Unraveling Oxygen Evolution on Iron-Doped Î²-Nickel Oxyhydroxide

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Unraveling Oxygen Evolution on Iron-Doped #-Nickel Oxyhydroxide: the Key Role of Highly Active Molecular-like Sites John Mark P. Martirez, and Emily A. Carter J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 13 Dec 2018 Downloaded from http://pubs.acs.org on December 13, 2018

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Journal of the American Chemical Society

Unraveling Oxygen Evolution on Iron-Doped β-Nickel Oxyhydroxide: the Key Role of Highly Active Molecular-like Sites

John Mark P. Martirez1 and Emily A. Carter2,* 1

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Department of Mechanical and Aerospace Engineering and

School of Engineering and Applied Science, Princeton University, Princeton, New Jersey, 08544-5263, United States *[email protected]

Abstract The active site for electrocatalytic water oxidation on the highly active iron(Fe)-doped β-nickel oxyhydroxide (β-NiOOH) electrocatalyst is hotly debated. Here we characterize the oxygen evolution reaction (OER) activity of an unexplored facet of this material with first-principles quantum mechanics. We show that molecular-like four-fold-lattice-oxygen-coordinated metal sites on the (1̅21̅1) surface may very well be the key active sites in the electrocatalysis. The predicted OER overpotential (𝜂OER ) for a Fe-centered pathway is reduced by 0.34 V relative to a Ni-centered one, consistent with experiments. We further predict unprecedented, near-quantitative lower bounds for the 𝜂OER , of 0.48 V and 0.14 V for pure and Fe-doped β-NiOOH(1̅21̅1), respectively. Our hybrid density functional theory calculations favor a heretofore unpredicted pathway involving an iron(IV)-oxo species, Fe4+=O. We posit that an iron(IV)-oxo intermediate that stably forms under a low-coordination environment and the favorable discharge of Ni3+ to Ni2+ are key to β-NiOOH’s OER activity.

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Introduction Electrochemical water splitting involves both the reduction and oxidation of water into molecular hydrogen (H2) and oxygen (O2), respectively, simultaneously occurring in physically separated chambers. The reductive hydrogen evolution reaction, or HER, (2H2 O + 2𝑒 − → H2 + 2OH − ) and oxidative oxygen evolution reaction, or OER, ( 2H2 O → O2 + 4H + + 4𝑒 − ) require distinct catalysts. Extensive research has been done on both fronts, aiming to improve the efficiency of the aqueous (photo)electrochemical cell.1-4 Of primary interest is optimization of the electrodes by improving their chemical activity, conductivity, and stability. In the aqueous phase, the thermodynamics from H2O to its oxidation products are well known and measured. The corresponding Latimer diagram in alkaline solution (pH = 14) is 0.50 V

O2 (𝑔) →

1.04 V

O− 2 (𝑎𝑞) →

1.69 V

HO− 2 (𝑎𝑞) →

OH − (𝑎𝑞)

(1)

where the standard reduction potentials are shown above the arrows, referenced relative to the reversible hydrogen electrode, or RHE, (-0.828 V vs. the standard hydrogen electrode, SHE, at pH = 14).5-6 The reversible potential to go from O2 all the way to H2O is 1.23 V vs. RHE at any pH. However, equation (1) indicates that a 1.69 V bias potential is needed if water oxidation is to occur via the hydroperoxide anion (HO− 2 ) intermediate. One therefore can define a thermodynamically limiting overpotential ( 𝜂OER ) of at least 0.46 V for OER in solution. Quantum-mechanical modeling has been used widely to identify likely elementary steps in the OER on a range of catalysts, including metals, metal oxides, and metal oxide clusters.7-10 From the calculated free energies of the elementary steps, 𝜂OER can be defined for the active site of a given catalyst. 𝜂OER thus can be used as a measure of the intrinsic activity of a catalyst toward OER, since it represents the lowest possible overpotential needed to make all steps spontaneous.7-10 One of the obvious


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limitations of this metric is that it does not reflect the actual rate-limiting kinetic barriers. 𝜂OER therefore, formally represents the lower bound of the minimum excess potential required for the OER on a given material and active site. An obvious route toward optimization of OER catalysts is to find electrode materials able to stabilize or bypass formation of high-energy intermediates. Biological catalysts, most notably the oxygen-evolving complex (OEC) of photosystem II, collect all four oxidizing equivalents prior to O-O bond formation. In the OEC, which consists of a Mn4CaO5 cofactor, three of the four Mn3+ ions are oxidized: two to Mn4+ and one to Mn5+ (forming an electrophilic terminal oxo species: Mn5+≡O or Mn4+=O∙), after which O2 forms.11-12 Fe-doped nickel oxyhydroxide (NiOOH) is one of the most promising catalysts for the alkaline electrochemical OER.13-21 Fe-doping is essential for the material’s exceptional activity.1415, 18, 22-23

For example, a study measured an overpotential of 0.529 V at 10 mA/cm2, increasing to

0.605 V after 3 days, for Fe-free Ni(OH)2/NiOOH catalysts when using rigorously purified KOH solution.18 In the same study, the overpotential decreases to 0.280 - 0.287 V at 10 mA/cm2, even without intentionally adding Fe, when unpurified KOH solution containing trace amounts of Fe is used (≤ 0.66 ppm Fe).18 They found that the catalyst can contain more than 10% Fe near and at the surface after about a five-day immersion in the unpurified alkaline electrolyte.18 In a separate study, intentional Fe doping (20-40 atomic % Fe) registered overpotentials between 0.275 and 0.300 V at 10 mA/cm2.14 For the purpose of identifying new catalysts, first-principles studies of the activities of the Fe-doped (0001)24-27 and {011̅𝑁} 16, 28-32 family of surfaces have populated the literature. The rationale for studying these surfaces is that the former surface is the most stable,25, 33-34 while the latter is presumed and subsequently shown to be more active. Atomic-scale quantum mechanical


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models based on density functional theory (DFT), using a semilocal exchange-correlation (XC) functional with Hubbard-like self-interaction (+U) corrections16, 28-29, 32 or a hybrid XC functional (B3PW91),30 found that the Fe-doped {011̅𝑁} surfaces have a lower theoretical 𝜂OER than their corresponding pure surfaces. Furthermore, when comparing studies of the Fe-doped (0001) and {011̅𝑁} surfaces within a similar theoretical framework, it becomes apparent that the latter surface is more active than the former. Experiments that deliberately favor low-coordination sites upon synthesis of the oxide observed higher OER yields. For example, using {111}-faceted Ni nanoparticles as precursors, βNiOOH shells that expose the oxide’s {100} facets were preferentially exposed.35 NiFe-hydroxide electrodes hydrothermally synthesized on Ni foam produced vertically aligned, highly faceted, hexagonal nanoflake arrays with long-lasting high OER activity.19-20 A highly porous NiFeoxyhydroxide electrode was synthesized through a chemical etching method that effectively leaches and depletes Cr out from a Cr-doped NiFe-oxyhydroxide. The porous catalyst was found to be 31% more active than the NiFe-oxyhydroxide synthesized similarly but without Cr-doping.36 Recently, we predicted that water can stabilize β-NiOOH surfaces featuring low-latticecoordinated atoms, due to the affinity of water for these sites.34 Although the (0001) basal plane was found to be the most stable facet (with a very low surface energy of 0.19 J m-2), other families of surfaces, i.e., {011̅𝑁} and {112̅𝑁}, are nearly as stable (0.40 – 0.60 J m-2), which therefore gives rise to hexagonal nanoplatelets,34 as observed experimentally.19-21 Of note, the {112̅𝑁} surfaces are very similar in energy to the {011̅𝑁} surfaces (e.g., the most stable surfaces of these families, (1̅21̅1) and (101̅0), have surface energies of 0.53 and 0.45 J m-2, respectively).34 {112̅𝑁} surfaces feature four-fold lattice-oxygen-coordinated metal sites and thus are expected to be more molecular-like in terms of chemical reactivity. In contrast, the (0001) and {011̅𝑁}


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surfaces exhibit six- and five-fold lattice-oxygen-coordinated surface cations, respectively. The {112̅𝑁} surface, featuring what is referred to as “corner” sites, was only recently suspected22-23 and experimentally demonstrated to be the likely OER-active surface of (Ni,Fe)OOH.23 Here, we computationally explore the OER activity of the (1̅21̅1) surface of β-NiOOH, a stable surface belonging to the {112̅𝑁} family, with and without Fe-doping. The quantummechanical simulations were conducted via DFT+U using the Perdew-Burke-Ernzerhof (PBE)37 XC functional, and via DFT using the more accurate but costly hybrid Heyd-Scuseria-Ernzerhof HSE0638-39 XC functional, with exact Fock exchange fractions α = 0.25 and 0.15. We find dramatic differences between the OER performance of the Ni- and Fe-centered active sites in all theories, and unprecedented, near-quantitative lower bounds for the 𝜂OER from HSE06 (α = 0.15). We show that OER activity of the Fe-doped β-NiOOH is a combination of the ability of surface Fe3+ to be oxidized to Fe4+ (stabilized by a terminal oxo moiety), and the “dischargeable” nature of Ni3+ sites (reduced to Ni2+). Much like the biological OEC, we find the system collects most of the oxidizing charge prior to O-O bond formation and is able to bypass generation of superoxo-like species.

Results and discussion Model and ab initio theories. Description of the surface. The β-NiOOH(1̅21̅1) surface is the result of a cleavage plane bisecting two Ni-O bonds per Ni.34 As a result, the exposed Ni (or Fe) is coordinated to only four lattice O (Fig. 1a). This frees a surface cation to form two additional bonds, dative or covalent, with adsorbates (e.g., water) to complete a hexacoordinate environment. For example, in Fig. 1a, two hydroxo ligands are attached to the surface dopant Fe. In Ref. 34, we


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computationally show that this surface (the {112̅𝑁} family in general) very favorably dissociates one water per surface Ni3+ site, resulting in a five-fold coordination sphere (OH − and H + going to the four-fold Ni and two-fold coordinated O atoms, respectively). Adsorption of a second water is nearly in equilibrium (vide infra).34 The strong affinity of the surface toward water makes this surface one of the thermodynamically favorable facets, along with the (0001) and the {011̅𝑁} surfaces, despite the higher number of broken Ni-O bonds upon its formation.34 XC validation. Accurate description of the highly correlated and localized nature of d electrons in transition metals is a challenge for DFT that uses approximate local and semilocal XC functionals. Hubbard-like self-interaction (+U) corrections therefore are commonly used on top of DFT to correct for the electron self-interaction that leads to spurious delocalization.40-42 The hybrid HSE0638-39 XC functional, on the other hand, includes a fraction of the exact Fock exchange (α) to alleviate such interaction. PBE+U was found to be inadequate for accurately describing the electronic structure of β-NiOOH.34, 43-45 The reparametrized HSE06 in contrast offers significant improvement over PBE+U (UNi, UFe = 5.5, 4.3 eV)28, 46 for predicting the electronic structure of pure β-NiOOH, Fe-doped β-NiOOH, pure α-FeOOH, and H2O, along with the thermodynamics of reactions involving OER-relevant molecules: H2O, H2, O2, H2O2, and HO2 (Section 1, Figs. S1S3, and Tables S1-S2 in the SI). We also explored the effects of the parameter α on the abovementioned properties (i.e., standard HSE06 has α = 0.25). We confirmed that α = 0.15 best represents the redox behavior of Fe-sites in β-NiOOH (as is found in other Fe-containing oxides),47-48 without compromising the description of the electronic structure of β-NiOOH (Section 1.1 and Figs. S1-S2 in the SI) and the chemistry and structural parameters of the OER-relevant molecules (Section 1.2 and Tables S1-S2 in the SI).


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Simulation models and partitioning formalism. We employ a nine-layer (9L) inversionsymmetric 2×2 slab (36 formula units) to model the (1̅21̅1) surface (Fig. 1a) using PBE+U (UNi, UFe = 5.5, 4.3 eV).28, 46 To be able to calculate energetics using the more expensive HSE06 XC, we utilize four-layer (4L) 2×2 slabs (16 formula units). The 9L and 4L slabs are equivalent except in their thicknesses (Fig. 1b). The energy then is evaluated in the spirit of the “our own n-layered integrated molecular26 orbital and molecular mechanics” (ONIOM)49 partitioning method. The free HSE06 energy of the reaction from HSE06 within the ONIOM scheme, ∆𝐺ONIOM , is evaluated via the

following equation: HSE06 PBE+𝑈 HSE06 PBE+𝑈 ∆𝐺ONIOM = ∆𝐺9𝐿 + (∆𝐸4𝐿 − ∆𝐸4𝐿 )

(2)

PBE+𝑈 PBE+𝑈 ∆𝐺9𝐿 and ∆𝐸4𝐿 are the reaction free energy (containing vibrational energy) and internal

energy changes evaluated from PBE+U for the 9L and 4L slabs, respectively (both structurally HSE06 relaxed). ∆𝐸4𝐿 is the DFT energy change for the reaction according to HSE06, structurally HSE06 PBE+𝑈 relaxed for α = 0.25 (see Methods). ∆𝐺9𝐿 and ∆𝐺ONIOM for α = 0.15 and 0.25 are shown in 𝐻𝑆𝐸06 with α = 0.15 is presented within the discussion, Tables 1 and 2 for comparison, although ∆𝐺𝑂𝑁𝐼𝑂𝑀

as it was demonstrated to be the most valid theory (Sections 1.1 and 1.2 in the Supporting Information, SI). Comparison of the results from the different theories employed here and theoretical models in the literature are presented in Section 1.3 in the SI.


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̅𝟐𝟏 ̅𝟏) surface. a, Ball-and-stick models of the 2×2 9L Fig. 1. Slab models for the β-NiOOH(𝟏 slab, showing two different side view profiles. The blue dashed-line borders the surface supercell. b, Model of the 2×2 4L slab. Side view profile as in the second panel in a.

Definition of the reference electrode. All potentials quoted here are relative to the reversible hydrogen electrode (RHE)50 at pH=14 (e.g., Eqn. 1), and energies and potentials calculated here are equivalent to having the RHE at pH=14 as the reference: 1⁄2 𝐺H2 ° − 𝑒𝐸RHE = (𝐺H+ ° + 𝐺𝑒 − ), where 𝐸RHE = 0.00 − 0.0592 × pH = −0.828 V at pH = 14, and 𝐺H2 °, 𝐺H+ °, and 𝐺𝑒 − are the standard Gibbs free energies of H2(g) and H+(aq), and the free energy of an electron at the electrode, respectively (see Methods). pH = 14 is chosen because most experiments for OER using NiOOH are conducted under very alkaline conditions (pH = 13 -14).13-21 Note however that when an RHE, which has the same pH (same electrolyte) as the working electrode, is used as a reference, the pH dependence in the Nernst equation vanishes for reduction (oxidation) reactions that consume (produce) equal numbers of protons (𝑛H+ ) and electrons (𝑛e− ), e.g., the OER reaction: O2 (𝑔) + 4(H + + 𝑒 − ) → 2H2 O.50-51 Thus, with this convention, when 𝑛H+ = 𝑛e− , whether the reactions are balanced with H+ and 𝑒 − or H2O, OH − , and 𝑒 − , the energetics remain


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the same (as they are simply differences in nomenclature) and the thermodynamic driving force for H2O to O2 oxidation becomes pH independent. However, pH dependence still arises when the dominant form of the redox-active species depends on pH and when 𝑛H+ ≠ 𝑛e− .51 Here, when comparisons are made against reduction potentials in the literature, the reduced and oxidized forms most stable at pH=14 are chosen, and potentials relative to the SHE are converted to relative to the RHE by subtracting 𝐸RHE (i.e., by adding 0.828 V at pH=14).


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̅𝟐𝟏 ̅𝟏) surface. Ball-and-stick models Figure 2. OER mechanism on the Fe-doped β-NiOOH(𝟏 showcase different intermediates on the Fe-centered active site. Structures shown are from the 9L models as predicted by PBE+U. Only the active site is shown for clarity: side view roughly along the [0001] direction (an example of the actual model is shown in Fig. 1a). The structures are named according to their fifth (and sixth) ligand(s) and named X’ or X’’ in the absence of both. Four categorically different routes are studied that can be defined by their distinct key intermediates: (1) η1-O2H route (Pathways A and B), (2) cis-dioxo route (C), (3) oxo route (D), and (4) dihydrogen peroxide (η1-O2H2) route (E and F). In Pathway D (light blue), top view, perspectives are included to show the Ni𝛾 -OH group. The eyeball icon depicts the viewing direction for the side-view perspective relative to the top view. The circles that outline some of the Ni and Fe atoms indicate approximate oxidation states as depicted in the legend; all other cations are in the +3 state. Table 1. PBE+U and ONIOM-HSE06 reaction free energies of the various possible elementary steps involved in the OER on the Fe-doped β-NiOOH(1̅21̅1) surface (Fig. 2). Product osb,c Reaction free energy vs. RHE a a (eV)c,d Step Chemical equation : Fe, Ni (α, β, γ) PBE+U α = 0.25 α = 0.15e + − A-1 1.48 FeOH + H2O → Fe(OH)2 + (H + 𝑒 ) 4↑, 3, 3, 3 1.56 1.92 A-1a 3, 3, 3, 3 -0.21 --FeOH + H2O → Fe(OH)(OH2) + − A-1b 1.77 --Fe(OH)(OH2)→ Fe(OH)2 + (H + 𝑒 ) 4↑, 3, 3, 3 + − A-2 1.83 Fe(OH)2 → FeOOH + (H + 𝑒 ) 4, 2↓, 3, 3 1.56 2.07 + − A-3 0.45 -0.20 0.37 FeOOH + H2O → O2(g) + FeOH2 + (H + 𝑒 ) 3↓, 2, 3, 3 + − A-4 1.35 1.37 1.00 FeOH2 → FeOH + (H + 𝑒 ) 3, 3↑, 3, 3 + − B-3 0.74 0.12 0.64 FeOOH → O2(g) + Fe + (H + 𝑒 ) 3↓, 2, 3, 3 + − B-4 1.05 1.05 0.73 Fe + H2O → FeOH + (H + 𝑒 ) 3, 3↑, 3, 3 + − C-1 = A-1 FeOH + H2O → Fe(OH)2 + (H + 𝑒 ) 1.56 1.92 1.48 4↑, 3, 3, 3 + − C-2 2.00 1.61 Fe(OH)2 → Fe(=O)(OH) + (H + 𝑒 ) 5↑, 3, 3, 3 2.15 C-3 1.85 Fe(=O)(OH) → Fe(=O)2+ (H+ + 𝑒 − ) 6↑, 3, 3, 3 2.10 1.92 C-4 -1.80 -2.04 -0.82 Fe(=O)2→ Fe + O2(g) 3↓, 2↓, 3, 3 + − C-5 = B-4 Fe + H2O → FeOH + (H + 𝑒 ) 1.05 1.05 0.73 3, 3↑, 3, 3 + − D-1 HOFeOH → HOFe=O + (H + 𝑒 ) 4↑, 3, 3, 3 1.72 1.89 1.37 HOFe=O + NiγOH + H2O → HOFe + O2(g) + D-2 0.31 0.02 1.23 3↓, 2↓, 3, 2↓ NiγOH2 + (H+ + 𝑒 − ) D-2a -0.51 -0.36 0.37 4, 2↓, 3, 2↓ HOFe=O + NiγOH→ Fe(𝜂2 -O2) + NiγOH2 2 2 D-2b 4, 2, 3, 2 0.01 0.04 0.08 Fe(𝜂 -O2) + H2O → Fe(𝜂 -O2)(OH2) D-2c 0.81 0.33 0.78 Fe(𝜂2 -O2)(OH2) →HOFe + O2(g) + (H+ + 𝑒 − ) 3↓, 2, 3, 2 HOFe + H2O + NiγOH2 → HOFeOH2 + NiγOH D-3 1.54 1.64 1.31 3, 2, 3, 3↑ + (H+ + 𝑒 − ) D-4 = A-4 HOFeOH2 →HOFeOH + (H+ + 𝑒 − ) 1.35 1.37 1.00 3, 3↑, 3, 3 + − E-1 FeOH + H2O → FeOOH+ (H + 𝑒 ) 3, 2↓, 3, 3 2.35 2.56 2.83 + − F-2 1.72 Fe(OH)2 + H2O → Fe(OOH)(OH) + (H + 𝑒 ) 3↓, 3, 3, 3 1.78 2.12 a

Text colors are the same as the colors of the corresponding pathway in Fig. 2. Chemical equations only show changes at the Fe site, except in steps D-2, D-2a, and D3, which also include Niγ.


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b

Oxidation states (os) of select cations in the product of the step, approximated from spin-density atomic projections (Table S3 in the SI). The α and β Ni indices correspond to the two nearest Ni neighbors of Fe (see “hydroxo”, Fig. 2), while γ refers to the Ni on an adjacent sheet with an OH adsorbate that acts as a proton acceptor for the active site (see, e. g., top view “oxo”, Fig. 2). Change(s) in os is (are) highlighted in bold. Arrow up or down means increase or decrease of the os relative to the reactant, respectively. c Entries in grey are groups of elementary steps comprised of non-PCET step(s) and a PCET step. d Entries in bold pertain to the limiting potential for each route. The routes requiring the lowest limiting potential for the different levels of theory have a colored background. e Structures frozen from HSE06 (α=0.25). Errors in ∆𝐺 relative to structures relaxed in α=0.15 are found to be negligibly small, for example for steps D-1, D-2, and D-2a they are only 2.1, -3.0, and -1.7 meV, respectively.

̅𝟐𝟏 ̅𝟏) surface. Fig. 2 displays the mechanisms explored. OER mechanisms on the Fe-doped (𝟏 Table 1 lists the corresponding energetics and associated oxidation state (os) changes predicted by the three XC approximations. The os of Ni and Fe cations are inferred from their net atomprojected spins as summarized in Table S3 in the SI. We next discuss the individual pathways explored (A-F). These pathways involve commonly suspected OER intermediates: OH, O, H2O2, HO2, and O2, with various effective charges and hapticity. Four proton-coupled electron transfer (PCET) steps are involved in a closed-loop cycle, sometimes including one or two low-energy, non-PCET chemical steps. OH − = (H2O − H+) can substitute as the reactant for steps where the addition of H2O and release of H+ are involved simultaneously.

Pathways A and B: η1-O2H route. The red (A) and blue (B) catalytic cycles in Fig. 2 begin with a five-fold-coordinated Fe3+ site (orange circle). The starting structure has a terminal hydroxo ligand. A-1: The first PCET oxidizes Fe3+ to Fe4+ to form a cis-dihydroxoiron(IV). A-1 involves an exoergic pre-equilibrium H2O adsorption (PBE+U: -0.20 eV), A-1a, followed by a single PCET, A-1b. A-2: The second PCET reduces the substrate (Ni3+ to Ni2+, labelled as Ni𝛼 ; henceforth this Ni is indexed as , while the other, nearest-neighbor Ni to Fe is hereafter referred to as β) while producing a two-electron oxidation of the two hydroxo ligands to form an end-on


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bonded (η1) hydroperoxo: η1-O2H ( 𝑟O−O [PBE + 𝑈, HSE06] = [1.436, 1.413] Å; 𝜐̃O−O [PBE + 𝑈] = 885 cm−1). A-3 and B-3: The η1-O2H may further oxidize to O2 (two-electron) after the third PCET with concomitant reduction of Fe4+ to Fe3+. The displacement of O2 may be assisted by the adsorption of H2O as in A-3, or not as in B-3 (blue). A-4 and B-4: The fourth PCET re-oxidizes the Ni𝛼 from +2 to + 3, recovering the starting state. B-4 requires H2O adsorption, while A-4 does not. The most potential-demanding step is A-2, with 𝜂OER [HSE06 (α = 0.15)] = 0.84 V (Table 1). The high 𝜂OER implies that this mechanism is not favorable under low overpotentials. Pathway C: cis-dioxo route. This route (violet) is a branch point after the A-1 step (C-1). It involves the formation of higher-oxidation-state Fe species (IV to VI). C-2: The second PCET further oxidizes Fe4+ to Fe5+, forming a terminal oxo from one of the hydroxo ligands, cisoxohydroxoiron(V):

𝑟Fe=O [PBE + 𝑈, HSE06] = [1.685, 1.643] Å; 𝜐̃Fe=O [PBE + 𝑈] =

727 cm−1 (Fig. S4). C-3: The third PCET oxidizes Fe5+ to, effectively, Fe6+ (based on simple electron counting and projected spin, Table S3), forming the second oxo ligand, cisdioxoiron(VI):

𝑟Fe=O [PBE + 𝑈, HSE06] = [1.706 & 1.714, 1.671 & 1.674] Å; 𝜐̃Fe=O [PBE +

𝑈] = 751,741, and 642 cm-1 (symmetric and asymmetric stretches, Fig. S4). C-4: The cisdioxoiron(VI) then very favorably decomposes into O2 (–0.82 eV), reducing Fe6+ back to Fe3+ and 2+ Ni3+ 𝛼 to Ni𝛼 (four-electron discharge). The original state of the active site is recovered via the

PCET step B-4 (C-5). The cis-dioxoiron(VI) that transiently forms through C-3 requires 𝜂OER [HSE06 (α = 0.15)] = 0.69 V, the highest in the cycle, suggesting that this pathway may be activated only at high overpotentials during electrolysis. The existence of a cis-dioxoiron(VI) intermediate for this system was first suggested and experimentally probed in Ref. 23, where it was electrochemically stabilized under non-aqueous environments.


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The cis-dioxoiron(VI) is similar to the tetrahedral tetraoxoferrate(VI) anion complex (FeO2− 4 ) that stably exists in alkaline solutions under strongly oxidizing conditions. The HSE06 (α = 0.15)-predicted potential to reduce cis-dioxoiron(VI) to hydroxoiron(III) , Ered = –Gred /ne =Gox/ne = G[C1+C2+C3]/(3e) = 1.67 V, where ne is the number of electrons, is similar to the experimental standard reduction potential of the half reaction: 1.55 V

− FeO2− 4 + 4H2 O + 3𝑒 →

Fe(OH)3 + 5OH −

(3)

(vs. RHE, pH=14) in alkaline solutions.5 This attests to the molecular chemical nature of Fe sites on this surface. For FeO2− 4 and similar transition-metal oxo complexes (V, Cr, Mo, and Mn) with high metal oxidation states, the π-bonding interactions between the metal and the oxo moieties are compulsory for their existence, as is also evident on this surface from the predicted iron-oxo bond lengths and stretching frequencies.52-54 The bond lengths and stretching frequencies of the surface Fe6+=O bonds (PBE+U: 1.71 Å and 750, 741 cm-1, respectively) are close to what is measured (and calculated from PBE + U, Fig. S5) for K 2 FeO4 (s): 1.66 – 1.67 Å (1.64, 1.65, and 1.66 Å), and ~ 800 cm-1 (817 cm-1), respectively.55 The chemical and coordination environments, however, are clearly different: Fe in the β-NiOOH(1̅21̅1) surface is in a six-fold coordination environment and shares lattice O covalently with Ni3+ ions, whereas Fe is in a tetrahedral environment in the 2− FeO2− 4 ion, embedded in a strongly ionic environment in K2FeO4 (Fig. S5a). Fe in the FeO4 ion

is also much more oxidized, with a PBE+U projected magnetic moment of only 1.6 𝜇B (Fig. S5) vs. 2.5 𝜇B (Table S3) on the surface, as well as pronounced radical character on the two oxo ligands, with magnetic moments of 0.5 and 0.7 𝜇B . Pathway D: oxo route. The terminal oxo route (light blue) is a branch point prior to step A-1. D-1: The route’s namesake species Fe4+=O, oxoiron(IV), is the product of the first PCET, from the oxidation of Fe3+-OH without addition of water (as in A-1), 𝑟Fe=O [PBE + 𝑈, HSE06] =


13


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[1.696, 1.639] Å; 𝜐̃Fe=O [PBE + 𝑈] = 733 cm−1 (Fig. S4). D-2: A second PCET generates O2 with the addition of water and concomitantly reduces two Ni,  and  (found on the adjacent oxide sheet, the  index is used hereafter), from Ni3+to Ni2+, and Fe4+ back to Fe3+ (for a total of three electrons discharged). This step can be divided into three steps, D-2a to D-2c. D-2a: In this step, the O−O bond may form via an attack of the terminal oxo onto the oxygen of Ni𝛽 OH, while 2+ simultaneously Ni𝛽 OH shuttles its H+ and an electron to Ni3+ 𝛾 OH forming Ni𝛾 OH2. The top view

of the oxo structure indicates these processes with orange arrows (Fig. 2, far left). In this step, the  and  Ni are reduced through the formation of a side-on-bonded peroxide: Fe4+-η2-O2 (twoelectron discharge). The O–O bond length and frequency are somewhat shorter and higher, respectively,

than

a

peroxo

bond

in

H2O2:

𝑟O−O [PBE + 𝑈, HSE06] =

[1.446, 1.420] Å; 𝜐̃O−O [PBE + 𝑈] = 910 cm−1 (Fig. S4). The oxidation state of Fe is also marginally less than +4, based on slightly lower net spin projection. D-2b: Water adsorbs at the Fe4+ site, expanding the coordination number of Fe, which consequently elongates the Fe-η2-O2 bond,

while

also

partially

contracting

the

O-O

bond:

𝑟O−O [PBE + 𝑈, HSE06] =

[1.435, 1.411] Å; 𝜐̃O−O [PBE + 𝑈] = 918 cm−1 . The nucleophilic attack of H2O or OH − on Fe therefore may facilitate O2 desorption. D-2c: A PCET destabilizes the Fe(IV)-aqua-η2-O2, resulting in O2(g) evolution and reduction of Fe4+ back to Fe3+ (one-electron discharge). Thus, a PCET and three-electron discharge all within D-2 provides all four oxidizing equivalents necessary to form O2. D-3 and D-4 (A-4): The two following PCET steps restore the active sites through the re-oxidation of  (D-3, an orange arrow marks the active H at the Ni site in the top view structure prior to oxidation) and  (D-4) Ni2+ to Ni3+. Pathway D presents the lowest 𝜂OER among the cycles, with 𝜂OER [HSE06 (α = 0.15)] = 0.14 V from D-1.


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Oxoiron(IV) species are observed in nature as the redox active site of cytochrome C oxidases,56 which catalyzes reduction of O2 to H2O, cytochrome P450 monooxygenase, which oxidizes nonactivated hydrocarbons,57 and in various non-heme Fe complexes.58-59 The π-bonding interaction between Fe4+ and O2- in known oxoiron(IV) complexes is possible due to partially occupied π* states. The two π and two π* states arise from the interaction of two of the O 2p (a πdonor ligand) with two of the Fe 3d orbitals, and thus in high-spin ferryl d4 complexes, the Fe-O bond has a bond order of 2 (Fig. 3).52 The predicted bond length and stretching frequency of the surface Fe4+=O is similar to known ferryl species: 1.65 – 1.69 Å, and 785 – 830 cm-1, respectively.56, 59 The formation of the O−O bond (D-2a) is slightly endoergic (0.37 eV). This endoergicity suggests that D-2 is also potentially a rate-limiting step. O−O bond formation is commonly hypothesized to be rate-determining for OER.60 The subsequent hydration of Fe4+-η2-O2 (D-2b) is found to be a near-equilibrium process (0.08 eV) which may facilitate a 𝑆N 2-type substitution mechanism for O2 generation. In such a mechanism, D-2b and D-2c occur concertedly through an attacking H2O or OH − nucleophile, while O2 simultaneously forms and desorbs. Since the 𝜂OER for D-1 and D-2 are similar, the rate-limiting step is not be easily identified from thermodynamics. Identifying whether D-1 or D-2 is rate limiting will be the subject of future work.


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Figure 3. Ligand-field splitting for Ni and Fe 3d orbitals exhibiting C4v symmetry. Upper panel, schematic representation of the frontier orbital interactions of the transition metal, M, and a -donor terminal O. Orbitals of the other ligands not shown. Note that 3𝑑𝑥 2 −𝑦 2 has / symmetry with respect to the equatorial ligands’ s and p orbitals (along x and y). nb = non-bonding. Lower panel, orbital occupations for M = Fe and Ni with different oxidation states. Pathways E and F: dihydrogen peroxide (η1-O2H2) route. The last pathways explored involve the synthesis of dihydrogen peroxides. This intermediate has not been observed in aqueous electrochemical conditions, although shown to form in a non-aqueous and OH-free environment.23 Investigation of these pathways therefore can be a means to rule out methodologies that predict otherwise. E-1: The production of η1-O2H2 via a PCET may occur prior to A-1, leading to the 2+ reduction of Ni3+ 𝛼 to Ni with the two-electron oxidation of water and the terminal hydroxo to

form the peroxide (Fig. 2, pink). F-2: η1-O2H2 may also form via a PCET after A-1, in which case the formation of the oxidized molecule also reduces the Fe4+ back to Fe3+ (Fig. 2, green). Both processes are indeed unfavorable, with 𝜂OER [HSE06 (α = 0.15)] = 1.60 V and 0.89 V , respectively (Table 1).


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̅𝟐𝟏 ̅𝟏) surface. The pathways explored for pure β-NiOOH are OER mechanisms on the pure (𝟏 A/B and D (Fig. 4) with the energetics in Table 2. Unlike Fe, Ni is not known to stably adopt oxidation states higher than +4; therefore, Pathway C (Fig. 2, purple) is not included. The hydrogen peroxide pathways (Fig. 2, pink and green) also were not modeled due to the significantly higher potentials found in the Fe-doped case compared to the other pathways.

̅𝟐𝟏 ̅𝟏) surface.Ball-and-stick models showcase Figure 4. OER mechanism on the β-NiOOH(𝟏 the different intermediates on the Ni-centered active site. Structures shown are from the 9L models as predicted by PBE+U. Only the active site is shown for clarity: side view roughly along the [0001] direction (an example of the actual model is shown in Fig. 1a). The structures are named according to their fifth (and sixth) ligand(s) and named X’ in the absence of both. Two routes are shown: (1) η1-O2H route (A and B), and (2) the initial step for the oxo route (D). The circles outlining some of the Ni atoms indicate approximate oxidation states as depicted in the legend (all other Ni atoms are in the +3 state).

Pathways A and B: η1-O2H route. The A and B pathways are similar to the Fe-catalyzed pathways. A-1: The Ni3+ oxidizes to Ni4+ with the addition of H2O (or OH − ) to form a dihydroxonickel(IV). A-2: η1-O2H is formed through a second PCET (𝑟O−O [PBE + 𝑈, HSE06] =


17


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[1.435, 1.416] Å; 𝜐̃O−O [PBE + 𝑈] = 896 cm−1 ), whilst Ni4+ reduces back to Ni3+. A-3 and B-3: O2 is generated via the third PCET with reduction of the active Ni to +2. B-3 can be divided into two steps, namely, B-3a: a PCET resulting in the oxidation of η1-O2H to a surface-bound η1-O2 with a partial superoxo character (–1.3 B atom-projected O2 spin, 𝑟O−O [PBE + 𝑈] = 1.263 Å; 𝜐̃O−O [PBE + 𝑈] = 1347 cm−1 ), and B-3b: O2 desorption. The projected spin of the active Ni with η1-O2 is slightly lower than what is calculated for a Ni2+ (1.55 vs. 1.7 B, see Table S3). A-4 and B-4: The active Ni is re-oxidized to +3. For these cycles, the production of the Ni4+(OH)2 and Ni3+-η1-O2H are the potential-determining steps, which equally require 𝜂OER [HSE06 (α = 0.15)] = 0.48 V (Table 2), and thus likely to explain the experimentally observed overpotential.18

Table 2. PBE+U and ONIOM-HSE06 reaction free energies of the various possible elementary steps involved in the OER on the pure β-NiOOH(1̅21̅1) surface (Fig. 4). Product Reaction free energy vs. RHE (eV)c,d a a Step Chemical equation osb,c : PBE+U α = 0.25 α = 0.15d Ni 4↑ A-1 NiOH + H2O → Ni(OH)2 + (H+ + 𝑒 − ) 1.90 2.03 1.71 3 A-1a NiOH + H2O → Ni(OH)(OH2) -0.05 --+ − A-1b Ni(OH)(OH2)→ Ni(OH)2 + (H + 𝑒 ) 4↑ 1.96 --+ − A-2 3↓ 1.36 1.50 Ni(OH)2 → NiOOH + (H + 𝑒 ) 1.71 2↓ A-3 0.40 0.12 0.63 NiOOH + H2O → O2(g) + NiOH2 + (H+ + 𝑒 − ) + − 3↑ A-4 1.26 1.26 0.87 NiOH2 → NiOH + (H + 𝑒 ) + − B-3 2↓ 0.59 0.37 0.80 NiOOH → O2(g) + Ni + (H + 𝑒 ) + 1 − B-3a NiOOH → Ni(𝜂 -O2) + (H + 𝑒 ) 2↓ 0.53 --1 2 B-3b Ni(𝜂 -O2) → O2(g) + Ni 0.06 --3↑ B-4 1.05 1.02 0.70 Ni + H2O → NiOH + (H+ + 𝑒 − ) 3 2.32 D-1 NiOH → Ni−O∙ + (H+ + 𝑒 − ) 2.13 2.07 a

Text colors are the same as the colors of the corresponding pathway in Fig. 4. Chemical equations only show changes at the active Ni site. b Oxidation states (os) of the active Ni in the product of the step, approximated from spin-density atomic projections (Table S3). Arrow up or down means the increase or decrease of the os relative to the reactant of the step, respectively. c Entries in grey is a group of elementary steps comprised of a non-PCET step and a PCET step. d Entries in bold pertain to the limiting potential for each route. dStructures frozen from HSE06 (α=0.25).


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Pathway D: terminal oxyl route. This route (light blue) forms a terminal oxyl radical after the first PCET, unlike Fe which forms a terminal oxo. Transition-metal cations in tetragonal symmetry with more than five electrons in the d orbitals are known not to form multiple metaloxygen bonds. This is due to the complete population of the π* orbitals for low-spin d6 configurations and beyond (referred to as the “oxo wall”).52 Fig. 3 shows the difference between the Ni4+ d6 and Fe4+ d4 in C4v symmetry, which illustrates the fully filled π* orbitals for Ni4+. The metal-oxyl bond for Ni3+ thus is longer and has a significantly smaller stretching frequency than Fe4+=O:

𝑟Ni−O [PBE + 𝑈, HSE06] = [1.764, 1.753] Å; 𝜐̃Ni−O [PBE + 𝑈] = 566 cm−1 .

The

excess spin on the terminal O confirms its radical character (0.7 B atom-projected spin). The oxyl radical picture, when Ni3+O is oxidized is consistent with a recent O K-edge electron energy loss measurement on thin NiOOH films.61 Since this step is very unfavorable compared to A-1, with 𝜂OER [HSE06 (α = 0.15)] = 0.84 V, this channel cannot be competitive for pure NiOOH on this surface.

̅𝟐𝟏 ̅𝟏) surfaces. Fig. S6 shows the free energy diagram of the OER on Fe-doped vs. pure (𝟏 different surface species shown in Figs. 2 and 4 as functions of the electrode potential vs. RHE. The Fe site exhibits a rich set of (meta)stable phases due to the range of oxidation states that may be achieved by Fe. We find that the energetics for Fe-doped and pure β-NiOOH(1̅21̅1) differ, as do the pathway each prefers. The Fe and Ni sites favor the Fe4+=O (Pathway D) and Ni4+-(OH)2 (Pathway A) on β-NiOOH(1̅21̅1), respectively. The onset overpotentials are different by 0.34 V, consistent with experiments.14, 18 The calculated 𝜂OER for the doped and pure surfaces (0.14 and 0.48 V) present quantitative lower bounds to the lowest measured overpotentials of 0.28 – 0.30 V14, 18 and 0.50 – 0.60 V14, 18 at 10 mA/cm2, respectively.


19


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The activity of the Fe-doped surface is a combination of the ability of surface Fe3+ to be oxidized to Fe4+ (stabilized by the terminal oxo moiety), with the favorable discharge of two Ni3+ to Ni2+ providing two of the four needed oxidizing equivalents for O2 to form, by-passing formation of a superoxo-like species. While reduction of Ni3+ to Ni2+ acts as an on-site “battery” discharge, reduction of Fe3+ to Fe2+ is not observed; the contrast is readily understood from their electronic structure. Fig. 3 illustrates that after addition of an electron to Ni3+, the increased Coulomb repulsion is mitigated by additional exchange interactions between like-spin electrons, whereas this is not the case for Fe3+ (no extra exchange stabilization results from addition of the down-spin electron). Therefore, while both cations are categorically catalytically active, one cannot exclusively perform OER with Fe3+ functioning as the primary O2 evolution site. The complementary chemical properties of Fe3+ and Ni3+ therefore may be the origin of the experimentally observed increased activity of Fe-doped NiOOH, with optimal activity at relatively low Fe concentrations.14-15,

18, 22-23

Because Fe is the oxygen-evolving center, it is

imperative that Fe occupy surface sites, the probability of which will increase at high doping concentrations. However, since the relatively facile discharge of the neighboring Ni3+ to Ni2+ provides the necessary oxidizing boost for the O-O bond to form, diluting Fe sites with Ni3+ both within and the adjacent layers provides the necessary condition for water oxidation to occur at the Fe sites with ease.

Contextualization with the experimental literature. Existence of Fe4+, Ni4+, and Fe6+, and the nature and redox properties of the active site. The presence of oxidation states higher than +3 for either Ni or Fe is contentious. First, it is crucial to probe the OER activity in operando to provide credence to the applicability of various measurements to the catalyst’s active state during catalytic


20

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turnover. Note further that the existence (or absence) of a certain oxidation state in the bulk material does not necessarily translate to its existence (or absence) at the surface. Identification of these high-oxidation-state species, either stably in the catalyst resting state or fleetingly en route to O2 formation, has been a focal point of many discourses. This focus is because the metal’s oxidation state may provide a clue into the mechanism of OER and the nature of the active site, even simply to address whether it is Ni or Fe that is the catalytically active species. Corrigan and Knight reported an average of +3.67 for the Ni oxidation state in 𝛾-NiOOH, one of the earliest pieces of evidence for the existence of Ni4+.62 However, Hunter, et al. recently pointed out that this early study did not account for unintentional Fe doping.22 Li et al. recently argued that Fe3+ promotes formation of Ni4+ (identified via Coulometric titration) without itself being oxidized.61 Axmann et al. used Mössbauer spectroscopy to demonstrate the existence of very stable high-spin Fe4+ in charged 𝛾-Ni,FeOOH that persists over ~3 months.63 Chen et al. also used Mössbauer spectroscopy to detect Fe4+ under steady-state OER conditions.64 From operando differential electrochemical mass spectrometry and X-ray absorption spectroscopy, Görlin et al. rationalized conflicting findings for the transition-metal oxidation states.65 They found that below 4% Fe, the majority of the Ni ions were in the +4 state, however above 4% Fe, Ni ions appeared to be in their low-valent +2 state, which is associated with a large increase in faradaic efficiency for O2.65 On the other hand, Fe ions remained in the +3 state, regardless of Fe composition. These findings were interpreted to be due to fast reduction of Fe+4 to Fe+3 and Ni3+/4+ to Ni2+, resulting in concomitant O2 evolution (𝑘OER ), which is faster than the rate of oxidation of the metal centers (𝑘M,ox ). With 𝑘OER >>𝑘M,ox , the accumulation of high-oxidation-state species is suppressed, which allows them to avoid detection in operando.65 We found the existence of Fe4+ is possible via formation of a stable Fe-oxo moiety and that the role of Ni3+ is to discharge to Ni2+, thereby providing the


21


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additional oxidizing equivalents to form the O-O bond. These two redox features are central to an efficient electrocatalytic OER. The potential-limiting nature of the formation of the oxoiron(IV) intermediate (Fig. 2, step D-1), shows that this species is likely consumed faster than it is produced. Moreover, because the formation of O2 involves the discharge of two Ni3+ to Ni2+ (Fig. 2, step D2), at high turnover rates, many Ni3+ ions will be reduced to +2, proportional to the number of active Fe sites. This is consistent with the findings of Görlin et al. discussed above. Ahn and Bard used surface-selective, time-dependent redox titrations to determine that the dispersed Fe is the active, “fast” site (OER rate constant k ~ 1.70 s-1), while Ni4+ is associated with a poor OER rate (k ~ 0.04 s-1).66 We found that indeed the existence of Ni4+ is inconsequential for the Fe-mediated-pathway, however this species is involved in the OER at the Ni sites, which occurs at a higher potential (1.4 vs. 1.7 V). Stevens et al. provided direct evidence that Fe ions that are rapidly incorporated in the NiOOH lattice (postulated to be at edge and defect sites) are responsible for OER activity, while Fe within the bulk simply modulates the voltammetric profile of bulk Ni.67 This experiment provided another framework to rationalize conflicting evidence on Ni and Fe oxidation states, and helped differentiate the effect of Fe in the bulk versus surface redox behavior of NiOOH. It also emphasized the primary role of “defect” sites (which may be interpreted as edges and corner sites) in OER.67 The oxidation step Ni2+ → Ni3+ + 𝑒 − for both doped and pure NiOOH requires low potentials (Fe-doped (path D): D-3 = 1.31 V, D-4 = 1.00 V, Table 1; pure (path A): A-4 = 0.87 V, B-4 = 0.70 V, Table 2) that are not potential limiting. Experimentally, the relative ease of bulk +2 to +3 Ni oxidation manifests as a pre-catalytic wave in cyclic voltammograms (Ni(OH)2 → NiOOH) that appears at overpotentials of ~0.1 V, shifting to more oxidizing potentials, ~0.2 V, with the incorporation of Fe.14-15, 18 The calculated potentials for the surface agree with experiment in that


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the oxidation of Ni2+ occurs at potentials lower than the H2O oxidation potential. The anodic shift for the Ni(III/IV) redox potential when near Fe, is also consistent with experiment. Hunter et al. were able to identify a range of oxidation states for Fe: +4, +5 and +6 in Fe-doped NiOOH, albeit in a non-aqueous environment, due to their high reactivity with water and hydroxide.23 They postulated that the +6 species, while short-lived in aqueous environments and thus avoiding detection, is the active O2-evolving species. Our calculations suggest that the OER pathway via the Fe6+ intermediate (pathway C), operates only at much higher potentials (> 1.92 V, Table 1); however at this potential, OER becomes facile at the Ni sites, washing out the contribution of this route. Moreover, as argued by Hunter et al., the existence of iron(VI)-dioxo is curtailed by its instantaneous decomposition.23 We predict that this process proceeds via formation of O2 and Fe3+, with concomitant reduction of Ni3+ to Ni2+ (Fig. 2, step C-4). Mechanism. A large kinetic isotope effect (KIE) for the OER was observed recently for Ni(Fe)OOH but not for pure NiOOH films, when using deuterated water.60 For the doped case, because formation of terminal O and O2 (probable rate-determining steps, vide supra) depends on the deprotonation of Fe3+-OH (D-1, Fig. 2) and shuttling of the proton from Ni𝛽 OH to Ni𝛾 OH (D2a, Fig. 2), respectively, a large KIE is expected for deuterated Fe3+-OD and Ni𝛽 OD. If step A-1 is indeed the rate-determining step for the pure NiOOH, then the lack of KIE can be explained by OH − being the direct reactant (thus the independence of the rate on deprotonation). The above mechanisms therefore may explain the pH dependence of the rate on both catalysts,60 although the rate-limiting step for the pure NiOOH need not involve a proton shuttle (which would otherwise lead to a KIE).


23


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Comparison with the theoretical literature. PBE+U theory, with varying U values, has been applied widely to study the OER of NiOOH. This is despite the predicted nearly metallic character of NiOOH using this method, contrary to experiments (Section 1.1) and G0W0 calculations.33 Perhaps even more surprising is the recent use of pure PBE on NiOOH doped with groups 4 to 9 transition metals, which found OH* → O* formation to be the potential-limiting step on a fivefold Fe site (analogous to step C-2, Fig. 2).31 Their prediction does not agree with the PBE+Ubased work by Friebel et al. on a similar surface, where it was found that *OOH formation is the potential-limiting step at the Fe site.16 The use of hybrid functionals on this system to describe the bulk electronic structure43-45, 68 and surface OER30 is slowly being adopted. However, it has been shown here and in the works of others that the use of the standard α = 0.25 for Fe is especially suspect and found to be worse than PBE+U.47-48 The surfaces explored in the literature are of the types (0001)24-27 and {011̅𝑁},16, 28-32 exhibiting six-fold and five-fold lattice-oxygen coordinations. PBE+U theoretical overpotentials ~0.5 - 0.6 V have been calculated for β-NiOOH(0001) on pure and Fe-doped surfaces.25, 27 In contrast, 0.46 and 0.26 V have been calculated for the pure and doped β-NiOOH(011̅5) surfaces,28 respectively, also from PBE+U, which are the among the lowest calculated overpotentials for {011̅𝑁} surfaces thus far. The latter prediction involves a near-surface interstitial O2 as an intermediate, whereas mechanisms involving conventional intermediates such as the hydroperoxide (OOH) give higher overpotentials, e.g., 0.56 and 0.43 V, for pure and doped γNiOOH(011̅2), respectively.16 Recently, a B3PW91 calculation predicts overpotentials of 1.22 and 0.42 V for pure and doped γ-NiOOH(100), but by using an entirely different definition. The overpotentials were defined by calculating the potential required to achieve a current of 10 mA/cm2 based on microkinetic models that assume the electron-transfer steps to be fast and at equilibrium,


24

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with O-O coupling as rate-determining steps and the computational thermodynamic potential as reference. Using the conventional definition, however, 𝜂OER = 1.21 and 0.81 V for pure and Fedoped cases can be calculated from their respective highest reported ∆𝐺 = 2.44 eV and 2.04 eV,30 using the experimental equilibrium OER potential of 1.23 V. The analogous steps that may be directly compared with the mechanism on five-fold active sites in previous theoretical models are steps A-1 (formation of *OH) and C-2 (formation of O*). Based on the energetics of these steps, five-fold coordinated sites of Fe-doped β-NiOOH will have an overpotential of at least 0.38 V (step C-2, Table 1). Confirmation of this trend involving the (101̅0) surface, which was found to be the most stable surface exposing five-fold-lattice-O-coordinated sites, will be subject of future studies.34

Future doping strategies. Co and Mn dopants also have been evaluated for their potential to enhance the OER on NiOOH. Experimentally, Co exhibits apparently mixed results, shown to both suppress69 and enhance70 NiOOH’s OER activity, whereas doping with Mn has a negligible effect on the oxide’s activity.17 Also of note, while pure FeOOH and CoOOH are superior to pure NiOOH for the OER, the activity of Fe-doped NiOOH is unmatched by Fe-doped CoOOH.17 We discussed above the dependence of the nature of the OER mechanism, and its efficiency, on the stability of the terminal metal-oxo bond. Seminal theoretical work of Ballhausen and Gray attributed the orbital interactions between V and O in VO(H2O)52+ (ligand to metal 𝜋-bonding) as responsible for the remarkable stability and resistance to protonation of this particular ion.54 This work established a working principle for the stability of certain metal-oxo ions based on ligand-field theory (Fig. 3). They argued that the same principle may explain the stability of first-row transition metal ions of the same type. Carter and Goddard also studied metal-oxo bonds computationally,


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in representative early and late transition-metal oxide diatomic cations.71 They correlated bond strength with the relative population of the metal-oxygen 𝜋- and 𝜋*-bonding orbitals, which consequently yield variations in bond strengths and character between early- (e.g., VO+, CO-type triple bond) and late- (e.g., RuO+, biradical O2-type double bond) transition-metal oxide diatomic monovalent cations. Holm, after comprehensive compilation of known metal-oxo complexes, concluded that no stable M=O functional group – with a conventional double bond – occurs for any transition metal to the right of group 8 and for metal centers with more than four valence d electrons.53 Later, Winkler and Gray coined the term “oxo wall”, referring to the inability of transition metals to the right of Fe-Ru-Os to support a terminal oxo ligand in a tetragonal environment.52, 72 Applying the “oxo-wall” theory,52 Fe3+, Ru3+, and Os3+ are dopants deemed to produce optimal M4+=O stabilization (high-spin d4), as a conventional double bond can form. By contrast, far to the left of the wall (e.g., Ti4+ to Mn4+, d0 – d3), the metal-oxo bond will be too strong, and to the right of the wall, the metal-oxo bond will be too weak (Co4+, d5) or produce a less stable oxyl radical (e.g. Ni4+−O or Ni3+−O∙, d6 or d7). This theory is consistent with the earlier valence bond theory put forth by Carter and Goddard,71 in which early transition metals can form strong, triple bonds to oxygen as in carbon monoxide because of a combination of empty and singly occupied d-orbitals, whereas late transition metals form weak, diradical-type double bonds to oxygen as in dioxygen because of a combination of singly and doubly occupied d-orbitals. Rather than focusing on oxidation state, this analysis suggests that creating opportunities for high-spin d4 transition metal ions to form is key. This implies that Mn2+ and Cr+, then oxidized to Mn3+ and Cr2+ d4 ions could be worth exploring, although stabilization of these species against oxidation to their higher oxidation states may pose a challenge at potentials ≥ 1.23 V.


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Mixed doping could be another effective strategy, since the OER activity of the doped oxide is coupled to the local discharge of Ni3+ to Ni2+ near the Fe4+ site. For example, Cu3+ may hold more oxidizing power than Ni3+, because Cu2+ has a higher ionization energy to +3 than Ni2+ (36.841 vs. 35.187 eV).73 However the reduction potential of the dopant from +3 to +2 should also be within 1.23 V, which will depend on how the dopant interacts electronically and structurally with the NiOOH lattice. A highly efficient Cu-doped Co(OH)2 OER catalyst has been recently synthesized,74 thus an analogous Cu-doped NiOOH may also be in reach. Note that the ionization potential of Co2+ (33.50 eV)73 is much lower than Ni2+, therefore Co3+ has lower oxidizing power than Ni3+, which may explain why NiOOH is a better host oxide than CoOOH for Fe-doping.17

Conclusions To conclude, HSE06 (α = 0.15) predicts unprecedented near-quantitative lower bounds for the 𝜂OER , with values of 0.49 V and 0.14 V for pure and Fe-doped β-NiOOH(1̅21̅1), respectively. We show that this material’s OER activity is due to the ability of surface Fe3+ to be oxidized as Fe4+ (stabilized by the terminal oxo moiety in a low-coordination environment), in concert with dischargeable Ni3+ sites. Low Fe3+ doping is expected to favor higher intrinsic OER activity. However, this work shows that a balance between the number of active sites (Fe) and number of adjacent Ni sites is required. Our findings therefore corroborate the low optimal Fe-doping concentration for OER found experimentally, 14, 18 and suggest that the (1̅21̅1) surface, while not the most dominant facet, may be largely responsible for the electrocatalysis observed.

Methods


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Spin-polarized PBE+U. Spin-polarized Kohn-Sham DFT calculations were performed using VASP 5.3.575 within the all-electron, frozen-core, projector augmented-wave (PAW) formalism,76 using a planewave basis with a kinetic energy (KE) cutoff of 750 eV. Standard PAW potentials were used with 3p, 4s, and 3d; 2s and 2p; and 1s explicit valence for Ni and Fe, O, and H, respectively. The UNi and UFe values were derived respectively from linear response theory performed on bulk NiOOH28 and from unrestricted Hartree-Fock calculations on electrostaticallyembedded Fe3+ oxide clusters.46 Slabs with symmetric surfaces were derived from the (1×2×1) triclinic unit cell reported recently (lattice parameters: α, β, γ = 89.4°, 70.3°, 120.6°; a, b, c = 2.947, 5.984, 5.004 Å).34 The 9L thickness is necessary to replicate a bulk-like mid-layer electronic structure.34 The slab supercell dimensions are 13.214 Å ×10.153 Å × 30 Å (in-plane vectors angle of 133.2°). These correspond to a vacuum size of ~ 14 Å along the surface normal. Dipole corrections were included to eliminate spurious interactions between periodic images along said direction. The Brillouin zone (BZ) was sampled using a 2 × 2 x 1 Γ-point-shifted mesh for the slab.77 A Gaussian electronic smearing was used with a smearing width of 0.01 eV for structural relaxation and vibrational energy calculations. Final energies and densities of states were evaluated using the tetrahedron method with Blöchl corrections.78 The magnetic structure was initialized with ferromagnetic low-spin Ni and high-spin Fe, which was found to be most favorable here and in the literature.34, 43 The ionic coordinates were relaxed while keeping the equilibrium lattice vectors fixed. The maximum absolute atomic force threshold was set to 0.01 eV/Å during relaxation. The coarse grid fast-Fourier-transform (FFT) mesh spacing used was two times the corresponding wavevector of the KE cutoff (Gcut), while the fine grid mesh is four times Gcut (PREC = Accurate). Details of the bulk and gas phase calculations are presented in Sections 3.1


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to 3.3 in the SI. The surface vibrational free energy is evaluated for 9L models within PBE+U, PBE+𝑈 which is contained in the ∆𝐺9𝐿 term in equation (2) (Section 3.4 in the SI).

4L slab PBE+U and HSE06. The KE cutoff was reduced to 620 eV for 4L slabs for both PBE+U and HSE06 XC functionals. The exact exchange was evaluated at the Γ-point. PBE+U wavefunctions were used to initialize HSE06 (α = 0.25), while the wavefunctions of the latter were used to initialize HSE06 (α = 0.15). The supercell dimensions are 13.214 Å ×10.153 Å × 20 Å. The coarse grid FFT-mesh spacing used was 1.5 times Gcut, with the fine-mesh spacing three times Gcut. The same grid was used for the exact exchange (PREC = PRECFOCK = Normal). All other computational parameters are the same as above. The structures for HSE06 (α = 0.15) were taken from the optimized HSE06 (α = 0.25) structures. The difference in the PBE+U-predicted reaction energies between the 9L and 4L models are not always negligible (Table S4 in the SI). The energy deviations justify the need for the 9L energy term in equation (2).

Determination of oxidation states of transition metal cations. The net atomic spin projections are used to define oxidation states (Table S3), which are the most sensitive measure of the local electronic structure, and yield oxidation states most consistent with the conventional definition of oxidation states, at least for transition metals.

Supporting Information. XC validation tests for bulk Fe-doped β-NiOOH and α-FeOOH, and OER-relevant molecules, bulk electronic structures, gas-phase molecular properties, comparison of the predicted OER energetics between the different XC functionals, additional insights into the redox properties of the high-valent Fe site, additional methods details for calculating bulk Fe-


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doped β-NiOOH and α-FeOOH densities of states (DOS) and gas phase molecules, details for calculating bulk K2FeO4 phonon DOS, details on vibrational energy calculations, evaluation of the effect of PCM on adsorption energetics, table of electronic spin moments and oxidation states of Fe and Ni, difference in the PBE+U-predicted reaction energies between the 9L and 4L models, visualization of some vibrational modes, and plot of the relative surface free energies vs. electrode potential. (PDF)

Compressed slab and bulk structure files in VASP format. (ZIP)

Corresponding Author *[email protected] Notes The authors declare no competing financial interests.

Acknowledgements This article is based upon work supported by the Air Force Office of Scientific Research under AFOSR Award No. FA9550-14-1-0254. E.A.C. would also like to thank the High Performance Computing Modernization Program (HPCMP) of the U.S. Department of Defense and Princeton University’s Terascale Infrastructure for Groundbreaking Research in Engineering and Science (TIGRESS) for providing the computational resources. We thank Ms. Nari L. Baughman for proofreading the manuscript. The atomic structures are visualized using VESTA.79

References


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Unraveling Oxygen Evolution on Iron-Doped Î²-Nickel Oxyhydroxide

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