An Electrostatically Embedded QM/MM Scheme for Electrified Interfaces

Atomistic modelling 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 semi-conducting 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 towards 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 have 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 popular 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) an Mo anti-site 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. Our results demonstrate that electrostatic embedding leads to almost indistinguishable results compared to the implicit solvent for apolar systems, but has a significant effect on polar sites. This demonstrates the reliability of the hybrid QM/MM, electrostatically embedded solvation model for electrified interfaces.