Modeling the Electrochemical Hydrogen Oxidation and Evolution Reactions on the Basis of Density Functional Theory Calculations

Abstract

Density functional theory calculations have been performed for the three elementary steps-Tafel, Heyrovsky, and Volmer-involved in the hydrogen oxidation reaction (HOR) and its reverse, the hydrogen evolution reaction (HER). For the Pt(111) surface a detailed model consisting of a negatively charged Pt(111) slab and solvated protons in up to three water bilayers is considered and reaction energies and activation barriers are determined by using a newly developed computational scheme where the potential can be kept constant during a charge transfer reaction. We determine the rate limiting reaction on Pt(111) to be Tafel-Volmer for HOR and Volmer-Tafel for HER. Calculated rates agree well with experimental data. Both the H adsorption energy and the energy barrier for the Tafel reaction are then calculated for a range of metal electrodes, including Au, Ag, Cu, Pt, Pd, Ni, Ir, Rh, Co, Ru, Re, W, Mo, and Nb, different facets, and step of surfaces. We compare the results for different facets of the Pt electrode to experimental data. Our results suggest that the most important parameter for describing the HOR or the HER activity of an electrode is its binding free energy of H. We present a detailed kinetic model based entirely on the density functional theory calculations reactions and show that the exchange current follows a volcano curve when plotted against the H adsorption free energy in excellent agreement with experimental data.

Understanding the electrocatalysis of oxygen reduction on platinum and its alloys

“…42,43 The theoretical modelling of electrochemical reactions is equally complex, as it needs to account for the effect of the solvent on the adsorbed intermediates, the highly charged electric field in the double layer, the free energy of the electrons in the solid and the free energy of the solvated reactants as a function of potential. [44][45][46][47][48][49][50][51][52][53][54] However, it turns out that the overall trends can be 7 ‡ We note that a fuel cell would probably be operated at potentials lower than 0.9 V, to maximise the power output. However, catalysts are typically benchmarked at 0.9 V to minimise artefacts from the measurements.…”

Joint density functional theory of the electrode-electrolyte interface: Application to fixed electrode potentials, interfacial capacitances, and potentials of zero charge

“…More recently, modeling the electrolyte by a layer of explicit hydrogen atoms was shown to provide a source of electrons for charged surface calculations while keeping the unit cell neutral. 20 Again, however, this approach requires either judicious choice of the locations of the corresponding protons which make up the corresponding reference electrode or computationally intensive thermodynamic sampling.…”

Electrochemical Kinetics: a Surface Science-Supported Picture of Hydrogen Electrochemistry on Ru(0001) and Pt/Ru(0001)

“…In addition, the quantification of electrochemical signals to determine such adlayer coverages is often fraught with uncertainties due to the presence of parasitic side processes which can introduce their own pseudocapacitance. However, the determination of accurate thermodynamic and kinetic parameters relevant in electrocatalysis, including those pertaining to the long studied hydrogen evolution reaction (HER) and hydrogen oxidation reaction (HOR), actually depends on these coverages being determined with a reasonable precision [14][15][16][17]. Therefore, in this work, we relate the desorption kinetics obtained in vacuum with the electrocatalysis of the HER/HOR, and we analyse the electrochemical behaviour in view of the surface coverage according to cyclic voltammetry data (with and without H 2 in the solution).…”

“…From understanding gained from temperature programmed desorption (TPD) of D 2 molecules, we highlight that it is important to account for the actual adsorbate coverage under real electrochemical conditions [55,56], rather than simply assuming that the results obtained from DFT calculations at an adsorbate coverage of 0.25 ML [57], as commonly used for other noble metals, or 1 ML [15], as used in the models of Nørskov et al on Ru(0001), are representative of real reaction conditions. Due to the scaling of the computational cost of density functional theory (DFT) models with the system size, such models are often constrained to examine only periodic, fixed stoichiometric adlayer coverages, such as 0.25, 0.5, or 1 ML, neglecting the fact that the relevant adlayers under reaction conditions may be disordered and/or non-stoichiometric.…”