Fig. 5: Errors from neglecting double layer effects and their sensitivity to model parameters.

Approximate errors for Ni₁Cu(111), Ni₁Cu(100), and Cu(111) from (a) computing the adsorption free energy of nitrate (\(\Delta {{\varPhi} }_{{{{\rm{ads}}}}}^{{{{{\rm{NO}}}}}_{3}^{* }}(U)\)) with the CHE model versus the aGC-DFT method, and (b) computing the activation free energy for nitrate dissociation (ΔΦ^‡(U)) with no potential dependence versus the aGC-DFT method. Errors at each potential were computed with a relative permittivity (ε_r) of 78.4 (water) and double layer thickness (d) of 3.0 Å. The star indicates the potential at which we considered the variations in errors with double layer properties for Ni₁Cu while \({U}_{\min }\) is the potential at which the error is minimized. A heat map of computed error at  −0.55 V for (c) nitrate adsorption and (d) nitrate dissociation, showing the variation in the computed errors with relative permittivity (ε_r) and double layer thickness (d). The stars represent the error computed with a ε_r of 78.4 (water) and d of 3.0 Å.