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A Density Functional + U Assessment of Oxygen Evolution Reaction Mechanisms on #-NiOOH Alexander J. Tkalych, Houlong L. Zhuang, and Emily A. Carter ACS Catal., Just Accepted Manuscript • DOI: 10.1021/acscatal.7b00999 • Publication Date (Web): 03 Jul 2017 Downloaded from http://pubs.acs.org on July 3, 2017

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ACS Catalysis 1

A Density Functional + U Assessment of Oxygen Evolution Reaction Mechanisms on β-NiOOH

Alexander J. Tkalych,† Houlong L. Zhuang,‡ and Emily A. Carter§,* †

Department of Chemistry, Princeton University, Princeton, NJ 08544, USA

‡

Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ

08544, USA §

School of Engineering and Applied Science, Princeton University, Princeton, NJ 08544, USA

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ABSTRACT

NiOx has long been studied both as a battery cathode material and electrocatalyst for the oxygen evolution reaction (OER). Numerous investigations have demonstrated that Fe-doped nickel oxyhydroxide (NiOOH) is one of the most active OER catalysts in alkaline media. Despite extensive research, however, many unanswered questions pertaining to the OER mechanism on this material remain. Here, using density functional theory (DFT)+U calculations, we compare several surfaces of β-NiOOH studied for the OER and determine that unlike some earlier models selected, the (001) surface is the most stable surface under electrochemical conditions. We then examine several magnetic states of this material and predict that, unlike bulk β-NiOOH, (001)-βNiOOH manifests a slight preference to be ferromagnetic. We then use the resulting structural model to compare in detail four commonly proposed OER mechanisms. In addition to excluding a proposed mechanism involving hydrogen peroxide formation, we identify multiple binuclear mechanisms with slightly lower overpotentials than the commonly studied associative mechanism. All exhibit overpotentials that coincide well with measured values. However, the similarity in calculated overpotentials highlights the fact that several mechanisms are likely to be operative under electrochemical conditions on β-NiOOH. This finding suggests that much of the complexity of studying the OER on NiOOH is due to multiple competing mechanisms occurring under given conditions, which should be accounted for in subsequent analyses.


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INTRODUCTION The production of fuels using renewable energy resources is a particularly promising path to enabling large-scale energy storage for future use.1-4 Catalytic water splitting using solar energy is among the most active areas of research in this field, either to produce renewable hydrogen or the protons and electrons required to reduce carbon dioxide. Despite substantial efforts, significant challenges remain for designing an optimal (photo)electrocatalytic system. Perhaps the most important problem is the large energy input required for water splitting. This energy requirement is a function of the high thermodynamic potential of the overall reaction (1.23 V) and the high anodic overpotential of the oxygen evolution reaction (OER).5-7 Moreover, some of the most active catalysts for the OER are based on scarce and costly materials like RuO2 and IrO2,4,

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limiting practical implementation. Improved fundamental understanding of the

underlying structural and mechanistic properties of OER catalysts could contribute to future design of practical catalytic water splitting systems. Among the many materials evaluated for their potential use as OER catalysts, one with a long history and great promise is nickel oxyhydroxide (NiOOH). First studied over a century ago by Jünger in Sweden10-11 and Edison in the U.S.A.,12-13 nickel hydroxide and nickel oxyhydroxide (collectively termed NiOx) was initially of interest due to its suitability as a battery electrode. It was used as the cathode material in a variety of battery chemistries in the ensuing decades, including MH–Ni, Cd–Ni, Fe–Ni, and Zn–Ni secondary alkaline batteries.14-17 Because of its commercial importance, NiOx was extensively investigated in order to improve its performance as a cathode material. Among the many properties considered was the onset potential for the OER. In batteries, the OER is a parasitic side reaction that reduces the discharge capacity of the cell.18-19 Thus, the motivation of numerous early studies was to increase the OER


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onset potential. In 1987, Corrigan discovered that small additions of Fe led to an unfortunate reduction of the OER onset potential, drastically undermining the performance of NiOx as a battery electrode.20 However, what initially led to deterioration in battery performance ultimately yielded improvement in electrocatalytic OER performance. This work thus was resurrected and extended by many groups 25 years later, most notably by Trotochaud et al.21-23 In particular, they demonstrated that pure NiOOH scavenges Fe from solution upon repeated electrochemical cycling, which results in an OER catalyst whose performance equals and even exceeds that of state-of-the-art catalysts such as RuO2 and IrO2.24-25 Much of the foundational work on NiOx was done in the 1970s by Witte and coworkers2628

Their work revealed that NiOx consists of four phases: β-Ni(OH)2, α-Ni(OH)2, β-NiOOH, and

γ-NiOOH. Each of these phases consists of NiO2 layers intercalated with hydrogen atoms in tetrahedral sites.29 Among the four phases, only the structure of β-Ni(OH)2 is known with a high degree of confidence.30 β-Ni(OH)2 is a compact, layered structure that contains only hydrogen atoms in the inter-layer space.31 Its space group is P 3 m1 (brucite) and its experimental lattice parameters are: a = b = 3.12 Å and c = 4.66 Å.32 Its major structural features are retained during the phase transition from β-Ni(OH)2 to β-NiOOH.29, 33-34 In previous work, we examined the electronic and structural features of β-Ni(OH)2 and β-NiOOH, proposing a new structural model for β-NiOOH more consistent with the experimental crystal structures of β-NiOOH than previously proposed geometries.35 Despite being extensively studied for over half a century, there is still little mechanistic consensus on the OER.36 This is partly due to the complexity of the reaction: it involves four electron and four proton transfer steps and a multitude of possible intermediates and pathways. Early work by Krasil’shchikov,37 O’Grady et al.,38 Kobussen and Broers,39 Bockris and


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Otagawa,40-41 and more recent work by Doyle et al.36 and Bediako et al.,42-43 invoked a variety of mechanisms for the OER on oxide surfaces. Many of these are summarized in an article by Doyle et al. (see Table 2 there).36 One of the reasons for the persistent ambiguity surrounding the OER is the difficulty in assigning measured kinetic parameters to a given proposed mechanism. In conventional electrochemical analysis, parameters such as the Tafel slope or the reaction order can be used to resolve basic mechanistic questions, e.g., the type of rate-determining step or the number of active sites involved.6,

44-45

However, the values of the kinetic parameters

corresponding to a given pathway are not unique, as shown in a comparison of several proposed mechanisms.36 For example, measurement of a particular Tafel slope cannot necessarily be used to identify the operative mechanism under a set of given conditions. Furthermore, the kinetic parameters might change for the same system under different conditions, suggesting that more than one mechanism might be occuring. Doyle and Lyons observed two different Tafel slopes for hydrous FeOx electrodes.46-47 Although they acknowledged that this could be the result of masstransport limitations, such as reduction in the effective electrode surface area with increasing gas evolution at the higher applied potentials, multiple corroborating experiments suggested that the observed differences were in fact mechanistically significant. Further difficulties in unravelling the mechanism arise due to uncertainties surrounding the exact nature of the surface structure of the catalyst.48-50 It is known that it is a metal-oxide surface and not a metal-terminated one that catalyzes the reaction.51 The most thermodynamically stable surfaces are not metal-terminated at the high potentials required to drive the OER. The significant hydrophilic character of these surfaces combined with the electrophilic species in solution result in these surfaces becoming extensively hydrated or hydroxylated.52-53 These hydrated phases often intermingle with the solution phase; under certain


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conditions, it might even be appropriate to think of the surface as containing multiple metal oxide complexes with molecular properties.54 Furthermore, there is persistent disagreement as to whether β-NiOOH or γ-NiOOH is more active towards the OER. Several studies claim that the β-NiOOH phase is more active,55-58 whereas others state that the γ-NiOOH phase is more active.23, 25, 43 Computer simulations of the OER may be able to assist in clarifying some of the ambiguity associated with this reaction on NiOx, and, together with experiments, provide greater understanding of the underlying processes. For example, theory can provide a thermodynamic assessment of the electrochemical activity of the OER. Of particular value is the ability to access individual reaction intermediates and free energy changes for each elementary step in a given mechanism. As such, several groups have examined the activity of both pure and doped NiOx towards the OER. Work by Li and Selloni in 2014 compared the OER activities of β-NiOOH, γNiOOH, Fe-doped β-NiOOH, Fe-doped γ-NiOOH, and NiFe2O4.58 Their calculations found that Fe-doped β-NiOOH has the lowest overpotential of all systems studied, with η = 0.26 V. In 2015, Friebel et al. also examined the OER activity of Fe-doped γ-NiOOH.59 They predicted an overpotential of η = 0.43 V, similar to Li and Selloni’s η = 0.48 V for the same material. More recently, Fidelsky and Toroker examined the effect of both H and OH vacancies on the OER activity of β-NiOOH.60 They found that while pure β-NiOOH exhibits an overpotential of η = 0.61 V, introduction of OH vacancies can reduce the overpotential to η = 0.26 V. In follow-up work, Fidelsky and Toroker examined the effect of Fe-doping on the OER activity of β-NiOOH and found that the overpotential was lowered to 0.36 V.61 Work by Doyle et al. examined the effect of the interlayer spacing on both undoped and Fe-doped β-NiOOH.62 They found that the overpotential for the OER varies from 0.35 V for Fe-doped β-NiOOH to 0.43 V for undoped β-


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NiOOH. These studies differed in numerous ways, including the phases of NiOOH considered, structural models used, surfaces on which the calculations were performed, and OER mechanism considered. The present work thus first seeks to justify the assumptions going into the theoretical model used to study the OER on β-NiOOH, using experimental evidence as benchmarks. We then use this fully vetted model to unravel fundamental aspects of the structural, electronic, and mechanistic details of the OER on β-NiOOH. In what follows, we first consider some of the surface facets proposed for studying the OER on β-NiOOH. We then contextualize our findings with those in the experimental literature. We then examine the effect of various magnetic states on the energetics of the surface model studied here, emphasizing careful consideration of the magnetic structure of β-NiOOH. Finally, we compare and contrast four different OER mechanisms that have been proposed for NiOx. In so doing, we uncover some of the reasons for the persistent ambiguity in identifying the OER mechanism for this material.

METHODOLOGY AND COMPUTATIONAL DETAILS Spin-polarized density functional theory (DFT) + U calculations were performed within the Vienna Ab-initio Simulation Package (VASP) version 5.3.3.63-66 The DFT+U method67-68 approximately and inexpensively addresses standard DFT’s spurious electron self-repulsion and missing derivative discontinuity in exchange-correlation (XC) that over-delocalizes electrons, thereby ameliorating the particularly poor description of first-row transition metal cations in DFT.69-70 A U−J value of 5.5 eV for Ni(III) was used in the Dudarev et al.70 DFT + U functional in combination with the Perdew-Burke-Ernzerhof (PBE) XC functional.71 This value, calculated using linear response theory, was taken from Li and Selloni’s work on β-NiOOH.58 In previous work, we confirmed that this value leads to accurate replication of the structural and electronic


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properties of β-NiOOH.35 Blöchl’s all-electron, frozen-core, projector-augmented-wave (PAW) method was used.72-73 PAW potentials acted on the self-consistently optimized 3d/4s electrons of Ni, 2s/2p electrons of O, and 1s electron of H. The total energy was converged to less than 1 meV/atom using a plane-wave kinetic energy cutoff of 750 eV and Γ-point-centered MonkhorstPack k-point meshes74 of 3 × 3 × 1 for unit-cell calculations involving β-NiOOH and 1 × 1 × 1 for supercell calculations of β-NiOOH. Structural parameters are provided in the Supporting Information. The positions of all atoms were allowed to relax during optimization whereas the lattice parameters were fixed to their equilibrium bulk values using the equilibrium in-plane lattice vectors predicted earlier.35 Structures were converged to a force threshold of 0.01 eV Å-1. The Brillouin zone was integrated using Gaussian smearing with a smearing width of 0.01 eV for geometry optimizations. Total energies were calculated using the tetrahedron method with Blöchl corrections.75 Vibrational frequencies of each surface with its adsorbed intermediates were calculated to determine whether the reaction intermediates were minima or saddle-point structures. Numerical Hessian matrices were constructed from finite differences of displacements and force components on each atom. The adsorbed atom/molecule, as well as the Ni/O/H atoms in the first layer nearest to the intermediate, were displaced by ±0.02 Å in all three Cartesian directions from their equilibrium positions. The resulting Hessian matrix then was diagonalized to yield vibrational frequencies corresponding to each mode. Enthalpic and entropic contributions were calculated using the ideal gas, rigid rotor, and harmonic oscillator approximations at standard state conditions to evaluate respectively the translational, rotational, and vibrational terms for the adsorbates prior to adsorption, along with only vibrational terms for the NiOOH slabs and


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adsorbates once bound to the surface. All energies reported herein are for structures that have been confirmed to be true minima. Several low-index cleavage planes, each composed of multiples of the NiOOH formula unit, were considered to determine the most stable surfaces of β-NiOOH. Initial structures therefore were cleaved along (1 0 0), (0 1 0), (0 0 1), (1 0 1), and (1 1 1) planes in order to

(

)

generate slabs. We also considered the 0115 surface studied by both Li and Selloni58 and Fidelsky and Toroker.60,

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The cleavage surfaces were selected so as to minimize dangling

bonds. A vacuum layer of 15 Å, enough to prevent interactions between periodic images of the slabs, was introduced between the slabs. Dipole interactions between slabs were addressed by introducing a priori dipole field and energy corrections in the direction perpendicular to the surface, resulting in an energy correction of no more than 0.02 eV. Slabs of five layers were used for all surface calculations. This thickness was found to accurately replicate the bulk density of states in the middle layer, which suggests that the surface layers of the slab experience a bulklike electronic structure from the interior layers. To compute the energy of a surface slab in a liquid environment, we adopted a polarizable continuum model within the framework of joint density functional theory (JDFT)77 where the solvent is treated as a dielectric continuum. This model also captures the physics of the polarization of the solvent molecules caused by the electric field resulting from the solute or surface. In the implementation of the JDFT model within VASPsol,78 the electrostatic potential of the electrons and nuclei is modified to take into account this polarization. We used water as the solvent (i.e., dielectric constant, ε = 78.0). In addition to including a polarizable continuum model of solvation for the calculation of the surface energies, solvation effects were approximated by covering each exposed metal ion with at least one surface-adsorbed species.


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This approximation is considered accurate for capturing trends in structurally similar systems and is consistent with previous computational work on this system.58,60 Possible effects related to the presence of a water overlayer were not considered, as related work on hematite found that an explicit monolayer of water had little effect on the calculated relative energies.79 The solvated surface energy is calculated using the same procedure outlined in our previous work.80

Mechanisms Numerous factors complicate the task of experimentally identifying the OER mechanism on NiOx. The mechanism can be affected by the pH,81 applied potential,46 the cyclic voltammetry voltage sweep rate,82 electrode substrate,83 and phase of NiOOH present.25,

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The ability to

explicitly set several of these factors in a simulation thus could contribute to a better understanding of the OER on this system. Among the useful data that can be obtained from calculations is the theoretical overpotential. The step with the largest positive free energy between two elementary steps in a mechanism determines the overall thermodynamics of the OER and is the rate-determining step (RDS) if under thermodynamic control. The difference between the potential corresponding to this free energy change and the overall thermodynamic reaction potential (here +1.23 V) gives us a lower bound for the overpotential, which could be higher due to kinetic barriers. It is important to distinguish between the concept of the thermodynamic RDS defined here and the potential-determining step (PDS), which is the step with the largest positive free energy between two elementary steps involving an electron transfer.84 The PDS identified in a mechanism need not be the overall RDS; the theoretical overpotential is not directly comparable to the overpotential derived from electrokinetic studies.85 However, as alluded to above, the theoretical overpotential represents a lower bound to the experimentally observed onset potential.86 Although the theoretical overpotential and onset


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potential are not the same, theoretical predictions can provide experimental guidance by identifying those steps in the mechanism hindering the overall reaction rate. The performance of a catalyst ultimately could be improved by reducing the energy of the intermediate state corresponding to the RDS. Despite the high level of ambiguity surrounding the mechanism, several experimental observations are useful for establishing both structural models and mechanisms. First, the active sites on oxide catalysts are generally considered to be coordinatively unsaturated sites that allow formation of adsorbed intermediates.87-88 In early mechanisms proposed for the OER on oxide surfaces, the initial step was assumed to be an initial discharge of hydroxide ions at a catalytically active surface site M.37, 39 This site then adsorbs a series of surface intermediates such as MOH, MO, and MOOH.39 Here, each reaction step is potential-dependent and involves transfer of a single proton and electron. This mechanism, i.e., the associative mechanism involving water adsorption onto an adsorbed oxygen, has been used by numerous theoretical groups to study the OER on various oxide surfaces.88-92 This was also the mechanism studied by both Friebel et al.59 and Fidelsky and Toroker60 in their work on NiOx. Despite the ubiquity of this pathway in the computational literature, numerous other OER mechanisms have been proposed over the past several decades. Our aim is to compare several of the more commonlyproposed mechanisms in the present work. Another major class of proposed OER mechanisms for NiOx involves a binuclear reaction path. Here, two oxygen adatoms combine to form O2 after a series of deprotonations. Such mechanisms were proposed by several groups, including those of Krasil’shchikov37 and Bockris and Otagawa.40 Su et al. compared the single-site, associative mechanism introduced above with a direct O2 recombination mechanism on β-MnO2.93 They found that the overpotential for the


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binuclear reaction path was nearly the same as, only 0.08 eV lower than, the single-site mechanism. Another notable mechanism proposed by O’Grady et al.38 has the reaction facilitated by redox transitions at the active metal site. The metal site was proposed to undergo oxidation during the adsorption of OH− and reduction during the release of the oxygen molecule. This mechanism was invoked to explain the low Tafel slopes often observed experimentally, without requiring strong surface adsorption of the various intermediates. Finally, several groups proposed that the electrocatalytic activity of oxide films is due to the presence of octahedrally-coordinated, anionic metal complexes (called surfaquo groups) rather than stoichiometric oxyhydroxide groups.36, 94-95 These surfaquo groups were introduced to rationalize the super-Nernstian E-pH shifts observed for several transition metal oxides, including NiOx. Our work here focuses on two types of mechanisms: the commonly-studied associative mechanism and binuclear mechanisms. The associative mechanism, based on work by Kobussen and Broers,39 is shown as Mechanism I below (the slab geometries are given in section S1 of the Supporting information). Three different binuclear mechanisms are considered, shown as Mechanisms II – IV below (the slab geometries are given in section S2 of the Supporting information). The intermediates for these mechanisms are shown in Figures 1 and 2. The first two of the binuclear mechanisms are based on the Bockris-Otagawa electrochemical path.40 These two mechanisms differ in the sequence by which the two water molecules are deprotonated. In the first mechanism, one of the water molecules is completely deprotonated before the second water molecule is deprotonated, whereas in the second mechanism, the two water molecules alternate one after another in their deprotonation sequence. These mechanisms were compared to establish whether or not the sequence in which the surface intermediates are deprotonated impacts the overpotential of the reaction. The last mechanism involves formation


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of a physisorbed hydrogen peroxide molecule intermediate. This mechanism was tested due to previous experimental studies hypothesizing its formation during the course of the reaction.40-41, 96

Note that this selection of mechanisms is by no means exhaustive. Rather than seeking to

identify the exact mechanism by which the OER proceeds on β-NiOOH, our work seeks to compare in detail some of the more commonly proposed mechanisms on an equal basis. OER free energy profiles were calculated for these four mechanisms. For steps involving the formation of H+ + e−, we obtain the free energy of that step implicitly by referencing it to the free energy of H2 using the standard hydrogen electrode (SHE, pH = 0, p = 1 atm, T = 298 K).97 As is commonly done, a correction of 0.84 eV was added to the energy of the O2 molecule to bring the bond energy into agreement with experiment, to compensate for the known overbinding of O2 by DFT-GGA.98 Zero-point energy and thermal corrections, added to the electronic total energy to obtain the free energy G of each species, are given in Section S3 of the SI. The theoretical overpotential does not depend on pH, as it is difference in two potentials at a given pH, so all results were calculated for pH = 0, in keeping with previous theoretical studies on this system.58-60 The theoretical overpotential is defined for a mechanism in which the most endoergic elementary step involves oxidation (or reduction). It is calculated by subtracting the cumulative free energies of all of the steps in the mechanism divided by the number of electrons involved (here four) – which gives the theoretical thermodynamic potential – from the potential of the most endoergic elementary redox step.


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Mechanism I: Single-site, associative mechanism


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Mechanism II: Binuclear H2O-O mechanism

Mechanism III: Binuclear OH-OH mechanism

Mechanism IV: Binuclear H2O2 mechanism


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Figure 1: Intermediates for Mechanism I. * denotes an adsorbed species, which are colored differently here and in Figure 2.

Figure 2: Intermediates for Mechanisms II – IV.


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RESULTS

Structural model We first set out to identify the surface on which to perform our OER calculations. βNiOOH may adopt numerous bulk structures; many of these are highlighted in work by Conesa.99 Here we focus on our previously proposed staggered proton model35 of β-NiOOH because of its predicted stability and its excellent agreement with measured structural and electronic properties. Previous computational studies on NiOOH considered only high-index

(

)

(

)

facets such as the 0115 or 0112 surfaces.58-60 These surfaces were studied because they were found to have high activities towards the OER in theoretical studies of CoOx, and because cleavage along those planes results in Ni-terminated surfaces in the structural models employed in those studies.100-101 However, we were unable to find experimental support justifying consideration of these high-index surfaces. We thus sought to first determine the most stable facet of β-NiOOH among these surfaces. To do so, we compared six different low-index facets and two types of terminations. Surfaces were cleaved along (100), (010), (001), (101), and (111) planes in order to generate slabs. For each facet, we considered both the Ni-terminated surface

(

)

and the OH-terminated surface. We also considered the 0115 surface studied by Li and Selloni58 and Fidelsky and Toroker.60 To include the effect of solvation, we also calculated what we call the solid-liquid interface formation energy: Einterface = Esolvation − E vacuum + Esurface .

Esolvation and Evacuum refer to the energies of the surface slab immersed in a liquid (here water, described by the continuum solvation model in VASP) and vacuum, respectively. Esurface denotes the energy cost to cleave a surface from the bulk. Therefore, Einterface can be thought of as the


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energy required to form a given facet in solution from the bulk structure. Full details on this calculation are provided in our previous work.80 The results of these calculations are shown in Table 1 below. Esurface (Surface Energy) (J m-2)

Einterface (Solid-Liquid Interface Formation energy) (J m-2)

Vacuum

Solvated

Ni(100)

1.50

1.15

Ni(010)

1.48

1.02

Ni(101)

2.39

1.87

Ni(111)

0.96

0.18

OH(100)

1.32

1.03

OH(010)

0.85

-0.38

OH(001)

0.09

-0.40

OH(101)

1.27

0.20

OH(111)

0.98

-0.25

Ni( 0115 )58, 60

0.87

0.01

Ni( 0112 )59

0.91

-0.02

Surface Termination (Cleavage Plane)

Table 1: β-NiOOH surface and solid-liquid interface formation energies; lowest energy shaded.

These predictions indicate that the OH-terminated (001) surface is most favorably formed in vacuum and in solution. This is to be expected, because formation of this surface only involves rupture of weak hydrogen bonds as opposed to other surfaces that require breaking strong Ni-O bonds to form. This result also corroborates a broad range of experimental data. First, it has been repeatedly observed that the (001) surface of β-NiOOH is the dominant facet formed under electrochemical conditions.14, 102-103 Second, metal-oxide surfaces have significant nucleophilic character, resulting in an extensively hydrated or hydroxylated surface. Finally, high


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OER activities are associated with systems operating under high pH values. Such conditions would naturally lead to a hydroxylated surface. These results therefore suggest that (001)-βNiOOH is the relevant surface on which to perform mechanistic calculations, not the higherindex surfaces studied previously. It bears noting that numerous synthetic procedures produce a catalytically active βNiOOH OER catalyst. It is not necessarily the case that a specific facet or surface character of βNiOOH is required for catalyzing the OER.23 Indeed, a study by Landon et al. compared the activities of Fe-doped β-NiOOH catalysts prepared using a variety of experimental procedures.104 They found that the surface areas of the resulting catalysts varied by almost a factor of three. When the OER activities were normalized by their respective masses, the authors found that the activities were similar. They therefore concluded that the observed variations in oxygen evolution activities could not be explained in terms of variations in electrocatalyst surface area. Trotochaud et al. suggested that, under certain conditions, most of the nickel atoms are electrocatalytically active.23 Thus, it is likely that intercalation of aqueous species, corresponding to the formation of the γ-phase of NiOOH, makes all nickel atoms accessible. Because intercalation occurs along the (001) plane, this further justifies studying the OER activity of the (001) surface.

Magnetism - Spin Configurations Inspired by Chen and Selloni’s study of the related material Co3O4,105 we examined several possible magnetic states (spin configurations) for (001)-β-NiOOH. Bulk Co3O4 is paramagnetic but Chen and Selloni showed that Co3+ becomes ferromagnetic (FM) at the surface. This led us to consider the possibility of spin configurations other than those found for bulk β-NiOOH. A number of previous theoretical studies of β-NiOOH neglected to examine the


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effect of various magnetic states.58-60 We therefore set out to identify the lowest-energy spin configuration among four different possibilities for Ni3+ in (001)-β-NiOOH: FM, antiferromagnetic (AFM), mixed spins (MS), and a “free” spin configuration. FM has all Ni3+ ion magnetic moments aligned throughout the sample. AFM has AFM coupling within and between the planes of Ni3+ ions. MS consists of FM Ni3+ at the surface and AFM Ni3+ in the layers beneath the surface. This configuration is analogous to the lowest-energy spin state found for Co3O4, where the surface consisted of FM Co3+ and nonmagnetic Co3+ within the bulk.105 Finally, the “free” spin configuration is merely the spin state resulting from not specifying an initial spin configuration in VASP, as appears was done in previous theoretical studies. We calculated the energy for slab thicknesses ranging from a single stoichiometric NiOOH layer up to five layers for each spin configuration. This was done to establish whether or not there was a thickness beyond which certain configurations became favorable.

Figure 3: Spin configuration relative stabilities for unit-cell and supercell structures

The results of this investigation are shown in Figure 3. The first important observation is that failing to specify the initial spin configuration for the calculations generally leads to slightly


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higher energy states. Secondly, the results indicate that the various spin configurations are nearly degenerate for both the unit-cell and supercell surface models. As the slab becomes thicker, the difference in energy between the various spin configurations is diminished. However, the FM configuration is lowest in energy for both the unit-cell and supercell surfaces and for all thicknesses considered. This finding contrasts with our previous work on bulk β-NiOOH, where the lowest energy spin configuration is AFM.35 Yet, as shown for both the unit cell and supercell, the difference in energies between various spin configurations becomes smaller as the surface becomes thicker. We therefore speculate that the AFM configuration becomes the electronic ground state after some critical thickness is reached. These results are consistent with those of Zaffran and Toroker, who examined the effect of the exchange-correlation functional on the magnetic properties of bulk β-NiOOH.106 Their work found that the difference between FM and AFM states was generally very small (< 0.1 eV difference). Experimentally, it has been shown that OER currents are maximized for thin films of NiOOH of fewer than 10 monolayers,21-22 which should therefore show a slight preference for the FM state. Based on these results, we set an FM initial spin configuration for all subsequent calculations.

Thermodynamics We first examine the influence of β-NiOOH surface hydroxylation on OER thermodynamics. Previous work in our group studied the OER on the (0001) surface of pure and doped hematite (α-Fe2O3).79 That study focused on the associative, unit-cell mechanism. An overpotential of 0.77 V was calculated for the pure hematite surface, in reasonable agreement with the measured overpotential of 0.5-0.6 V. That work found that the hydroxylated Fe2O3 (0001) slab is more energetically favorable than the O-terminated Fe2O3 (0001) slab. However, Rossmeisl et al. found that the OER overpotential on RuO2 was lower on an O-terminated slab


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than on an OH-terminated slab.88 We thus examined the effect of hydroxylation extent on the overpotential in each of the mechanisms considered in this work. Because a fully O-terminated slab model is not stable for NiOOH, we instead used a stoichiometric slab model (with half of the surface oxygen atoms hydroxylated) to assess the performance of a surface with less than full hydroxylation. The fully hydroxylated slabs have stoichiometries of Ni16O31H17 for the unit cell slab and Ni64O126H70 for the supercell slab. There is one coordinatively unsaturated Ni on one side of the slab in the unit cell and two in the supercell. The cumulative ∆G298 for all reactions, the calculated water splitting reaction energy, is predicted to be 4.68 eV. The predicted electrochemical reaction potential is therefore 1.17 V (4.68 eV/4e = 1.17 V), in close agreement with the experimental value of 1.23 V. As noted earlier, the theoretical overpotential is calculated from the difference between the most endoergic oxidation step in the mechanism and the water splitting reaction potential. Our calculated overpotential is lower on the fully OH-terminated surface (0.62 V) than on the stoichiometric surface (0.75 V; see Figure 4) and is nearly identical to Fidelsky and Toroker’s value on (001)-βNiOOH (0.61 V). This mechanism exhibits a small surface concentration dependence: when these calculations were repeated on a 2 x 2 supercell consistent with the supercells used for the other mechanisms, the overpotential on the stoichiometric surface decreases from 0.75 V to 0.61 V and from 0.62 V to 0.56 V on the hydroxylated surface; these ~0.1 V decreases actually serve to strengthen our ultimate conclusion (vide infra). These calculations predict that this mechanism’s PDS is formation of the OOH species by addition of H2O to an oxygen adatom followed by release of a solvated proton and electron (reaction D of Mechanism I). This PDS differs from what was predicted for hydroxylated α-Fe2O3 (the PDS there involves OH deprotonation)79 but is line with Rossmeisl et al.’s predicted PDS for OER on RuO2, IrO2, and


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TiO2.107 It is also consistent with measured overpotentials: Trotochaud et al. determined that the overpotential is >0.400 V upon rigorous exclusion of Fe.23 Fe-free β-NiOOH films at 10 mA cm−2 exhibited an overpotential of 0.529 V that increased with aging, stabilizing at 0.605 V after 3 days.108 Our results thus compare favorably with measured overpotentials, suggesting that the reaction is not kinetically but rather thermodynamically limited and occurs more easily on the fully hydroxylated surface. Note that our results here and below correspond to undoped βNiOOH, with the active Ni sites in the Ni3+ oxidation state – as judged by the DFT+U magnetic moments - regardless of the degree of surface hydroxylation. As suggested by Trotochaud et al., previous experimental work aimed at unravelling the OER on β-NiOOH may have been influenced by incidental iron contamination.23 Therefore our results are comparable only to those experimental studies in which trace Fe has been rigorously removed from the electrolyte. Predictions for the binuclear mechanisms involving the supercell surface models are shown in Figures 5 – 7 (see also section S4 of the Supporting Information). The first noticeable finding is that Mechanism IV, involving formation of a physisorbed hydrogen peroxide intermediate, is highly unfavorable. Secondly, the PDSs are the same for both Mechanisms II and III, namely deprotonation of a hydroxyl group, suggesting both pathways would be expected to occur. The overpotential for Mechanisms II and III is ~0.1 V lower than that found for the unit-cell, associative mechanism (Mechanism I). Mechanisms II and III produce O2 via direct coupling of two surface oxygen atoms. Other types of binuclear mechanisms that would involve O-O bond formation from OH and O coupling to form OOH, or via coupling of two OH to form OOH and a solvated proton and an electron, were also explored briefly, even though such pathways are not among those most frequently proposed. Compared to Mechanisms II and III, the former showed a negligible difference in overpotential (0.01 V) while the second exhibited a


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large increase in overpotential (~0.7 V) and thus could be ruled out. Thus, a binuclear mechanism involving direct combination of two oxygen atoms to form O2 or direct combination of OH and O to form OOH therefore appear slightly more probable under experimental conditions than the pathway involving only a single active surface site. This prediction is consistent with Su et al.’s prediction of an 0.08 V lower overpotential on β-MnO2 for a binuclear mechanism compared to an associative mechanism.93 However, these differences in overpotentials are not necessarily physically meaningful; such small differences in energy could be due to systematic errors in the DFT+U calculations. Our results thus suggest that pinpointing a single mechanism for the OER on β-NiOOH is ill-posed. Instead, the OER on β-NiOOH most likely occurs via multiple competing mechanisms.


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Figure 4: Cumulative free energies of reaction (∆G298) for stoichiometric and fully hydroxylated surfaces for the associative, single-site mechanism (Mechanism I). Each letter represents an elementary step and the height of each step is the free energy of the reaction denoted at the midpoint of the upper terrace of the step. Hence here reaction D is the PDS. The overpotential for the same mechanism calculated on the 2x2 cell is shown in parentheses. The same labelling convention applies to Figures 5-7.


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Figure 5: Cumulative free energies of reaction (∆G298) for stoichiometric and fully hydroxylated surfaces for the binuclear H2O-O mechanism (Mechanism II).


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Figure 6: Cumulative free energies of reaction (∆G298) for stoichiometric and fully hydroxylated surfaces for the binuclear OH-OH mechanism (Mechanism III).


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Figure 7: Cumulative free energies of reaction (∆G298) for stoichiometric and fully hydroxylated surfaces for the binuclear H2O2 mechanism (Mechanism IV).


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SUMMARY AND CONCLUSIONS The four most commonly proposed OER mechanisms for β-NiOOH were evaluated in detail, after determining the most realistic structure of the electrode surface. Analysis of surfaceliquid interface formation energies of several facets and terminations of β-NiOOH identifies the OH-terminated (001) surface to be the most stable under electrochemical conditions. Analysis of various magnetic states of films of varying thickness indicates that β-NiOOH thin films should be adopt a FM state, although other spin configurations are only slightly higher in energy. This preference in the thin film contrasts with the AFM state exhibited by bulk β-NiOOH. Using the robust structural model developed, reaction pathways for four different proposed OER mechanisms were evaluated in detail: the single-site, associative mechanism and three binuclear mechanisms. Two of the binuclear mechanisms, Mechanisms II and III, exhibit the same, lowest overpotential (~0.5 V), slightly lower than the value calculated for the associative mechanism (~0.6 V), and in excellent agreement with experimentally-determined values (0.53-0.61 V). Another mechanism with a PDS of OH and O coupling to form OOH prior to deprotonation to form oxygen exhibits essentially the same overpotential. By contrast, a mechanism involving hydrogen peroxide formation (Mechanism IV) was ruled out on the basis of the much higher predicted overpotential (~1.00 V), as was a mechanism involving direct coupling of two hydroxyl groups for the same reason (much higher overpotential). The small range among the lower values, however, highlights the likelihood that multiple mechanisms are operating on βNiOOH, illustrating at least part of the reason for the difficulty in unravelling the details associated with its electrochemical behavior.


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￭ ASSOCIATED CONTENT Supporting Information Optimized geometries and detailed energetics for each mechanism are provided. Zero-point energies and thermal corrections for each species are also given. This material is available free of charge via the Internet at http://pubs.acs.org. ￭ AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] Notes The authors declare no competing financial interest.

￭ ACKNOWLEDGMENTS We are grateful to the Air Force Office of Scientific Research for funding (Grant No. FA955014-1-0254). We acknowledge use of the TIGRESS high performance computer center at Princeton University. We also acknowledge use of the COPPER high performance computer center at the Air Force Office of Scientific Research High Performance Computing Center. We also thank Ms. Nari Baughman and Dr. Johannes M. Dieterich for critical reading of this manuscript.


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