Grand Canonical Ensemble Approaches in CP2K for Modeling Electrochemistry at Constant Electrode Potentials

In electrochemical experiments, the number of electrons of the electrode immersed in the electrolyte is usually variable. Additionally, the numbers of adsorbed substances on the surface of the electrode, the solvent molecules, and counter charge ions in the near-surface region can also vary. Treating electrochemical solid-liquid interfaces with the typical fixed electron number density functional theory (DFT) approach tends to be a challenge. This can be addressed by using grand canonical ensemble approaches. We present the implementation of two grand canonical ensemble approaches in the open-source computational chemistry software CP2K that go beyond the existing canonical ensemble paradigm. The first approach is based on implicit solvent models and explicit atomistic solute (electrode with/without adsorbed species) models, and includes two recent developments: (a) grand canonical self-consistent field (GC-SCF) method (