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. In this record, we provide the generic input file used to generate the calculated energies of Fig. 4.