Cooperative Effects Drive Water Oxidation Catalysis in Cobalt Electrocatalysts through the Destabilization of Intermediates

A barrier to understanding the factors driving catalysis in the oxygen evolution reaction (OER) is understanding multiple overlapping redox transitions in the OER catalysts. The complexity of these transitions obscure the relationship between the coverage of adsorbates and OER kinetics, leading to an experimental challenge in measuring activity descriptors, such as binding energies, as well as adsorbate interactions, which may destabilize intermediates and modulate their binding energies. Herein, we utilize a newly designed optical spectroelectrochemistry system to measure these phenomena in order to contrast the behavior of two electrocatalysts, cobalt oxyhydroxide (CoOOH) and cobalt–iron hexacyanoferrate (cobalt–iron Prussian blue, CoFe-PB). Three distinct optical spectra are observed in each catalyst, corresponding to three separate redox transitions, the last of which we show to be active for the OER using time-resolved spectroscopy and electrochemical mass spectroscopy. By combining predictions from density functional theory with parameters obtained from electroadsorption isotherms, we demonstrate that a destabilization of catalytic intermediates occurs with increasing coverage. In CoOOH, a strong (∼0.34 eV/monolayer) destabilization of a strongly bound catalytic intermediate is observed, leading to a potential offset between the accumulation of the intermediate and measurable O2 evolution. We contrast these data to CoFe-PB, where catalytic intermediate generation and O2 evolution onset coincide due to weaker binding and destabilization (∼0.19 eV/monolayer). By considering a correlation between activation energy and binding strength, we suggest that such adsorbate driven destabilization may account for a significant fraction of the observed OER catalytic activity in both materials. Finally, we disentangle the effects of adsorbate interactions on state coverages and kinetics to show how adsorbate interactions determine the observed Tafel slopes. Crucially, the case of CoFe-PB shows that, even where interactions are weaker, adsorption remains non-Nernstian, which strongly influences the observed Tafel slope.


XAS
The Co and Fe K-edge XAS was performed B18 of the Diamond Light Source.Fe foil was used to calibrate the monochromator.XAS data for all the reference materials were collected using fluorescence mode in using a home built teflon cell, in which the sample was placed ~2 mm from a Kapton foil window.The energy of the incident X-ray beam was selected using a Si (111) monochromator, and measurements were performed in fluorescence mode.

XPS
XPS was performed on a Thermo Scientific K-alpha+ instrument.Powdered samples were attached to a stainless-steel plate using conductive carbon tape.The instrument uses monochromated and microfocused Al Kα (hν = 1486.6eV) radiation to eject photoelectrons which are then analysed using a 180° double-focusing hemispherical analyser with a 2D detector.Spectra were collected at 2x10 −9 mbar base pressure.A flood gun was used to minimize sample charging.All samples were referenced against the C-C peak of adventitious carbon in the C 1s spectrum at a binding energy of 284.8 eV to correct for any charge that is not neutralised by the flood gun.Further effects were then accounted for by taking the separation from the O 1s oxide peak.Data was analysed using the CASA XPS package.XRD X-Ray diffraction (XRD) patterns were measured in the range 5º ≤ 2θ ≥ 70º, step size 0.02º, using a Bruker D2 Phaser instrument (Cu Kα radiation source).

SEC
Spectroelectrochemistry was performed using a stabilized 10mW tungsten-halogen light source from Thorlabs (SLS201L) was used with a collimating add on (SLS201C).The light emitted from the lamp was transmitted through the sample and collected using a 1 cm diameter liquid light guide (Edmund optics).Light transmitted to the spectrograph was first columnated and refocused using two 5 cm planoconvex lenses (Edmund) in order to optimally match the optical components of the spectroscope (Kymera 193i, Andor), CCD camera (iDus Du420A-BEX2-DD, Andor).The detector was maintained at -80 o C during the measurements to ensure high signal-to-noise ratio.An Ivium Vertex potentiostat was used.Data acquisition was facilitated by a custom-built LabView software, freely available at www.opensourcespectroscopy.com.Measurements were made in potentiostatic mode using a Pt mesh as counter and a AgAgCl (Sat.dKCl) as reference.Samples were measured in a homemade polyether ether ketone (PEEK) cell, were light is light transmitted through the sample via two quartz windows.
Unlike typical spectroelectrochemistry, samples were scanned continuously thought their operational JV curve at a set scan rate.The change in absorbance (∆) was calculated with respect to the starting potential of the scan according to: Where   is the intensity of transmitted light at some measured potential (after iR correction) and  0 is the intensity of transmitted light at the potential (i.e. at the start of the scan).The MATLAB code for converting raw data to absorbance (SEC_V_3_2_KYMERA_iR.m) is freely available at www.opensourcespectroscopy.com [4][5][6] DFT Spin-polarised density functional theory (DFT) calculations were performed with the Vienna Ab-initio Simulation Package (VASP), 7 and the Atomic Simulation Environment (ASE) was used to set up and analyse the calculations. 8A plane-wave basis with an energy cutoff of 700 eV was used, and the effects of exchange and correlation were described with the RPBE functional. 9e oxygen evolution reaction is assumed to follow the pathway: The adsorption energies of the reaction intermediates calculated by DFT (Eads,DFT) are corrected for changes in zero point energy (∆ZPE) and entropy (-T∆S) and the effect of an applied potential (U) is calculated using the computational hydrogen electrode, 10 i.e. the free energy of adsorption is calculated as: Where n is the number of electrons involved in the reaction.

S7 Calculation of component spectra from SEC data and an explanation of the physical significance of fitted data and calculation of redox currents.
The absorbance for a given species (i) is Where I0 is incident intensity of light, I is the transmitted intensity of light,   is the molar absorptivity of species i, in units of  −1  3  −1 ,   is the concentration in units of  1  −3 and  is the path length in units of cm.
Note on the units used for SEC.
However, in spectroelectrochemistry, the dimensions of the  do not lend themselves to the experiment, as transformations of solids are measured, rather than solutions with a 1 cm path length.
Here, the absorbance of a solid film in 1 cm 2 area (not concentration) is measured and correlated with charge.To address this problem, we modify the units of concentration and extinction by (1) converting units relating to volume from dm 3 to cm 3 (i.e.division and multiplication by 1000 to convert C and ).
(2) multiplication of the units of  into  to give an area density in units of Mol cm -2 .(3) Conversion of molar units to an equivalent charge (assuming that one moiety is generated by a 1 e -couple) by multiplication and division by faradays constant.This re-expresses concentrations in terms of a charge density   (in units of  −2 ) and extinction coefficients as coulometric attenuation coefficient in units of  2  −1 .We note that because the redox transitions in question are thought to be coupled to the generation of water, charge here does not imply an electrostatic charge on the electrode surface but rather, only monitors the number of electrons that have passed around the external circuit up until a potential U.
=      =     For a given conversion process:

𝑛𝑋 → (𝑛 − 𝑚)𝑋 + 𝑚𝑌
The change in absorbance in terms of traditional concentrations and extinction coefficients is: Where   and   are the extinction coefficients of species X and Y and CT is the total concentration of species present in the system, which is used to substitute the concentrations of X (  )in terms of the concentration of Y (  ) and the total concentration, with is a conserved quantity (  ): =   +   Analogous equations can be written in terms of     : Where Δ is the coulometric differential attenuation coefficient, assuming a single electron couple.The conserved quantity here is not the total concentration but concentration converted to a charge assuming a single electron couple: (ℎ → )  =   Rationale for fitting using the example of a single redox process.
The above equations state that differential spectra do not a-priori give absolute populations, but rather track the number of interconverting moles (i.e. the charge passed).Thus, differential absorption tracks the extent of a redox transition (), not the absolute population.Even in this simple case, one would not know the value of   until the redox transition in complete (ℎ  =   ).This can clearly be seen by defining  for this simple process.Hereafter referring to   simply as : We can therefore write Δin terms of the extent of reaction: The differential attenuation coefficient normalised by its peak value (hereafter Δ ̅̅̅̅ = Δ() Δ(  ) ) can be extracted from the data.To show this, we re-write Δ in terms of Δ ̅̅̅̅ :

𝚫𝑨 = 𝑸 𝑻𝒐𝒕 𝜽𝚫𝜶 ̅̅̅̅ (𝛌)𝚫𝜶(𝝀 𝒑𝒆𝒂𝒌 )
If we now normalise Δ by its peak value we may extract Δ ̅̅̅̅ : This shows that the normalised differential absorbance corresponds to the normalised differential coulometric actuation coefficient in the case of a single conversion process.Using this information we may devise a fitting procedure, as we can obtain.By grouping terms: We see that: This is the rational for the fitting procedure used herein where we use Δ ̅̅̅̅ to fit the data.
Using an experimentally determined normalised differential coulometric actuation coefficient (see following sections), one may fit the measured Δ as a function of the applied potential (U).
If, from a separate experiment, one may measure Δ(  ), then  can be extracted.

Note on the isolation of normalised differential coulometric actuation coefficient spectra (i.e. component spectra used for fitting) in the case of multiple redox processes.
In the case of the materials studies herein, multiple overlapping redox transitions are observed.The differential absorbance observed in a system exhibiting multiple processes is: Where    and Δ   refer to the partial charge transferred and the differential coulometric actuation coefficient arising from the i th redox transition.The partial charges that are extracted from a given redox transition dominate different regions.If there exists a region where the charge extracted arises from only redox process, the difference of two Δ values evaluated in this region will be: If in the region between U and  −    ≠   ) are not progressing (i.e.charge is only being extracted from one redox process), then all terms corresponding to other processes will be cancel: Here we again have a linear correspondence between differential absorbance and charge via a single differential coefficient.This situation is analogous to the single conversion process shown above and it is trivial to show that in region where only one redox transition is proceeding that: This form enables the extraction of the normalised differential coulometric actuation coefficient spectra.From this, the fitting procedure for multiple redox transitions can be obtained: In experimental data (ΔA) δ is approximated by subtracting Δ(U) and Δ(U-20mV) (hereafter ∆ =20 or more simply ∆ 20 ).A plot of ∆ 20 is given for CoOOH and CoFe-PB in S7 (a) and (b) respectively below.In 7a, redox transition T1 is left out for clarity and a single characteristic dotted line is added characteristic of redox transition T1.We note that the transition from the characteristic spectrum of redox transition T2 (purple) to that of T3 (red) occurs at extremely positive potentials relative to the OER potential.The transition completes by ca.1.35 VRHE, after which a single normalised spectrum (T3) is observed.This indicates that at potentials above 1.35 VRHE incrementing the bias produces only conversion process; T3.7b shows the differential spectra for CoFe-PB.Here, an initial broad spectrum (T1, purple) changes to an asymmetric spectrum previously observed in spectroelectrochemical experiments and attributed to precatalystic states. 11This spectrum then broadens at potentials around the onset of OER to produce a third spectrum (redox 3), again consistent with previous findings. 11

Note on the constraints used in Fitting
From these spectra a sequential linear fitting procedure was applied with three key constraints: firstly, a spectrum cannot appear long before its component spectrum appears in Figure S7.This reflects the simple electrochemical reasoning that at an applied potential U<<U 0 where U 0 is the standard redox potential a process, no interconversion is expected.A second constraint is that component spectra cannot decay as no loss of absorption is observed that would indicate the condition where ∆ is negative (i.e. the case when ∆ =  2 −  1 ,  2 <  1 ).Finally, there is some degree of spectral similarity of redox 1 and 3 in CoFe-PB.For redox 1, both the population change and signal become saturated and stop changing before the onset of redox 3. To aid in fitting redox 1 absorbance was constrained in this region and changes are purely associated with redox 3 (as for redox 1 U>>U 0 applies, thus no change in absorbance should be observed).This last assumption is not necessary but aids in reducing noise during fitting and so is recommended but should be used with care.Fitting was performed using an in-house code written in Julia using gradient descent and the NLOPT package.

S8 calculation of attenuation coefficients
The information above enables the determination of potential regions where only one redox transition contributes to the current such that: Holds true.In a region of applied potential where only one redox process takes place the differential attenuation coefficient can be calculated as the gradient of a straight line linking the change in concentration to the change in absorption.

∆𝐴 𝑇 𝑖 = 𝑄 𝑇𝑖 ∆𝛼 𝑇𝑖 (𝜆 𝑝𝑒𝑎𝑘 )
To calculate  we use a square wave voltametric technique in a region known to contain only one redox process (see top panel of Figure 3 in main text for justification of potentials as these clearly show small regions were only one process contributes to charge).Spectra were checked to confirm their similarity to the normalised differential coulometric actuation coefficient spectra.∆  (  ) is the slope of the peak differential absorption plotted against the charge obtained from integrating

S8 Calculation of turnover frequency from initial rate
As we measure partial charge of different surface redox processes, an apparent TOF can simply be obtained by dividing the OER current by the partial charge needed to generate a given coverage of the rate limiting intermediate (Q T3 ): With the TOF equal to Q T3 is obtained by adding the partial charge of redox transition T3 at the starting potential (obtained from spectroelectrochemistry) to the jump in absorbance from applying the step in potential, converted to a partial charge.J optical,initalrate is the initial rate of the optical signal, obtained by a similar linear fitting, converted into a current.Note, this is a state specific turnover frequency and is independent of the number of states involved in the RDS.If one assumes that one state is present in the RDS, as is indicated from our data then the O2 turnover frequency is calculated by dividing the quoted numbers by 4 in order to compare directly to the literature.

S11. Fitting of coverage and current to electroadsorption isotherms and BEP rate equations
In S11a, the measured coverage as a function of potential is fitted using two electroadsorption isotherms for CoFe-PB (top panel) and CoOOH (bottom panel).The electrochemical analogue of Lanmguir adsorption (Lanmguir electroadsorption), and Frumkin electroadsorption.These equations differ by only one term, r/F*θ, which describes the change in adsorption enthalpy as coverage increases.Note that because of this term, the half wave potential no longer corresponds to the standard potential as at half coverage the Frumkin equation reduces to E1/2=E 0 +0.5r/F.In S11b, activation energy considered to be linear function of coverage as a result of the BEP theory.Here EA=aθ+b.The "a" parameter here is the BEP coverage coefficient it links the change in activation energy to the change in coverage.The "b" parameter is in principle the activation energy at zero coverage.However, in this case, "b" the fitted value of b is strongly affected by k, the calculated Eyring pre-factor.This value cannot be fitted by must rather be calculated according to version of the Eyring equation modified by Nhong et al. 12

𝑘 = 4|𝑒|𝑘 𝐵 𝑇 ℎ
N Where e is the elementary charge in C,    is the thermal energy at room temperature in eV, h is Plank's constant in eVs and N is the total number of available sites, which we calculate from our optical data to be 1.26x10 16 cm -2 and 1.5x10 16 for CoOOH and CoFe-PB which corresponds to around 5 and 6 x 10 10 C s -1 cm -2 respectively (to do this convert the completing charge of redox T2 into a number density using Faraday's and Avogadro's constants) .These numbers are fixed parameters during the fitting procedure, however any error in this calculation very strongly effects the fitted value for b and is thus we do not consider our values of b to be true values without an external measurement of activation energy to confirm this.This is the subject of an ongoing study.
Given the implicit potential dependence of J in this model i.To investigate the interaction between neighbouring sites we calculate the energy of the individual sites of a supercell, which are initially equivalent, in the two relevant transitions (µ1-* --> µ1-OH and µ2-OH --> µ2-O).As seen in Table S1, the energies of oxidation each site in the reaction differ, due to the interaction between the adsorbates.We calculate the free energy of the reaction at half coverage (∆G(=1/2)) as the average energy of the smallest and the largest reaction step, for comparison with the experimentally determined E0.The width, r, also given in Table S1, is calculated as the difference in energy between these two steps and corresponds to the interaction parameter in the Frumkin isotherm.The computed values for the first transition ((∆G(=1/2)=1.19 eV, r=0.13 eV) match very well with the experimentally measured values for redox 2 (E0 = 1.17, r=0), while the values for the second transition (∆G(=1/2)=1.44eV, r=0.37 eV) match the values of the measured redox 3 (∆G(=½) = 1.5, r=0.34 eV).These results are summarized in Figure 7 of the main paper.

OER intermediates at various potentials on the 𝟎𝟏𝟏𝟐 surface
The strong interaction observed for the last transition is expected to have significant influence on OER.The intermediates of OER at a series of applied potentials with and without µ2-OH oxidation is shown above in Figure S13b-d potential, the µ2-*OH covered surface is stable.The resulting energy diagram shown in Figure S13c demonstrates a significant overpotential for both sites.The modulation of intermediate energies by exchanging µ2-*OH for µ2-*O at the same potential is perhaps most clearly seen at this potential.Once all the µ2-OH is converted to µ2-O at a potential of 1.62 V the barrier for OER is minimal (Figure S13d).We note that these results are different to the ones obtained in ref 14 , where a significant barrier for OER was also found on this surface.The reason for this may be that a different surface structure was considered, and deprotonation of the µ2-OH sites was not investigated.

Calculation of the theoretical Frumkin isotherm.
Given the estimated values of ∆G(=1/2) and r, a theoretical Frumkin electroadsorption isotherm for these processes can be plotted from our DFT analysis.Here, the enthalpy of adsorption is considered to be a Langmuir electroadorption model modified by a coverage dependent interaction term, r, (  S14a, showing that the most stable stoichometric surface is covered by µ2-OH and empty µ1 sites, but adsorption of water on this surface to form µ2-OH + µ1-H2O results in a small stabilisation.The water is converted to µ1-OH at ca. 0.9 V and the µ2-OH groups of the surface are deprotonated around 1.5 V.The interaction energy is again calculated by calculating the energy of the individual steps in the two relevant transitions (µ1-H2O --> µ1-OH and µ2-OH --> µ2-O).The results are shown in Table S2 together with the corresponding values of ∆G(=1/2) and r for the Frumkin isotherm.The results from the first transition suggest that 2µ1-H2O + µ1-OH + 3µ2-OH becomes the most stable structure at 0.04 V, and the remaining µ1-H2O are transformed to µ1-OH at much higher potentials (∆G(=1/2) of 1.25 V), slightly higher than the first transition on the 0112 surface.The second transition then starts immediately, and is completed at 1.57 V, with a ∆G(=1/2) similar to that of the second transition on the 0112 surface.A considerable width is observed for both transitions.The transitions are summarized in Figure S14b.

OER Intermediates of the 𝟏𝟎𝟏𝟒 surface
We calculate the OER for the µ1-OH + µ2-OH and µ1-OH + µ2-O covered surfaces at both the µ1 and µ2 sites and plot the results in Figure S13c.The potentials of 1.25 V for the µ1-OH + µ2-OH surface and 1.62V for the µ1-OH + µ2-O surface are chosen to match the potentials of the energy diagrams for the 0112 surface in Figure S12c-d, but since the transitions happen at similar potentials for the two edgeterminated surfaces these values are also representative of the potentials at which these 1014 surfaces are stable.The energy diagram for the µ1-OH + µ2-OH surface demonstrates a significant overpotential for both sites, and the formation of *O will therefore begin before the reaction can proceed.µ2-OH is converted to µ2-O at a potential of 1.57 eV and the partly O-covered surface needs a potential of 1.73 eV for OER to happen on either of the two types of surface site.The calculated OER potential is similar to the one calculated for this surface in ref 14 , although the preferred surface structure and reaction pathway found in this work is different.
The prevalence of the different surface facets in our CoOOH crystals is unknown, however the overall trends of the 0112 and 1014 surfaces show clear similarities and correspond well with the experimental observations.The surfaces get covered by OH on both µ1 and µ2 sites at a relatively low potential (1.11-1.37V), matching well with the experimentally determined potential of redox 2. However, before OER becomes possible on this surface the µ2-OH sites (on top of the surface for the 1014 surface and on the side for the 0112 surface) are gradually deprotonated in a wide potential range, matching the wide redox peak of redox 3 and the accumulation of states before the OER onset.
Once the deprotonation of these sites is completed at a potential of ca.1.6V the resulting surface has a small barrier for OER, and the reaction is thus able to proceed before further deprotonation.

Prussian Blue Calculations
The lattice constant of bulk Prussian Blue (PB, KFeCo(CN)6) was optmised to 9.96Å.The most favourable spin configuration was found to be 0 for both Co and Fe atoms, corresponding to Fe(II) and Co(III), in agreement with previous calculations. 17The lattice constant of PB with ¼ Fe(CN)6 defects was also optimized, revealing a similar lattice constant of 9.92Å.Potassium is removed from the unit cell for charge balance.The spin state of the metal atoms changes around the defect, such that the electronic structure is better described as Co(II), Fe(III), except from the Co atom that is not a neighbour to the defect, which remains Co(III).This is different to the results obtained in 18 however in these calculations H2O was adsorbed on the defect sites, whereas our calculations show that the adsorption of H2O is not favourable at room temperature (see below).
Prussian Blue analogues have a rich and complex defect chemistry 19 and in the following it is assumed that OER proceeds at the defect sites.However, the electronic properties of Co atoms deposited at the surface of PB crystals would probably be similar.For calculation of the OER activity a unit cell consisting of one defect-free KFeCo(CN)6 unit and one unit with a Fe(CN)6 vacancy was created, using the averaged lattice constant from the two bulk optimisations (see figure S15).This unit cell contains two types of exposed Co atoms; two Co(CN)4 which have two neighbouring defect sites and two Co(CN)5 which have only one neighbouring defect site.The adsorption of H2O on the two Co(CN)5 sites is calculated to be 0.41 eV, showing that the bare catalyst is the most stable reference.The adsorption energies of *OH and *O on the two types of Co sites are given in Table S3.Adsorption on Co(CN)5 is found to be more favorable than on Co(CN)4, and *OH is adsorbed on both of these sites before adsorption on the Co(CN)4 sites begins.Note that the structure is calculated with no restrictions on the spin and with several different values of fixed total magnetic moment in order to find the lowest energy spin state, which is also given in Table S3.Together these results suggest that only Co(CN)5 sites are covered by adsorbates below a potential of 1.86 V, and it is thus the adsorption on these sites that give rise to the observed isotherms.
With only two adsorption sites of this type in the unit cell there are also only two different adsorption energies.However, one can imagine that the different values arise either from interactions across the vacuum at the vacancy or as a result of electronic effects through the bulk crystal.We therefore tried to calculate the adsorption energies in two other unit cells, one consisting of two bulk units and one defect (with two Co(CN)5 units) and another one consisting of three bulk units and one defect in a 2x2 arrangement (with four Co(CN)5 units).The calculated adsorption energies of *OH are given in Table S5, and span a range of 1.40-1.54eV, indicating an interaction parameter of 0.14 eV.This matches well with the experimentally observed redox 2 transition.A corresponding investigation of the *O adsorption energies (Table S6) reveals an energy range of 1.68-1.76eV,matching well with the observed redox 3 (E0 = 1.66V, r=0. a The two spin states were within 0.01 eV of each other b Identical adsorbates on opposite sides of the defect is found to be the most stable arrangement

Figure S1 .
Figure S1.Microscopy of CoOOH films.(a) Top-down SEM.(b) Cross sectional SEM false coloured to highlight the CoOOH layer in grey.(c) AFM.(d) Co and Fe 3p XPS spectra.This region is chosen as the Fe 3s and 2p regions overlaps with peaks from Sn emission from the FTO substrate.

Figure
Figure S2.(a) In situ-surface enhanced Raman spectra of CoOOH at a series of applied potentials showing the Co-O breathing mode.The change in signal amplitude is a result of the differential absorption changes in the film at increasing applied potential (see SEC data in main paper).Inset: 1100-1300 wavenumbers region previously suggested by Moysiadou to show a bridging superoxo intermediate 5 shows no discernible broad signal between 1100-1300 wavenumbers growing with applied potential.(b) Normalised spectra showing the change in breathing modes consistent with the conclusions of Bell and Co-workers, indicating that a comparable structure is produced herein. 4Conditions: purified 0.1 M KOH, Pt wire counter electrode sat.dKCl Ag/AgCl reference electrode.

Figure
Figure S4.(a) Top Down SEM image of CoFe-PB.(b) Cross sectional SEM image false coloured to highlight the CoFe-PB in purple the background.(c) XRD pattern of CoFe-PB films shown alongside standards for FTO, CoFe-PB and Co(OH)2

Figure S5 .
Figure S5.Fe (a) and Co (b) K-edge spectra of CoFe-PB at a series of applied potentials (vs RHE)

Figure S7 .
Figure S7.∆  −∆ −20 for CoOOH (a) and CoFe-PB (b).The spectra converge in two regions in both cases.For clarity spectra associated with the less significant component (redox transition 1) are not shown.Note the regions where the spectra converge.

Figure
Figure S8 Calculation of attenuation coefficients for redox transition T1 (a) ,T 2 (b) and T3 (c) for CoOOH.Left: the differential absorbance generated by a square wave voltage, Middle: the resulting current transients, Right The correlation of charge with optical absorbance.

Figure S8 .
Figure S8.Calculation of attenuation coefficients for redox transition T1 (d) , T2 (e) and T3 (f) for CoFe-PB.Left: the differential absorbance generated by a square wave voltage, Middle: the resulting current transients, Right The correlation of charge with optical absorbance.

Figure
Figure S9 Comparison of the differential absorbance spectra obtained at different step sizes to the normalised differential attenuation coefficient (component spectra) of redox transition T3 for CoOOH (a) and T2 and T3 CoFe-PB (b).

Figure
Figure S10 (a) Step potential induced accumulation and open circuit decay kinetics of CoFe-PB at a series of increasing step potentials.(b) TOF as a function of coverage, comparing TOF calculated by diving current by partial charge and initial rate of optical decay (represented as a current  , in the equations below) by partial charge.(c) Step potential induced accumulation and open circuit decay kinetics of CoOOH at a series of increasing applied potentials, with corresponding of initial rate and current derived TOF comparison (d).(e) Comparison of TOF observed herein forCoOOH to those obtained by measurements byBurke et.al.
e. (()).One may calculate the Tafel slopes empirically by simple substitution.() herein is given by adsorption isotherms whilst the () is empirically determined fit of current versus coverage, shown in Figure S11 b for CoFe-PB (top panel) and CoOOH (bottom panel).

Figure
Figure S11.(a) Fitting of potential as a function of coverage of CoOOH (bottom) and CoFe-PB (top) to frumkin and Langmuir electroadsorption isotherms.(b) Fitting OER current to a BEP driven rate equation for CoOOH (bottom) and CoFe-PB (top).

Figure S12b :
Figure S12b: Energy diagram for OER on the µ3 site of the 0001 surface at a potential of 1.62 V.The empty µ3 site is denoted by *.

Figure
Figure S13a (left): Pourbaix diagram for the 0112 surface (left) showing the most stable surface as a function of the potential.The investigated surface structures (right) are drawn with the colour of the frames matching the colours of the lines in the pourbaix diagram.Co atoms are green, O is red and H is white.(right) surface structures, color coded to match the colors in the left panel.
. At 0 V (S13b), both surfaces are technically unstable and the reaction is uphill due to the absence of strong driving potential.However, modulation of the *O intermediate with respect to *OH can clearly be seen when µ2 is covered by *O instead of *OH.This destabilization also affects the µ1 site (shown in cyan).At a driving potential of 1.25 V, close to the thermodynamic S13-b-d.Comparison of energy of the intermediates of on  OER when µ2 sites are covered with OH (left) and by O (right at (b) 0 VRHE and (c) 1.25 VRHE (d) 1.62 VRHE , leading to an interaction dependent standard potential at  0 =  1The 1014 surface is modelled in a 1x3 unit cell, such that interactions between adsorbates along the edge of the CoOOH sheet can likewise be investigated for this surface.The brilluoin zone is sampled by 4x3 k-points.The surface termination at different potentials is probed by considering the full coverage adsorption of *OH, *O and *H2O on the stoichometric surface, as well as deprotonation of OH sites at the surface.On the 1014 surface the adsorbates on the side of the sheets are coordinating to a single Co atom (µ1-OH, top-style adsorption) while the adsorbates on the top of the surface adsorb in a bridge configuration between two Co atoms (µ2-OH).The pourbaix diagram for the 1014 surface is shown in Figure

Figure
Figure S14a: (left) Pourbaix diagram of the 1014 surface (left) showing the most stable surface as a function of the potential.The investigated surface structures (right) are drawn with the colour of the frames matching the colours of the lines in the diagram.Co atoms are green, O is red and H is white.(right) Illustrations of the surfaces corresponding to each line in the lefthand panel.

Figure S14b :
Figure S14b: Summary of the surface transitions of the 1014 surface.

Figure S14c :
Figure S14c: Energy diagram for OER on the µ1-OH + µ2-OH CoOOH 1014 surface (left), and the µ1-OH + µ2-O surface (right), considering the two different possible active sites.Sites indicated with coloured arrows in the structures correspond with the colours of the energy diagrams below.Note that for the reactions on the µ1-OH site, it is favourable for the OOH intermediate to transfer a proton to a neighbouring µ1-OH to form µ1-O2+ µ1-H2O, while reactions on the µ2-OH/µ2-O site go through OOH.

Figure S15 :
Figure S15: Computational unit cell used to model OER in the CoFe PB analogue.The two different types of Co active sites around the defect site are marked.

Figure S16 :
Figure S16: Energy diagram for OER at 1.65V on the Co(CN)5 site of PB with and without OH adsorbed on the other Co(CN)5 site.
measured intermediate was inactive.One would still be able to measure this value, although the result would be meaningless.However, if the intermediate is active then the initial rate of decay of the intermediate under open circuit condition should be commensurate to the apparent TOF, as both are should measure inherent activity.As ΔA is a measure of partial charge the initial rate of decay is proportional to a current:

Table S1 :
Energies for the stepwise transitions between stable surface structures on the 0112 surface, and corresponding parameters for the Frumkin isotherm.

Table S2 :
Energies for the stepwise transitions between stable surface structures on the 1014 surface and corresponding parameters for the Frumkin isotherm.The values of ∆G(=1/2) and r are calculated from the 2 nd and 3 rd step only, since the first step is happening at much lower potential. a To calculate the overpotential for OER the adsorption energy of *O is also calculated.We focus on the Co(CN)5 sites, since they have the lowest *OH adsorption energies, considering *O adsorption both before and after the adsorption of the second *OH.The results shown in TableS4show that adsorption of *O happens at a potential of 1.72-1.75V,i.e. after the adsorption of the second *OH on Co(CN)5 but before the adsorption of *OH on the Co(CN)4.To ensure that OER proceeds before the adsorption on *OH on Co(CN)4 the energy of *OOH on the Co(CN)5 site (with and without *OH on the other Co(CN)5 site) is also calculated.The resulting energy diagram in FigureS16, shows that the limiting step in the reaction is the conversion of *OH to *O and the presence of *OH on the other Co(CN)5 site results in a destabilisation of all the reaction intermediates but a very similar overpotential.

Table S4 :
Differential adsorption energies of O on PB sites (in eV) and total spin of the structure.
a The two spin states were within 0.01 eV of each other

Table S5 :
19 eV).Differential adsorption energies of OH on Co(CN)5 sites (in eV) and total spin of the structure for different sized unit cells.
a Adsorption on nearest neighbour sites is found to be the most stable arrangement.

Table S6 :
Differential adsorption energies of O on Co(CN)5 sites (in eV) and total spin of the structure for different sized unit cells.