Atomistic
modeling of electrified interfaces remains a major issue
for detailed insights in electrocatalysis, corrosion, electrodeposition,
batteries, and related devices such as pseudocapacitors. In these
domains, the use of grand-canonical density functional theory (GC-DFT)
in combination with implicit solvation models has become popular.
GC-DFT can be conveniently applied not only to metallic surfaces but
also to semiconducting oxides and sulfides and is, furthermore, sufficiently
robust to achieve a consistent description of reaction pathways. However,
the accuracy of implicit solvation models for solvation effects at
interfaces is in general unknown. One promising way to overcome the
limitations of implicit solvents is going toward hybrid quantum mechanical
(QM)/molecular mechanics (MM) models. For capturing the electrochemical
potential dependence, the key quantity is the capacitance, i.e., the
relation between the surface charge and the electrochemical potential.
In order to retrieve the electrochemical potential from a QM/MM hybrid
scheme, an electrostatic embedding is required. Furthermore, the charge
of the surface and of the solvent regions has to be strictly opposite
in order to consistently simulate charge-neutral unit cells in MM
and in QM. To achieve such a QM/MM scheme, we present the implementation
of electrostatic embedding in the VASP code. This scheme is broadly
applicable to any neutral or charged solid/liquid interface. Here,
we demonstrate its use in the context of GC-DFT for the hydrogen evolution
reaction (HER) over a noble-metal-free electrocatalyst, MoS2. We investigate the effect of electrostatic embedding compared to
the implicit solvent model for three contrasting active sites on MoS2: (i) the sulfur vacancy defect, which is rather apolar; (ii)
a Mo antisite defect, where the active site is a surface bound highly
polar OH group; and (iii) a reconstructed edge site, which is generally
believed to be responsible for most of the catalytic activity. According
to our results, the electrostatic embedding leads to almost indistinguishable
results compared to the implicit solvent for the apolar system but
has a significant effect on polar sites. This demonstrates the reliability
of the hybrid QM/MM, electrostatically embedded solvation model for
electrified interfaces.