As shown in Fig. , we do see a significant increment in the total capacitance when increasing the position of image plane in the semi-classical simulations. The relationship between the image plane and the Gaussian width parameter in semi-classical models for both Au(100) and Au(111) can be found in Fig. and S3 in the Supporting Information. Results from these simulations agree quite well with those predicted using Eq. 5. Interestingly, when the total capacitance from the semi-classical simulations for Au(100) reaches the value of capacitance computed from finite-field DFTMD simulations, the corresponding image plane z im -z a of 1.29 Å is close to that we found for Au(100) slab in vacuum with DFT (z im -z a = 1.22 Å). However, the corresponding value for Au(111) obtained from DFT appears to be too large and go beyond the singularity point (-C M = C sol ). This is likely to do with the overestimation of the work function for our Au(111) slab (see Table in the Supporting Information). Instead, taking the cross-over point between the theoretical line using Eq. 5