# Charged Adsorbates on Metallic Surfaces from Periodic to Open Boundary Conditions

## TL;DR

This paper introduces a method to accurately calculate the energy of charged particles on metal surfaces using computational models.

## Contribution

The paper presents an analytical correction for finite-cell calculations of charged adsorbates on metallic surfaces.

## Key findings

- The method is demonstrated using Li+, Na+, and K+ adsorption on graphite.
- Periodic calculations show slow convergence with system size, emphasizing the need for infinite limit corrections.

## Abstract

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.