Sampling of grand canonical activation free energy in hydrogen evolution reaction

Accurate atomistic modeling of phenomena at the solid liquid interface is challenging because of the complexity and inhomogeneity of the electrochemical environment that enables multiple pathways for an electrochemical process. To illustrate this variability, we compute the distribution of grand-canonical activation free energies  for the Volmer step (∆Ω^†) in hydrogen evolution reaction on the Au(111) electrode, in the presence of metal (Na⁺) and nonmetal (NH₄⁺, CH₃NH₃⁺) cations. We find that ∆Ω^† is highly sensitive to the solvation structure of the reacting H₂O, with variation spanning a significant range: with Na⁺ in the electrolyte, it ranges from 1.03 eV to 1.65 eV with a mean value of 1.31 eV; with NH₄⁺ it varies from 0.94 eV to 1.44 eV with a mean value of 1.15 eV and with CH₃NH₃⁺ in electrolyte, it is spread from 0.88 eV to 1.36 eV with a mean value of 1.16 eV. The mean value of ∆Ω^† of Volmer step with the three cations thus follows the trend Na⁺>CH₃NH₃⁺>NH₄⁺, which is in excellent agreement with the trend in HER activity  in experimental observation [1]. Importantly, the large range of values of grand-canonical activation free energies reflects the variability introduced by inhomogeneity of the electrolyte and underscores the importance of extensive configurational sampling when modeling electrochemical interfaces.

[1] X. Feng et al (Private communication)