We applied a method previously developed for modeling the thermochemistry of electrochemical reactions based on density functional calculations.4b, 7, 9 The derivation of relations 2–5 is in the Supporting Information. The effect of liquid water was implicitly taken into account as we used liquid water as reference. However, the interaction of water with the intermediates at the surfaces has been neglected. The reason is that on the oxidized surface, there was no room for water molecules at the surface, where the interactions would have been the largest.7 We calculated ΔG1–4 using the computational standard hydrogen electrode (SHE) allowing us to replace a proton and an electron with half a hydrogen molecule at U=0 V vs SHE.9 The theoretical overpotential is independent of the pH or the potential values, because the free energies obtained by using Equations (2)–(5) vary in the same way with pH and U, thereby the potential determining step remains the same. Therefore, the analysis performed for the free energies is at standard conditions (pH=0, T=298.15 K) and U=0: ΔG1–40. Since the barriers between the intermediates are not included, the free energy diagrams we have produced represent a first step towards a complete picture of the reaction path. We expect that the thermodynamic analysis presented here will capture trends in activity, due to cancellation of errors when similar surfaces are compared; however, absolute activities are not obtained at this level of modeling.
A very important parameter which can be deduced from the free energy diagram is the size of the potential-determining step. This concept was developed in other previous papers for OER and ORR6–7, 9–10 and reviewed in two other recent papers.4 More precisely, the catalytic performance was estimated by the magnitude of the potential-determining step for the OER, GOER. This was the last step to become downhill in free energy as the potential increased, that is, the specific reaction step in the four-step mechanism with the largest ΔG [Eq. (6)]:
The energy diagram for the ideal (but nonexistent) oxygen evolution catalyst is shown in Figure 1 a. This ideal catalyst should be able to facilitate water oxidation just above the equilibrium potential. This requires all the four charge transfer steps to have reaction free energies of the same magnitude at zero potential (4.92 eV/4=1.23 eV). This is equivalent to all the reaction free energies being zero at the equilibrium potential, 1.23 V (Figure 1 a). The catalyst that fulfills this requirement is thermochemically ideal. Real catalysts do not show this behavior. The calculated free energy diagrams at standard conditions of the OER on the surfaces of LaMnO3 (strong binding), SrCoO3 (intermediate binding), and LaCuO3 (weak binding) are shown in Figure 1a,c,d. The most representative potentials are at U=0 V for which all steps are uphill, at standard equilibrium potential for oxygen evolution at U=1.23 V, when some of the steps become downhill but some still remain uphill, and at the GOER potentials when the potential-determining step becomes downhill. Accordingly, LaMnO3 had a rather large overpotential due to ΔG30. For SrCoO3, ΔG20 and ΔG30 were almost the same value and the overpotential was small, whereas for LaCuO3, ΔG2 was the potential-determining step.
Figure 1. Standard free energy diagram for the OER at zero potential (U=0), equilibrium potential for oxygen evolution (U=1.23), and at the potential for which all steps become downwards at pH 0 and T=298 K over: a) the ideal catalyst, b) LaMnO3, c) SrCoO3, and d) LaCuO3. Standard free energies at U=0 for e) the ideal catalyst, f) LaMnO3, g) SrCoO3, and d) LaCuO3. For all three cases, ΔGHOO*−ΔGHO* (vertical dashed lines) is approximately constant with an average value of 3.2 eV, whereas the optimum value is 2.46 eV. The variation of ΔGO* between ΔGHO* and ΔGHOO* differs for each one. For the ideal case, ΔGHO* is 1.23 eV, ΔGHOO* is 3.69 eV, and ΔGO* is in the middle at 2.46 eV.
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Figures 1g,f,h show that the bond strength of all the intermediates decreases from left to right (LaMnO3, SrCoO3, LaCuO3). Note that the levels of the intermediates moved together, that is, if one reaction energy changed, the others did too. This correlated energy phenomenon has been observed on metal and metal oxide surfaces as a result of the scaling relations between the intermediates.6–7, 11 An example is the linear relation between the binding energy of HO* and O*, for which the slope of one half reflects that oxygen has two bonds to the surface, whereas HO* has only one bond. The intercept is determined by the type of binding site, meaning that there are different intercepts for HO*(ontop) vs O*(ontop) scaling compared to the HO*(hollow) vs O*(hollow) scaling. This gives rise to different intercepts for metals and oxides because the binding sites are different. Figures 1e–h show that the free energy difference between HO* and HOO* is almost constant, independent of the binding strength to the surface. It was pointed out in a recent review by M. Koper4b that the bindings of HO* and HOO* are related to each other by a constant of approximately 3.2 eV both for metals and oxide surfaces regardless of the binding site, which implies that there is a universal scaling relation between HO* and HOO*.
Here, we established the formal scaling relationship between HO* and HOO* binding energies over a wide range of oxides. Figure 2 shows that the binding energies of HOO* and HO* species on the various oxide surfaces were linearly correlated, with a slope of approximately 1, and an intercept of 3.2 eV. The mean absolute error (MAE) of the linear fit was 0.17 eV, indicating an extremely strong correlation between the two species.
Figure 2. Adsorption energy of HOO* plotted against the adsorption energy of HO* on perovskites, rutiles, anatase, MnxOy, Co3O4, and NiO oxides. They were calculated using the relations (10) and (11) and do not include zero point energy and entropy corrections. Hollow symbols represent the adsorption energy on the clean surfaces: perovskites (○), rutiles (▵), MnxOy (□), anatase (◊), Co3O4 (+), NiO. The solid symbols represent the adsorption energies on high coverage surfaces, with oxygen atoms representing nearest neighbors. The best fit of all the points is ΔEHOO*=ΔEHO*+3.20 eV and with 68 % of the points within ±0.2 eV and 95 % within ±0.4 eV. The red star indicates the point at which the binding energies need to be for an ideal electrocatalyst. The relation for the perfect catalyst is: ΔEHOO*=ΔEHO*+2.44 eV.
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The slope of unity in the correlated binding energies of HO* and HOO* reflects the fact that both species have a single bond between an O atom and the surface. The constant intercept implies that HO* and HOO* normally prefer the same type of binding site. From the point of view of the surface, HO* and HOO* look very similar. This results in the approximately constant difference of ΔEHOO*−ΔEHO* of 3.2 eV for all the oxides considered. Notably, this difference is also observed on metal surfaces.6 Furthermore, ΔEHOO* and ΔEHO* are independent of potential and they only describe the interaction between the intermediates and surface oxides. However, ΔG1–4 changes with potential, pH, and temperature.
Interestingly, the constant difference between the adsorption energies of HO* and HOO* of 3.2 eV, regardless of the binding energy of O*, defines a lower limit for the OER overpotential.4b Since two proton and electron transfer steps separate the two intermediates, the perfect separation in terms of energy should be 2.46 eV, as illustrated in Figure 1 e. The difference in the energetic of these two steps between actual catalysts and an ideal one (3.2–2.46 eV)/2 e gives a minimum overpotential of 0.4–0.2 V, even if we could find a material in which the O* level is placed optimally between those of HO* and HOO*, as shown in Figure 1 g (with the value −0.2 V that comes from standard deviation of the population from 3.2 eV value: 2σ=±0.4 V with 95 % of the values expected to lie within this confidence interval). The thermochemically ideal catalyst is characterized by having ΔG10=ΔG20=ΔG30=ΔG40=1.23 eV at standard conditions, which can only be achieved at a specific binding of all intermediates indicated by the red star in Figure 2. It is seen that this point clearly falls outside the general trends and there is no oxide-based material in the classes considered here that provides an optimum binding of both HO* and HOO*. In this picture, the challenge is to find a way to modify oxide surfaces or the electrochemical interface, such that the relative stability of HOO* and HO* changes.
Descriptor and activity volcano
Given the constant difference between the HOO* and HO* levels, the variation in the overpotential, ηOER from one oxide surface to the next is determined by the O* adsorption energy. This means that, either step (2) or step (3) is potential determining [Eq. (8):
Plotting ηOER as function of Δ−Δ for the classes of materials considered here will therefore lead to a universal volcano relationship independent of the catalyst material. For clarity, the trends are shown separately for perovskites (Figure 3 a) and rutiles (Figure 4 a), and the points represent the calculated value for each oxide.
Figure 4. a) Activity trends towards oxygen evolution, for rutile, anatase, Co3O4, MnxOy oxides. The negative values of theoretical overpotential were plotted against the standard free energy of ΔGHO*−ΔGO* step. The effect of interaction with the oxygen from the neighboring site is considered: rutile oxides (▴), MnxOy (▪). For NiOb2, PbOb2, and SnOb2, cus sites (see Figure 5 a,b) are empty, and the reaction takes place on the bridge sites (a complete picture of the surface is given in the Supporting Information). Hollow triangles (▵) represent the low coverage regime. b) Theoretical overpotential vs the experimental overpotential in acidic media (•) and in alkaline media (○). Experimental data were taken from Y. Matsumoto and E. Sato.12 All experimental values were considered at 10 mA cm−2 and room temperature.
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This theoretical analysis leads to the following ordering of catalyst activities for the following perovskites: SrCoO3>LaNiO3>SrNiO3>SrFeO3>LaCoO3>LaFeO3>LaMnO3. The trend agrees well with experimental findings by Bockris et al. and Y. Matsumoto et al.3a, 12 under alkaline conditions (Figure 3 b). All experimental overpotentials were reported at 10 mA cm−2, because a large database of overpotentials are reported at this current density. Ideally, the comparison should be made with potentials obtained on single crystals. Even then, the quantitative comparison between theoretical and experimental overpotentials remains difficult. The theoretical overpotential is not directly comparable to experimentally determined values because the activation barriers were neglected. Furthermore, the experiments were performed using electrodes with oxide nanoparticles, for which the effective surface area is often unknown or not reported. Hence, the current per geometric area is not directly available. In addition, the experimentally measured overpotential depends on the current density at which it is measured. Despite these uncertainties, it should be possible to compare trends in overpotentials for a set of different oxides.
The comparison to the experiments can be seen in Figure 3 b for the perovskites. According to our calculations, SrCoO3 has a Δ−Δ of 1.48 eV, close to the very top of the volcano. The high activity of SrCoO3 was also predicted theoretically by Y. Matsumoto et. al.;13 however, the main problem lies in the experimentally determined value and is related to how to obtain SrCoO3 with perovskite-type structure, since experimentally SrCoO3 was obtained under a non-perovskite type structure and exists as SrCoO2.5 in composition.
For the other oxides such as rutiles (anatases), Mn oxides, and Co oxides, the activity order given by the theoretical calculations was extracted from Figure 4 a: Co3O4≈RuO2>PtO2−rutile phase≈RhO2>IrO2≈PtO2 β-phase(CaCl2)≈MnxOy≈NiOb2≈RuO2 and IrO2 anatase phase>PbOb2≫Ti, Sn, Mo, V, Nb, Re oxides. The anatase phases with crystallographic orientation 001, such as RuO2 and IrO2, showed approximately the same activity as the rutile phases. A similarly good agreement between the theoretical and experimental values of overpotentials on oxides other than perovskites is illustrated in Figure 4 b.
Even the comparisons between different experimental values were difficult to establish, due to many factors that affect the potential, such as pH, effective surface area, and particle size. A slight discrepancy exists between the calculated and measured Co3O4 activity. DFT calculations showed that Co3O4 was slightly more reactive than RuO2, whereas most of the experimental studies suggest that Co3O4 has a higher overpotential than RuO2 by 0.2–0.25 V.12 It was shown that Co3O4 is nonstoichiometric with an excess of oxygen and that the size of crystallites vary with the calcination temperature.3g Recently, Singh et al. synthesized a spinel type of Co3O4 thin film which showed a low overpotential14 in agreement with our calculations. It has also been reported that the overpotential on Co-oxide nanoparticle electrocatalysts is size-dependent with lower overpotentials on smaller particles.15 Other Co oxide structures with a low overpotential have been reported as well.16 In Figure 4 b, we compared for Co3O4, three experimental overpotentials from the literature to the computed overpotential. Starting from left to right, the most active was the value reported by Singh et al.,14 followed by three values reported by Esswein et al.15a A slight discrepancy was also obtained in the case of NiO, however, the theoretical value was calculated for a perfect single crystal NiO, whereas in reality, NiO is expected to have a more complicated composition, including species in higher oxidation states.3g, 17
We emphasize that the reaction mechanism is more flexible for the oxides close to the top of the volcano at which point the intermediates have a better compromise in interaction strength, which could be the case for MnxOy oxides (detailed results will be discussed in a future manuscript). However, at the top of the volcano, the overpotential is small and other reaction paths could be relevant if their overpotential is smaller than the values reported in this study. This flexibility of reaction mechanism might result in a slight variation in the theoretical overpotentials, and the details of this matter are out of the scope of this paper.
The actual surface of an oxide catalyst can experience oxidation and/or dissolution in the highly corrosive OER environment. For example, some oxides such as NbO2, ReO2, VO2, MoO2, and CrO217a are not stable. Still, the theoretical values may be interesting as a guide in designing mixed oxides that could show improved activity.18
Given the robustness of this theoretical model as applied to oxide materials of well-defined stoichiometry and crystal structure, one can also potentially apply these methods to nonstoichiometric oxide catalysts.