Refining Free-Energy Calculations for Electrochemical Reactions: Unveiling Corrections beyond Gas-Phase Errors for Solvated Species and Ions

As much of the theory related to computational electrocatalysis has been adapted from the thermodynamics of gas-phase reactions, it demands careful treatment and the implementation of proper corrections when investigating electrochemical systems. In this article, we present a comprehensive thermodynamic framework that incorporates all potential phases (gaseous or aqueous) and different forms (molecular or ionic) of reactants and products under ambient conditions. This framework elucidates systematic relationships governing the Gibbs free energy of reactants or products across diverse phases and different chemical species, employing Henry's volatility constant (KHor H), acid dissociation constant (Ka), and pH. We introduce a method for calculating both KH and Ka, detailing the associated challenges. Our study demonstrates that the calculation of free energies is influenced by Ka and pH, primarily due to the occurrence of unbalanced numbers of electrons and protons transfers during adsorption or desorption of ions. Our findings also highlight that the inclusion of aqueous reactants and products, whether in molecular or ionic form, significantly modifies the free-energy landscapes. In turn, the reported solvation and ion corrections are imperative to obtain correct activity predictions by descriptors such as the thermodynamic overpotential or the span model of Gmax(η), as deviations of more than 0.3 eV are observed if these contributions are ignored.