3.2.3. Fitting Procedure in Coarse-Graining the Quantum Response Fitting of continuum to quantum dynamics permittivity was performed using a sweep over three parameters: The permittivities of the inclusion, that of the interfacial shell, and the interface thickness. The inclusion volume and matrix relative permittivity were fixed at the Bader value and 9.3, respectively. A 1 Å interface was selected to avoid encroachment on cell boundaries for high volume loadings [Sec. S3.5]. More importantly, this interface thickness also resulted in lower average errors than 2 or 3 Å interfaces, or no interface. Fig. depicts the parameter search space as well as the average permittivity errors τ for the three systems of Fig. ,