds to the most 145 stable surface state. As the potential increases, deprotonation becomes more favourable at NiOOH(0001). Fig. 3(b) shows the results computed in the gas phase but by accounting for the interaction term of induced surface dipole by deprotonation with the electrode potential (Eq. 8). It is seen that the surface dipole can significantly facilitate the deprotonation by decreasing the free energy 150 of adsorption. This effect will be discussed later by computing ∆Φ as a function of the degree of deprotonation. Compared with the gas phase system in Fig. 3(a), surface water molecules tend 155 to prevent deprotonation by increasing the change in the adsorption free energy. In fact, water molecules stabilize surface OH species by forming hydrogen bonds with them. This effect has been explained in more detail in our previous work on the structure of water at NiOOH(0001) [23]. Fig. 3(d) shows the computed phase diagram by accounting for the shift in work function due to both 160 deprotonation and the presence of surface water molecules. As for the discussion on Fig. 3(b), the induced dipole decreases the change in the free energy of adsorption and thereby facilitates deprotonation at a given potential.  [49]. In the 175 case of cation adsorption, as reported in Table 3, the electron transfer is from  To understand the cation size effect on the electronic charge distribution, we  showing the 3D charge density difference, as presented in Fig. (b). Unlike Li + and Na + , electronic charge e − is accumulated on K + and Cs + . As shown in Moreover, the decrease was found to be larger for Cs + than Na + . In addi-215 tion, the same trend was reported for K + /Rh(111) [55], Cs + /W(100) [56], and for Na + , K + , Cs + adsorption on TiO 2 (100) [57]. A more recent experimental study reported that the local work function around an adsorbed K + decreases   explicit surface water molecules, as depicted in Figure 6(a), deprotonation becomes more favourable as the pH and potential increase; however, in this case 225 Li + adsorption is less favorable than deprotonation, thus its corresponding surface state does not appear in the diagram. This is mainly due to the large negative standard redox potential of alkali metals, which shifts ∆γ of the corresponding surface state to more positive values (see Eq. 4, Eq. 7, Table 2 and Figure 2). To balance this effect, one needs to further stabilize the cations on 230 the surface. Figure 6(b) shows the Pourbaix diagram generated from gas phase calculations but accounting for the dipole interaction term in the surface free energy of adsorption (Eq. 8). As previously discussed, the interaction of the induced dipole moment, that is caused by deprotonation, with the electrode potential further facilitates the deprotonation at lower potentials and lower pH 235 values; however, still with this correction Li + adsorbed state is less favorable than deprotonation states which is in contradiction with experiment [16].
Given the relatively large experimental Li + solvation free energy of -4.985 eV [45,59], it is crucial to include solvation effects for the adsorbed cations. As shown in Fig. 6(c) for the system at 5/6 ML water coverage, the strong interaction  Figure S1 illustrates the sensitivity of the generated Pourbaix diagrams to the hyperparameters of the model, namely, the potential of zero charge and the width of the double layer.
The computed Pourbaix diagrams for the adsorption of other alkali metal cations are shown in Figure S2. Whereas we also find a stability pocket for Na + adsorp-255 tion, no stable K + and Cs + adsorbate phases appear in the calculated Pourbaix diagrams. This is due to the fact that the larger the cations, the more positive the shift in their Gibbs free energy of adsorption. K + and Cs + might still adsorb on NiOOH(0001), but at lower concentrations which are associated with a smaller mutual dipole-dipole repulsion upon adsorption. Unfortunately, such 260 low concentrations are below the scope of the present study because of the significantly increased computational effort for larger surface unit cell required to model lower concentrations. Another possibility would be that K + and Cs + are present as non-specifically adsorbed cations.
The substantial difference between the Pourbaix diagrams in Fig. 6(a) and Fig-265 ure 6(d) indicates the importance of accounting explicitly for the surficial water layer and dipole interaction effects to obtain an accurate prediction of the stable interface structure for these systems. In this respect, oxide and hydroxide electrodes also behave differently compared to close-packed metal electrodes. For in contact with halide-containing aqueous electrolytes the explicit and also implicit presence of water can be safely neglected, still a semi-quantitative agreement with the experiment can be obtained [62]. This is due to the relatively weak and rather non-directional interaction of liquid water with close-packed metal electrodes [63]. In contrast, the interaction of water with hydroxide and 275 oxide surfaces has a much stronger covalent character leading to a much more directional bonding of the water molecules, which then becomes significantly modified in the presence of adsorbed cations.
This study represents the first important step towards a better understanding of the enhancement in the OER activity due to surface deprotonation and alkali 280 metal cation adsorption on NiOOH. We speculate that this enhancement is linked with the stronger polarizability of the cations that increases with their size and thereby also leads to larger decrease in the work function upon specific adsorption. Experimental strategies have been proposed to enhance the OER activity of NiOOH-based materials by manipulating the work function through 285 electron injection [64], which would support our speculation. However, we did not find stable specific adsorbate phases for the two largest cations K + and Cs + under operating conditions. Hence this change of the work function might also be caused by non-specifically adsorbed cations. Furthermore, it remains to be seen whether the direct interaction of the adsorbed alkali metal cations with 290 the reaction intermediates of the OER also contributes to the enhancement.
Further DFT-based computations are required to understand this effect.

Conclusions
In order to elucidate the role of the presence of alkali ions for the activity of the oxygen evolution reaction, we applied a grand-canonical scheme based on 295 the computational hydrogen electrode to determine the most stable interface structures of β-NiOOH/water under varying pH and electrode potential for the deprotonation and alkali metal cation adsorption processes. We discussed the crucial importance of double-layer effects due to induced surface dipole moment and the explicit treatment of surficial water molecules. We found that the

Acknowledgement
Financial support by the Alexander-von-Humboldt Foundation is gratefully acknowledged. This work contributes to the research performed at CELEST (Cen-310 ter for Electrochemical Energy Storage Ulm-Karlsruhe).