Charged Adsorbates on Metallic Surfaces from Periodic to Open Boundary Conditions

Understanding the thermodynamics of adsorbates on surfaces is central to many (electro)-catalysis applications. In first-principles calculations, additional challenges arise when considering charged adsorbates owing to long-range electrostatic interactions in the in-plane and normal directions. Here, we derive an analytical correction to obtain the energy profiles of individual charged adsorbates on metallic surfaces from finite-cell calculations in periodic boundary conditions. The method is illustrated by calculating the adsorption energy profiles of Li⁺, Na⁺, and K⁺ on graphite from first-principles, highlighting the very slow convergence with system size of the periodic calculations and the need to correctly recover the infinite limit.