Using Brønsted-Evans-Polanyi relations to predict electrode potential-dependent activation energies
Graphical abstract
Introduction
In a future of abundant renewable electricity, electrochemical energy technologies can serve to store energy by converting it to electricity or chemical fuels. Many electrochemical processes are reliant on the use of active and selective electrocatalysts with low operating overpotentials [[1], [2], [3]]. In order to facilitate the rational design of electrocatalysts for use in fuel cells or other energy conversion devices, a molecular scale kinetic understanding of the surface catalyzed processes is essential.
Over the past two decades, Density Functional Theory (DFT), as well as other advancements in quantum-chemical based approaches, have created the possibility of calculating elementary electrocatalytic reaction energies with reasonable accuracy, thus facilitating the screening of a large range of catalyst materials [[4], [5], [6], [7]]. The development of first-principles computational electrochemistry approaches [[7], [8], [9], [10]], including the computational hydrogen electrode (CHE) model [11], has allowed estimation of potential-dependent reaction energies of elementary surface-mediated dissociation and association of bonds occurring with the transfer of an ion-electron pair. The computational free energy method has been widely applied towards mechanistic determination of key electrochemical reactions, including methanol oxidation [12,13], CO2 reduction [[14], [15], [16], [17]] and oxygen reduction [[18], [19], [20], [21]]. However, this method does not directly assess elementary kinetic barriers. Determination of a reaction mechanism based on elementary step reaction energies can only be accomplished under the assumption that barriers for all reaction steps scale equivalently with reaction energy. Furthermore, it is only possible to compare the relative catalytic activity across metals under the assumption that activation barriers scale equivalently with reaction energies between the two metals. These assumptions have not been evaluated due to challenges in applying DFT methods for determination of electrochemical activation barriers. An accurate estimation of electrochemical barriers is essential for deciphering the elementary reaction mechanism.
Electrochemical elementary reactions within electro-catalytic sequences transport an ion from the bulk electrolyte to a surface adsorbate while transferring an electron from the electrode to the interfacial reaction center. Computing electrochemical barriers may require a comprehensive ab initio treatment of the electrified interface that explicitly accounts for electrode potential, electric double layer and fluctuations within the solvent. Several efforts have been made to incorporate these features to compute electrochemical activation barriers [[22], [23], [24], [25], [26], [27], [28]] but the computational cost of such undertakings has often proved prohibitive.
Our group has introduced a simple DFT-based method to approximate the potential-dependent activation barrier of an elementary electrochemical step at the reduced computational cost of a single hydrogenation barrier calculation [[29], [30], [31]]. The activation energy (ΔGACT) for an elementary electrochemical step (X* + Heq\a(+,(aq)) + e− → XH* where * denotes surface-adsorbed species), involving the transfer of a proton-electron pair, is extrapolated from a non-electrochemical hydrogenation/dehydrogenation reaction (X* + H* → XH*). The hydrogenation barrier is analogous to the barrier for the equivalent electrochemical redox step at a specific potential, U°. At this potential, the electrochemical and analogous non-electrochemical states have the same chemical potential. This allows the barrier to be referenced to the chemical potential of the aqueous phase ion. The potential-dependence is incorporated by extrapolating the barrier to other electrode potentials using a Marcus Theory based approach [29]. The method was previously applied to investigate the elementary kinetics of CO2 reduction [30,32]. We have demonstrated the transferability of the method by evaluating the electrochemical barriers of elementary steps involving CH, OH and NH bond formation on Cu (111) and Pt (111) surfaces [29].
In this study, we extend this method to evaluating the potential-dependent activation energies of CH, OH and NH bond formation across several different close-packed fcc(111) transition metal surfaces including Ag, Au, Cu, Ni, Pd, Pt and Rh. CH bond activation is crucial in the functionalization of hydrocarbons. OH and NH bond formation are intrinsic to O2 and N2 reduction, and their reverse dissociation steps impact the kinetics of water electrolysis and electrochemical ammonia oxidation. Two distinct reaction mechanisms for the formation of CH, OH and NH bonds are considered: 1) a Tafel-like mechanism in which the reduction of C*, O* and N* takes place via a direct surface hydrogenation process and 2) a Heyrovsky-like mechanism where the reduction of C*, O* and N* occurs via water assisted proton shuttling.
From a broader perspective, there is a strong interest in understanding the role of interfacial water on the reactivity of elementary steps including CH, OH and NH bond formation. Interfacial water is known to drastically affect the kinetics by altering the stability of transition states and the extent of charge separation [[33], [34], [35], [36], [37]]. Previous electrokinetic DFT based investigations of CO2 electroreduction on Cu (111) [30,32], report that, for all OH bond forming reactions including concerted COH dissociation, the barriers are lower for Heyrovsky-like reaction mechanisms. In contrast, elementary steps associated with CH bond formation on Cu (111) proceed through Tafel-like mechanisms. This demonstrates the importance of determining the role of interfacial water, either as an assistor or a spectator, in elementary electrochemical bond formation.
The explicit evaluation of barriers for electrochemical reactions over a large number of catalytic surfaces is non-trivial, even with the use of the simplistic DFT approach used in this study. To improve the efficiency of estimating the catalytic activity of electrode materials in heterogeneous catalysis, a popular approach makes use of linear correlations of the activation energy/transition state energy with the reaction energy of an elementary step. These correlations, known as Brønsted-Evans-Polanyi (BEP) relations, have been previously reported for a number of surface reactions on different transition metal surfaces [[38], [39], [40], [41], [42], [43], [44], [45], [46]]. The activation barriers and reaction energies for essential bond breaking and forming reactions, including CH, OH, NH, CC, CO, CN, NO, NN, OO, were found to be linearly correlated across different transition metals. BEP relations, coupled with binding energy scaling relationships, reduce the parameters needed to describe trends underlying the kinetics of a complex reaction pathway. Despite the utility of BEP relations, they have not been directly investigated for kinetic barriers of elementary electrochemical reactions due to challenges in computing potential dependent barriers.
We use the potential-dependent activation energies and reaction energies for electrochemical CH, OH and NH bond formation to answer three questions: 1) Do XH (XC, O, N) bond formations have the lowest barriers through Tafel or Heyrovsky elementary steps, and does this vary with X or metal, 2) Do ‘electrochemical BEP’ correlations hold to correlate the activation barrier with the elementary reaction energy for XH bond formation steps at a constant electrode potential across metals, and 3) Are the electrochemical BEP relationships for CH, OH, and NH bonds equivalent such that comparing their relative reaction energies is sufficient to determine rate limiting steps in complex multi-step electrocatalytic mechanisms?
In the following sections, we illustrate how our previously reported method to approximate potential-dependent activation barriers of elementary electrochemical steps is used to investigate the reaction mechanism of CH, OH and NH bond formation on fcc (111) transition metal surfaces. Additionally, we examined the potential-dependent kinetics of C* → CH4, O* → H2O and N* → NH3 reduction reaction series across the Pt (111) surface. In the last section, we construct Brønsted-Evans-Polanyi relations (BEP) for elementary CH, OH and NH bond activation across fcc (111) metals and assess the effect of electrode potential on the BEP relations.
Section snippets
Methods and computational details
Electronic structure calculations were performed using the plane-wave pseudopotential package, Vienna ab initio simulation package (VASP v. 5.3.5) [[47], [48], [49]] with the projector augmented wave (PAW) [50] method for core-valence treatment. The exchange-correlation energy was calculated using the Perdew, Burke, and Ernzerhof (PBE) [51] functional described within the generalized gradient approximation (GGA) [52]. A plane-wave basis set cutoff energy of 450 eV was used. The ionic
Results and discussion
In the following sections, we compute the potential-dependent activation energy of elementary CH, OH and NH reduction reactions on fcc (111) metal surfaces via two different reaction mechanisms, including the Tafel-like (direct surface hydrogenation) and the Heyrovsky-like (water assisted H shuttling) schemes. The preferred reaction mechanism for elementary CH, OH and NH reduction reactions and the kinetics of C* → CH4, O* → H2O and N* → NH3 reduction reaction series are discussed. We construct
Summary and conclusions
In summary, we have investigated the elementary kinetics of electrochemical CH, OH and NH bond formation on fcc (111) transition metal surfaces. We have examined the role of interfacial water, as an assistor or spectator, in the kinetics of these elementary electrochemical steps. On most considered close-packed transition metal surfaces, the Heyrovsky-like scheme, wherein the proton shuttles through the interfacial water, is the preferred mechanism for CH, OH and NH bond formation and yields
Acknowledgements
This work was supported by the National Science Foundation, Grant # CBET – 1264104. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575.
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2022, Current Opinion in ElectrochemistryCitation Excerpt :Thus, one has to determine (potential-dependent) activation energies and, therefore, identify transition states [17]. The potential-dependent activation energies are a first, necessary, step towards more approximate (linear-scaling-based) estimates that can then be used for catalyst screenings [18–20]. As discussed in the recent literature [13,21,22], the success of the CHE-derived catalyst screenings without the consideration of potential-dependent surface states and activation barriers is at least partially a happy coincidence.
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