  Reliable first-principles calculations of electrochemical processes require
accurate prediction of the interfacial capacitance, a challenge for current
computationally-efficient continuum solvation methodologies. We develop a model
for the double layer of a metallic electrode that reproduces the features of
the experimental capacitance of Ag(100) in a non-adsorbing, aqueous
electrolyte, including a broad hump in the capacitance near the Potential of
Zero Charge (PZC), and a dip in the capacitance under conditions of low ionic
strength. Using this model, we identify the necessary characteristics of a
solvation model suitable for first-principles electrochemistry of metal
surfaces in non-adsorbing, aqueous electrolytes: dielectric and ionic
nonlinearity, and a dielectric-only region at the interface. The dielectric
nonlinearity, caused by the saturation of dipole rotational response in water,
creates the capacitance hump, while ionic nonlinearity, caused by the
compactness of the diffuse layer, generates the capacitance dip seen at low
ionic strength. We show that none of the previously developed solvation models
simultaneously meet all these criteria. We design the Nonlinear Electrochemical
Soft-Sphere solvation model (NESS) which both captures the capacitance features
observed experimentally, and serves as a general-purpose continuum solvation
model.
