Kinetics of Electrocatalytic Reactions from First-Principles: A Critical

May 2, 2017 - ... Gmax(RI) rather than the highest free energy difference between consecutive reaction intermediates, ΔGloss, as a descriptor for the...
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Kinetics of Electrocatalytic Reactions from First-Principles: A Critical Comparison with the Ab Initio Thermodynamics Approach Kai S. Exner†,‡ and Herbert Over*,† †

Physical Chemistry Department, Justus-Liebig-University Giessen, Heinrich-Buff-Ring 17, 35392 Giessen, Germany Institute of Electrochemistry, Ulm University, Albert-Einstein-Allee 47, 89069 Ulm, Germany

‡

CONSPECTUS: Multielectron processes in electrochemistry require the stabilization of reaction intermediates (RI) at the electrode surface after every elementary reaction step. Accordingly, the bond strengths of these intermediates are important for assessing the catalytic performance of an electrode material. Current understanding of microscopic processes in modern electrocatalysis research is largely driven by theory, mostly based on ab initio thermodynamics considerations, where stable reaction intermediates at the electrode surface are identified, while the actual free energy barriers (or activation barriers) are ignored. This simple approach is popular in electrochemistry in that the researcher has a simple tool at hand in successfully searching for promising electrode materials. The ab initio TD approach allows for a rough but fast screening of the parameter space with low computational cost. However, ab initio thermodynamics is also frequently employed (often, even based on a single binding energy only) to comprehend on the activity and on the mechanism of an electrochemical reaction. The basic idea is that the activation barrier of an endergonic reaction step consists of a thermodynamic part and an additional kinetically determined barrier. Assuming that the activation barrier scales with thermodynamics (so-called Brønsted−Polanyi−Evans (BEP) relation) and the kinetic part of the barrier is small, ab initio thermodynamics may provide molecular insights into the electrochemical reaction kinetics. However, for many electrocatalytic reactions, these tacit assumptions are violated so that ab initio thermodynamics will lead to contradictions with both experimental data and ab initio kinetics. In this Account, we will discuss several electrochemical key reactions, including chlorine evolution (CER), oxygen evolution reaction (OER), and oxygen reduction (ORR), where ab initio kinetics data are available in order to critically compare the results with those derived from a simple ab initio thermodynamics treatment. We show that ab initio thermodynamics leads to erroneous conclusions about kinetic and mechanistic aspects for the CER over RuO2(110), while the kinetics of the OER over RuO2(110) and ORR over Pt(111) are reasonably well described. Microkinetics of an electrocatalyzed reaction is largely simplified by the quasi-equilibria of the RI preceding the rate-determining step (rds) with the reactants. Therefore, in ab initio kinetics the rate of an electrocatalyzed reaction is governed by the transition state (TS) with the highest free energy G#rds, defining also the rate-determining step (rds). Ab initio thermodynamics may be even more powerful, when using the highest free energy of an reaction intermediate Gmax(RI) rather than the highest free energy difference between consecutive reaction intermediates, ΔGloss, as a descriptor for the kinetics.

1. INTRODUCTION

screening as introduced by Norskov and co-workers is founded.9 Due to the conceptual simplicity of ab initio thermodynamics this approach has become so popular in electrocatalysis that even experimentalist are using the underlying reasoning to rationalize their experimental data. However, recent kinetic studies from first-principles have indicated that ab initio thermodynamics is not always able to identify the critical step in the (often complex) kinetics of electrocatalytic reactions. Over the past years detailed ab initio kinetics studies have emerged in electrocatalysis10−15 so that a critical comparison of

Over the past decade, research in electrocatalysis has been spurred by theoretical calculations and predictions based on simple ab initio thermodynamics where often the binding energy of a single reaction intermediate only is considered to govern the performance of an electrocatalyst and the underlying kinetics of an electrocatalyzed reaction.1−7 The connection between thermodynamics and kinetics has been established by a generalized Sabatier principle according to which reaction intermediates must not be too strongly nor too weakly bound to the catalyst’s surface in order to realize an active catalyst. Applying Brønsted−Polanyi−Evans (BEP) relations in combination with scaling relations allows then constructing volcano plots8 on which theoretical material © 2017 American Chemical Society

Received: February 6, 2017 Published: May 2, 2017 1240

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fraction α (so-called symmetry factor or transfer coefficient) of the thickness xHe of the Helmholtz double layer. Biasing the electrode by an anodic overpotential η > 0 V (cf. Figure 1), the free energy of the TS decreases by αeη while that of the oxidized species is lowered by 1eη. For η > 0 V the anodic current density is now higher than that of the cathodic (reversed) process, resulting in a net current density j that is given by the so-called Butler−Volmer equation:16

ab initio thermodynamics and ab initio kinetics is topical and a subject of general interest in electrocatalysis. We start in section 2 with a tutorial about the general concepts of the kinetics in electrocatalyzed reactions and how this leads to the generalized Butler−Volmer equation. The underlying free energy landscape can be fully or partly determined by ab initio kinetics or ab initio thermodynamics, respectively. In section 3, we compare critically the results of ab initio kinetics with those from ab initio thermodynamics for three prototypical electrocatalytic reactions over single crystalline model electrodes, namely the chlorine and oxygen evolution over RuO2(110) and the oxygen reduction reaction over Pt(111). For all of these reactions, also dedicated surface electrochemistry experiments are available allowing for a direct theory versus experiment comparison. In section 4, we conclude with an assessment of the merits and shortcomings of ab initio thermodynamics in the field of electrocatalysis and how this powerful concept can be improved.

⎧ ⎛ αeη ⎞ ⎛ −(1 − α)eη ⎞⎫ j(η) = j0 ⎨exp⎜ ⎟ − exp⎜ ⎟⎬ kBT ⎝ ⎠⎭ ⎩ ⎝ kBT ⎠ ⎪

⎪

⎪

⎪

(1)

with e = elementary charge of an electron. The free energy term eη is actually the driving force of the electrochemical reaction and has two major consequences: (a) η shifts the free energy of the product relative to the educts (thermodynamics) so that either the anodic (η > 0 V) or the cathodic (η < 0 V) current is dominating the total current density above |η|>30 mV (so-called Tafel regime). (b) The overpotential η affects the free energy G# of the TS (kinetics) by the interplay with the symmetry factor via αeη or by (1−α)eη in case of the anodic or cathodic reaction, respectively. The effect of the employed electrode material on the current density and therefore to the rate of product formation (Faraday’s law) is coined electrocatalysis. According to the Butler−Volmer equation (eq 1), the electrode material enters only j0 and α. As the transfer coefficient α is frequently 0.516 and hardly affected by the electrode material, the objective of electrocatalysis is to increase the exchange current density j0 for an electrochemical reaction by optimizing the electrode material, i.e., by reducing the free energy G# of the TS.

2. GENERAL DISCUSSION OF KINETICS IN ELECTROCATALYSIS 2.1. Simple Butler−Volmer Equation for Elementary Reaction

We consider first an elementary redox reaction step: Red → Ox +e− such as encountered with the dissolution of silver Ag → Ag+ + e− in a AgNO3 electrolyte solution where the reduced species (Red: Ag) is transformed to the oxidized species (Ox: Ag+) via a single electron transfer taking place within the (Helmholtz) double layer region. The free energy diagram in Figure 1 is depicted for the case of thermodynamic equilibrium

2.2. Free Energy Landscape of a Complex Electrocatalyzed Reaction

In a complex electrochemical (redox) reaction under equilibrium conditions (η = 0 V) z electrons are transferred consecutively, thereby defining at least (z − 1) reaction intermediates (RI) and z transition states (TS). Each additional purely chemical step will add an additional RI and TS to the energy diagram. In Figure 2, the free energy diagram is depicted of a typical four-electron process for η = 0 V such as encountered with the OER and the ORR, including one additional purely chemical reactions step. Under typical electrochemical conditions all RIs ((i)−(iii)) before the TS #3 with the highest free energy are in equilibrium with the reactants: quasi-equilibrium. For this situation, the rate of the electrochemical reaction is determined by the TS with the highest free energy G#rds, manifesting also the rate-determining reaction step (rds: kinetics). The transition between consecutive RI with the highest free energy difference defines ΔGloss (thermodynamics)2 (cf. Figure 2) and the potential-determining step (pds) in case of an electrochemical reaction step. For the specific free energy landscape in Figure 2, the transition over TS #3 corresponds to the rds and the transition from RI(iii) to RI(iv) represents the pds that is equal to the rds in our case. How to determine the free energy landscape? The free energies of the RI (including reactants and products) on the electrode surface can be determined by ab initio thermodynamics (TD) and are indicated by blue bars in Figure 2. More specific, the most stable electrode surface structure is

Figure 1. Free energy diagram of a single electron transfer between a metal electrode (e.g., Ag) and the electrolyte solution (e.g., Ag+) within the Helmholtz double layer of thickness xHe is shown for two overpotentials η = 0 V (equilibrium) and η > 0 V (anodic polarization).

of our redox reaction; i.e., the electrode potential is equal to the equilibrium potential U0. The deviation of the electrode potential U from the reversible electrode potential U0 defines the overpotential η = U − U0. The total current density j is zero at η = 0 V, although the respective anodic and the cathodic current densities are nonzero in a dynamical equilibrium. The exchange current density j0 is defined by the anodic respectively cathodic current density at equilibrium (η = 0 V) and is proportional to exp(−G#/kBT) with G# = the free energy of the transition state (TS: #), T = absolute temperature in Kelvin, and kB = Boltzmann’s constant. The location of the TS is given as 1241

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2.3. Generalized Butler−Volmer Formalism of a Complex Electrocatalyzed Reaction

Assuming that all RI preceding the TS with the highest free energy (defining the rds; Figure 2) are in equilibrium with the reactants, the generalized Butler−Volmer equation reads:16,19 ⎧ ⎛ (γ + r α )eη ⎞ rds rds j(η) = j0 ⎨exp⎜ ⎟ k ⎠ ⎩ ⎝ BT ⎪

⎪

⎛ −(z − γ − rrdsαrds)eη ⎞⎫ − exp⎜ ⎟⎬ kBT ⎝ ⎠⎭ ⎪

⎪

(2)

with γ = number of electrons transferred before the rds, rrds = 0 for a chemical step and rrds = 1 for an electrochemical reaction step of the rds, αrds = transfer coefficient of the rds, and z is the total number of electrons transferred in the overall reaction. The number of electron transfers γ before the rds depends critically on the definition of the first reaction step and therefore on the starting electrode surface. As soon as one of the RI preceding product formation becomes lower in free energy with increasing η than the starting surface then the starting surface changes to this RI and affects accordingly γ. The exchange current density j0 incorporates the intrinsic catalytic property of the electrocatalyst, namely the transition state free energy G#rds of the rds:

Figure 2. Energy diagram for a four electron process including one pure chemical reaction step (ii) → (iii) for η = 0 V (solid line) and η > 0 V (dashed line). Thermodynamics is indicated in blue, kinetics in red, while the rds in dependence of the applied overpotential is marked in violet.

determined as a function of the electrode potential and the pH value under reaction conditions, but suppressing the actual reaction (constrained TD), culminating into a so-called Pourbaix diagram.17,18 The initial electrode surface structure at the reversible redox potential from which the electrochemical redox reaction starts is defined by the structure with lowest free energy among the RI preceding product formation; notice that the starting surface may change when applying an overpotential as observed with OER over RuO2(110)13 and ORR over Pt(111).14 The free energies of the TS (red in Figure 2) are calculated by computing-time demanding density functional theory (DFT) calculations within (harmonic) transition state theory (kinetics from first-principles). Once the free energy landscape is determined for η = 0 V (solid line in Figure 2), the variation with overpotential η of the free energy landscape can easily be accounted for by counting the number of transferred electrons (dashed line in Figure 2). The free energies of the RI are affected by z′eη, where z′ is the number of electron transfers to produce the RI starting from the reactants and the initial electrode surface. The free energies of the TS #k between RI′ and RI″ are affected by (z′ + (z″ − z′)αk)eη, with z′ and z″ being the number of transferred electrons for generating RI′ and RI″, respectively, and αk is the transfer coefficient of the considered reaction step k. The reaction step (i) to (ii) in Figure 2 is a one-electron process. Therefore, the free energy of RI(ii) is lowered by 1eη, while that of the TS #1 is decreased by α1eη. The next step (ii) → (iii) is of pure chemical nature. Therefore, the free energy of RI (iii) and TS #2 are both reduced by 1eη as RI(ii). The reaction step (iii) → (iv) is again of electrochemical nature so that the free energy of RI (iv) is lowered by 2eη and the TS #3 is lowered by (1 + α3)eη. The remaining two electrochemical steps can be treated accordingly (for details, see Figure 2). From this variation of the free energy diagram with overpotential η, we can draw two general conclusions: (a) With increasing η, the rds and pds may move toward the reactants: In Figure 2, the rds shifts from #3 to #2, while the pds remains the step RI(ii)→ RI(iii). (b) Upon increasing η, the free energy of one RI may become even lower than the starting surface. This requires a redefinition of the starting surface and a renumbering of the reaction steps.

j0 =

⎛ −G # ⎞ kBTze Γact exp⎜⎜ rds ⎟⎟ h ⎝ kBT ⎠

(3)

with h, Γact denoting the Planck’s constant and the surface density of active sites, respectively. A fundamental quantity in the field of electrode kinetics is the so-called Tafel slope, which quantifies by how much the applied electrode potential has to be raised to increase the current density by one order of magnitude. The Tafel slope b follows from the generalized Butler−Volmer equation b=

k T ln(10) dη = B d log j e(γ + rrdsαrds)

(4)

and depends on the apparent transfer coefficient (γ + rrdsαrds). In Table 1, we summarize the experimentally derived Tafel slopes taken from single crystalline model electrodes. Tafel slopes can be determined by ab initio theory.20 Table 1. Experimental Tafel Slopes for the CER and OER over RuO2(110) and the ORR over Pt(111) system

Tafel slope b

ref

CER-RuO2(110)

low η: 40 mV/dec high η: 88 mV/dec low η: 59 mV/dec high η: 118 mV/dec low η: 59 mV/dec high η: 118 mV/dec

21

OER-RuO2(110) ORR-Pt(111)

22 23 24

2.4. Ab Initio Thermodynamics Used in Electrocatalysis

In material search/optimization,8 it is assumed that the reaction mechanism does not change within a homologous series of materials so that the optimization strategy is based on ab initio TD: “The lower ΔGloss, the better the catalyst”. However, the ab initio TD approach is also used to draw kinetic conclusions in electrocatalysis by determining the pds, 1242

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reaction step. However, Gmax(RI) may still be helpful as a descriptor.

tacitly assuming that pds = rds and the activation barriers are governed by thermodynamics (endogenic steps) (cf. Figure 3). This crude approximation is justified only, if the additional kinetic barriers are small such as encountered with proton transfer reactions for ORR and OER (0.25−0.30 eV).

3. PROTOTYPICAL ELECTROCATALYZED REACTIONS 3.1. Chlorine Evolution Reaction (CER) on RuO2(110) at pH =0

The chlorine evolution reaction (CER) constitutes the anodic process of the chlor-alkali electrolysis and of the electrochemical HCl oxidation. Two chloride anions are successively discharged at the dimensionally stable anode (DSA) thereby forming gaseous chlorine: 2 Cl− → Cl2 + 2e−.25 The catalytically active component of the DSA is RuO2 that can be properly modeled by a RuO2(110) surface.21 With ab initio thermodynamics the most stable adsorbate structure can be found as a function of the applied electrode potential U vs SHE (standard hydrogen electrode) and the pH value (Pourbaix diagram; Figure 4).18,26

Figure 3. Energy diagram for a four electron process including one pure chemical reaction step (ii) → (iii) for η = 0 V (red) and pds = rds.

The connection of ab initio TD with kinetics is established by the so-called thermodynamic overpotential ηth, which is defined by ηth=ΔGloss/e for a one-electron reaction step.2 Applying η = ηth results in an energy diagram where all reaction steps are exergonic or energy neutral. Rossmeisl and coworkers2 take ηth as a measure for the activity of the electrode surface: The lower ηth, the higher the activity. There are two principal ways to comprehend a free energy landscape. One is based on free activation energies and the other on free energies of the transition states. For electrochemical reactions with quasi-equilibria of the RIs, the TS with the highest free energy constitutes the rds and determines therefore the kinetics without considering explicitly the coverage of the RI. Quite in contrast, the kinetics in terms of activation barriers or ΔGloss leads inevitably to the introduction of surface coverages of reaction intermediates that vary with overportential.15 In case pds = rds (cf. Figure 3), a BEP relation between free energies of pds and rds can be formulated:

Figure 4. Pourbaix diagram of the electrocatalyst RuO2(110) in equilibrium with H+, Cl−, and H2O at T = 298 K and a(Cl−) = 1.

The stoichiometric RuO2(110) surface27 exposes two kinds of undercoordinated sites, the bridging oxygen atoms Obr and coordinatively unsaturated ruthenium atoms Rucus. Under CER reaction conditions all Rucus sites are capped by surface oxygen Oot, while the Obr sites are not or partially covered by hydrogen depending on the actual pH value and the electrode potential (cf. Figure 5). The adsorption and discharge of chloride on the RuO2(110) surface proceeds solely on Oot atoms, thereby forming OClot as the RI for U ≥ 1.7 V (2Obr + 1OClot 1Oot in Figures 4 and 5c).18 Since one electron is transferred in the OClot formation, the corresponding Gibbs energy loss for the formation of OClot amounts to ΔGloss = 0.34 eV for U = 1.36 V (ηCER = 0 V) that is equal to Gmax(RI) for a simple two-electron process with a single RI. Under CER conditions (pH = 0, U > 1.36 V vs SHE) the (1OHbr1Obr + 2Oot) termination (cf. Figure 5a) is identified as thermodynamically most stable surface phase.15 Raising the applied electrode potential, the concentration of active Oot next to Obr sites increases, since for U > 1.55 V the hydrogen free (2Obr + 2Oot) termination becomes energetically favored (cf. Figures 4 and 5b). Hence, both active sites Oot next to Obr and Oot next to OHbr have to be considered in a kinetic study of the CER over RuO2(110). Full kinetics from first-principles shows that the CER proceeds via the Volmer-Heyrovsky mechanism.15 The adsorption and discharge of the chloride anion (Volmer step) on the oxygen-covered RuO2(110) surface forms OClot and is followed by its direct recombination with another chloride anion from the electrolyte solution (Heyrovsky step):

# Grds = G(iii) + β1ΔG loss + ß2

so that a variation of j0 among different materials is governed by ΔGloss: j0 = =

⎛ −G # ⎞ kBTze Γact exp⎜⎜ rds ⎟⎟ h ⎝ kBT ⎠ ⎛ −G(iii) ⎞ ⎛ β1ΔG loss + β2 ⎞ kBTze Γact exp⎜ ⎟exp⎜ − ⎟ h kBT ⎝ kBT ⎠ ⎝ ⎠

(5)

The term exp(−G(iii)/kBT) defines the surface concentration of RI(iii) preceding the rds. In such cases simple ab initio TD is helpful for material optimization by minimizing ΔGloss as long as G(iii) is varying in the same way. A more robust free energy parameter than ΔGloss that is also closer to kinetics, i.e., G#rds, is the highest free energy among the RI, Gmax(RI) (cf. Figure 3). In general, the more electrons are to be transferred the higher is Gmax(RI) and the less important are additional kinetic barriers. In case pds ≠ rds, ΔGloss is neither a helpful descriptor for material optimization nor for the mechanistic studies since the optimization of the free energy profile takes place at a wrong 1243

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eq 3), the Oot next to Obr configuration reveals a higher activity than the Oot next to OHbr site. How far could one get using ab initio thermodynamics only? According to Figure 6 ΔGloss is reduced from 0.34 eV (Oot next to Obr) to 0.25 eV for the Oot next to OHbr site so that ab initio TD infers the Oot next to OHbr configuration to be of higher catalytic activity. This conclusion conflicts, however, with microkinetics based on the complete free energy diagram in Figure 6.15 This obvious failure of ab initio thermodynamics may thus challenge the use of ΔGloss as a robust measure for the activity in Volcano plots.8 The main reason why mechanistic studies on the basis of ab initio thermodynamics approach may fail (cf. section 2.4) is attributed to the fact that pds and rds are not associated with the same elementary reaction step. Indeed the pds is associated with the Volmer step (i), while the Heyrovsky step (ii) constitutes the rds. Lowering the free energy of the OClot from 0.34 eV (Oot next to Obr) to 0.25 eV (Oot next to OHbr) results in a decrease of the TS free energy of the preceding Volmer step (i) from 0.68 eV (Oot next to Obr) to 0.53 eV (Oot next to OHbr). However, the thermodynamics of the Heyrovsky step rises from −0.34 eV (Oot next to Obr) to −0.25 eV (Oot next to Obr), which in turn leads to an increase of the TS free energy of the Heyrovsky step (ii) from 0.79 eV (Oot next to Obr) to 0.97 eV (Oot next to OHbr). These findings are fully consistent with BEP relations. Since the Heyrovsky step is an electrochemical reaction step (rrds = 1) with one-electron transfer preceding (γ = 1) and assuming αrds = 0.5, eq 4 predicts a Tafel slope of 39 mV/dec in remarkable agreement with the experimental found value of 40 mV/dec (cf. Table 1) for low overpotentials. The experimental Tafel slope of CER over RuO2(110) switches from 40 mV/dec to 88 mV/dec.21 if the applied overpotential ηCER is increased above 0.1 V. With increasing overpotential ηCER the TS free energy of the Volmer step is reduced by α1eηCER, while the TS free energy of the Heyrovsky step is lowered by (1+α2)·e·ηCER. Assuming α1 = α2 = 0.5, the TS free energy of the Volmer step becomes higher than that of the Heyrovsky step for ηCER > 0.11 V (cf. Figure 7), thus evidencing a switch in the rds. Applying eq 4, the Tafel slope is 120 mV/dec (α1 = 0.5) for the Volmer step (γ = 1, rrds = 0) being rds; a quantitative agreement with experiment (88 mV/ dec cf. Table 1) is, however, achieved with α1 = 0.67.

Figure 5. Ball and stick model of the fully oxygen-covered RuO2(110) surface with H (small grey) and Cl (large grey) adsorption depending on the applied electrode potential. Large green spheres: oxygen; small red and blue spheres: Ru atoms.

Oot + 2Cl− → OClot + e− + Cl−

(Volmer)

OClot + e− + Cl− → Oot + Cl 2 + 2e−

(i)

(Heyrovsky) (ii)

The free energy diagrams along the reaction coordinate for both, the active Oot next to Obr and Oot next to OHbr configurations are compared in Figure 6 for ηCER = 0 V. For both surface configurations, the Heyrovsky step (ii) constitutes the rds with TS free energies of 0.79 and 0.97 eV for the active Oot next to Obr and Oot next to OHbr site, respectively. Since the TS free energy of the rds directly scales with the activity (cf.

Figure 6. Free energy diagram along the reaction coordinate of the CER over the oxygen-covered RuO2(110) surface for two different actives sites: Oot next to Obr (thick line) and Oot next to OHbr (dashed line).

Figure 7. Free energy diagram along the reaction coordinate for the CER over the oxygen-covered RuO2(110) surface for ηCER = 0 V and ηCER = 0.2 V. The rds is indicated in violet and switches from #2 to #1 for ηCER > 0.11 V. 1244

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required in order to make all reaction steps exergonic. This value is substantially higher than typical overpotentials of 0.3− 0.4 V for the OER over RuO2(110). The theoretical study of Fang and Liu13 can be compared to experiments from Castelli et al.22 who measured an initial Tafel slope of 59 mV/dec. Since the formation of the OOHot species (first Step) constitutes the rds, a Tafel slope of 59 mV/dec leads to γ = 1 and rrds = 0 according to eq 4. This may indicate that the first reaction step is composed of an electrochemical reaction step that is followed by a rate determining chemical reaction step. Actually, this is indeed the case.13 The electrochemical formation of the OOHot adsorbate has been determined as pds in previous ab initio thermodynamics studies.2,28,29 Since pds = rds, qualitative conclusions drawn from ab initio thermodynamics agree with those from ab initio kinetics.

Quite in contrast, the ab initio thermodynamics approach cannot explain the switch of the Tafel slope. Ab initio thermodynamics predicts a Tafel slope of 120 mV/dec for the complete overpotential range, when the Volmer step (pds) is assumed to be rate determining. 3.2. Oxygen Evolution Reaction (OER) on RuO2(110) at pH =0

The OER is a sluggish four-electron process. For low overpotentials, the oxygen-covered RuO2(110) surface (1OHbr1Obr + 2Oot) is identified as thermodynamically most stable phase (cf. Figure 8). The reaction mechanism of

3.3. Oxygen Reduction Reaction (ORR) on Pt(111) at pH = 0

For electrode potentials above 0.97 V, the fully O covered Pt(111) surface constitutes the most stable surface, while for lower potentials the Pt(111) surface is covered by OH.14 Since the reaction mechanism needs always to start from the stable surface of the fully O-covered Pt(111) surface, we modified the free energy profile of Hansen et al.14 at η = 0 V accordingly (cf. Figure 10). The ORR is a sluggish process with four

Figure 8. Pourbaix diagram of the electrocatalyst RuO2(110) in equilibrium with H+ and H2O at T = 298 K.

OER over RuO2(110) and the corresponding free energy diagram along the reaction coordinate13 are summarized in Figure 9. We consider only steps with a single electron transfer,

Figure 10. Free energy diagram along the reaction coordinate for the ORR over the oxygen-covered Pt(111) surface for ηOER = 0 V.14 Rds and change of active surface are indicated in violet and purple, respectively. Asterisk (*) stands for the active site on the electrode surface. Figure 9. Free energy diagram along the reaction coordinate for the OER over the oxygen-covered RuO2(110) surface for ηOER = 0 V.13 *ot stands for active site Rucus on the electrode surface.

electrochemical steps that may include chemical steps. The first step consists of a protonation of adsorbed O atoms that is followed by a second protonation step, forming the product water. These two steps are energetically uphill. The third step leads to the formation of OOH; actually this step includes a chemical step, namely the adsorption of molecular oxygen. The third step is almost energy neutral. Last, the OOH species is protonated to form water, thus recovering the original surface structure and closing the catalytic cycle. The formation of OOH (third step) constitutes the rds since the corresponding TS reveals the highest free energy of 1.36 eV, while the second reaction step (formation of *) is the pds with ΔGloss = 0.49 eV and Gmax(iii) = 0.78 eV. From eq 4 and using (γ = 2, αrds = 0.5, rrds = 1) the Tafel slope can be determined to be 24 mV/dec., which conflicts with the experimental value of 59 mV/dec (Table 1).23,30 This discrepancy may be a problem of theory, but more likely is

so that these steps may contain further chemical steps. Exposing the (1OHbr 1Obr + 2Oot) surface at low overpotentials to water leads to the formation of OOHot, thereby releasing one electron and one proton. This reaction step is endergonic by 0.63 eV, defining ΔGloss = Gmax(RI). The corresponding free energy of TS #1 is 1.09 eV, thus making the first reaction step rate and potential determining. A second deprotonation step transforms the OOHot species into the desired product O2. The resulting vacancy is then filled in by dissociative water adsorption, forming OHot and a third H+ and e− pair. The last step is the deprotonation of the OHot, thereby recovering the catalyst’s surface and closing the catalytic cycle. The Gibbs energy loss of 0.63 eV, which is equal to Gmax(RI), reveals that an applied overpotential of at least ηth = 0.63 V is 1245

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insufficient treatment of the solvent, the double layer, the transfer coefficient and the electrode potential as well as the calculations of the free energies within the DFT approach. Therefore, the comparison with experiment is imperative to assess the accuracy of ab initio kinetics and thus their predictive power. But why is material screening based on ab initio TD still successful at all in predicting promising electrode materials? The trick is that these materials are searched for within a class of materials with similar structure where the reaction mechanism and in particular the rds is assumed to not change. Among these homologous materials ΔGloss is only a reasonable descriptor of the activity variations as along as pds = rds. The ab initio TD approach allows for a rough screening of the parameter space with low computational cost and represents an “educated guess” that is much better than any unbiased materials screening. Microkinetics of an electrocatalyzed reaction is simplified due to the presence of quasi-equilibria of the RI preceding the rds with the reactants. This leads directly to the generalized Butler−Volmer equation, a simple formula for the (exchange) current density and the definition of the rds being the TS with the highest free energy. Consequently, we propose that the RI with the highest free energy Gmax(RI) is a more robust thermodynamic descriptor for the kinetics than ΔGloss. This is particularly the case for electrochemical reactions with many transferred electrons when comparing the present systems CER versus OER or ORR.

that the Pt(111) surface is not stable under such high electrode potentials (i.e., low overpotentials), forming instead a surface Pt-oxide layer with a different kinetics.30 For high overpotentials, say η = 0.35 V, the free energy landscape changes in a way, that the OH covered Pt(111) surface is now the stable surface and therefore the starting surface (light blue bar in Figure 10); for this high overpotential or low electrode potential an oxidation of Pt(111) is not expected. Now, the first protonation step toward OOH becomes the rds and also the pds. From eq 4 and (γ = 0, αrds = 0.5, rrds = 1), the Tafel slope can be determined to be 118 mV/dec, which agrees with the experimental value of 118 mV/ dec.23,24,30 Consistent with pds = rds, it was found that the volcano plot based on ab initio TD agrees remarkably well with a kinetic volcano based on ab initio kinetics.14 We may note that RI(iv) is even lower in free energy, but this RI succeeds the product formation and can therefore not be the starting configuration. An alternative way to resolve the actual reaction mechanism with the switch of the Tafel slope has been proposed by Wei and co-workers.31 The active surface consists of Pt(111)−(2 × 2)O on which an O2 molecule adsorbs. Depending on the electrode potential the adsorbed O2 species dissociated either H+-assisted (including electron transfer) or O2 is first protonated (including electron transfer) and subsequently dissociates without any further electron transfer. Further experiments will be required to resolve the actual reaction mechanism.

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4. CONCLUDING REMARKS Modern theoretical modeling of an electrocatalyzed reaction comprises three consecutive steps:15 (a) Identify the stable surface structure and reaction intermediates (RIs) under constrained reaction conditions, (b) determine the free energies (kinetics) of the TS, and (c) conduct microkinetic modeling based on the free energy surface. Ab initio TD is pivotal for kinetics studies from first-principles since the free energies of the RIs are of utmost importance for the reaction mechanism. The RI with the lowest free energy defines the starting surface. The starting electrode surface can change when increasing the overpotential such as encountered with the OER over RuO2(110)13 and ORR on Pt(111).14 In order to draw reliable conclusions from ab initio TD for the kinetics and the mechanism of an electrocatalyzed reaction, the pds needs to be equal to the rds. This is often but not always met. However, one does not know when ab initio TD is failing so that mechanistic conclusions drawn from ab initio TD need to be taken with great caution (cf. CER over RuO2(110)). The connection between kinetics and ab initio TD is based on the thermodynamic overpotential ηth (derived from ΔGloss) that is defined as the minimum electrode potential that makes all elementary reaction steps exergonic.2 To our opinion this approach is conceptually misleading: The overpotential is not required to make all reaction steps exergonic, but rather to ensure that the effective free activation energy G#eff(η) = G#rds − (γrds + αrds)eη is lower than 0.7−0.8 eV to allow for a sufficiently high current density at room temperatures. The effective free activation energies of the three studied reactions are indeed in this range: (a) CER over RuO2(110) at η = 0.1 V: G#eff = 0.64 eV; (b) OER over RuO2(110) at η = 0.35 V: G#eff = 0.74 eV; (c) ORR over Pt(111) at η = 0.35 V: G#eff = 0.65 eV. However, ab initio kinetics has shortcomings as well, which originate from the underlying approximations, including a

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Herbert Over: 0000-0001-7689-7385 Notes

The authors declare no competing financial interest. Biographies Dr. Kai S. Exner started his chemistry studies in 2008 at the Justus Liebig University (JLU) in Giessen, Germany and received his Ph.D. in the field of theoretical electrochemistry in the group of Prof. Over in 2015. His current research interests focus on the application of ab initio methods in electrocatalysis and battery research. Professor Dr. Herbert Over studied physics and mathematics at the TU Berlin, Germany. In 1991, he graduated at the FHI and received his Ph.D. from the chemistry department at the FU in Berlin. In 2002, he was appointed C3 professor at the JLU in Giessen. He focuses on an atomistic understanding of elementary reaction steps on transition metal (oxide) surfaces of heterogeneously catalyzed and electrocatalyzed reactions.

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ACKNOWLEDGMENTS H.O. thanks financial support from the BMBF (project: Verbundprojekt 05K2016-HEXCHEM).

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REFERENCES

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DOI: 10.1021/acs.accounts.7b00077 Acc. Chem. Res. 2017, 50, 1240−1247