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The Ewald3D sum with the tinfoil boundary condition (e3dtf) evaluates theelectrostatic energy of a finite unit cell inside an infinitely periodicsupercell. Although it has been used as a {\it de facto} standard treatment ofelectrostatics for simulations of extended polar or charged interfaces, thefinite-size effect on simulated properties has yet to be fully understood.There is, however, an intuitive way to quantify the average effect arising fromthe difference between the e3dtf and Coulomb potentials on the response ofmobile charges to contact surfaces with fixed charges and/or to an appliedexternal electric field. While any charged interface formed by mobilecountercharges that compensate the fixed charges slips upon the change of theacting electric field, the distance between a pair of oppositely chargedinterfaces is found to be nearly stationary, which allows an analyticfinite-size correction to the amount of countercharges. Application of thetheory to solvated electric double layers (insulator/electrolyte interfaces)predicts that the state of complete charge compensation is invariant withrespect to solvent permittivities, which is confirmed by a proper analysis ofsimulation data in the literature.

Analytic Theory of Finite-size Effects in Supercell Modelings of Charged Interfaces