A simple method to calculate solution-phase free energies of charged species in computational electrocatalysis

Determining the adsorption potential of adsorbed ions in the field of computational electrocatalysis is of great interest to study their interaction with the electrode material and the solvent, and to map out surface phase diagrams and reaction pathways. Calculating the adsorption potentials of ions with density functional theory and comparing across various ions requires an accurate reference energy of the ion in solution and electrons at the same electrochemical scale. Here we highlight a previously used method for determining the reference free energy of solution phase ions using a simple electrochemical thermodynamic cycle, which allows this free energy to be calculated from that of a neutral gas-phase or solid species and an experimentally measured equilibrium potential, avoiding the need to model solvent around the solution phase ion in the electronic structure calculations. While this method is not new, we describe its use and utility in detail and show that this same method can be used to find the free energy of any ion from any reaction, as long as the half-cell equilibrium potential is known, even for reactions that do not transfer the same number of protons and electrons. To illustrate its usability, we compare the adsorption potentials obtained with DFT of I^*, Br^*, Cl^*, and SO₄^*on Pt(111) and Au(111) and OH^*and Ag^*on Pt(111) with those measured experimentally and find that this simple and computationally affordable method reproduces the experimental trends.