New developments in probing coupled proton electron transfer barriers with density functional theory in the grand canonical ensemble

Simulation of coupled proton electron transfer (CPET) pathways with density functional theory (DFT) is critical to our understanding of electrocatalysis and in guiding electrocatalyst design. Despite this, numerous challenges remain with the state-of-the-art models for studying CPET activation barriers with DFT, particularly for reactions involving hydroxide, and there is little consensus in the field regarding which model most accurately reproduces the actual system. In this work, we present new developments in tackling this critical challenge, through the lens of a hybrid implicit/explicit electrolyte model, grand canonical in the applied bias. By applying this model to the hydrogen evolution reaction and carbon dioxide reduction on copper, we illustrate that many cathodic reactions (particularly at high overpotential) should be utilizing water as a proton donor, as opposed to hydronium. Although the challenges with modeling hydroxide are well known, we illustrate that simple corrections leveraging the computational hydrogen electrode can allow for accurate modeling of the energetic minima involving hydroxide in the grand canonical ensemble. We conclude by highlighting the remaining challenges for investigating the activation barriers of such pathways and present one potential pathway to overcome them.