Analytic theory of finite-size effects in supercell modeling of charged interfaces

Abstract

The Ewald3D sum with the tinfoil boundary condition (e3dtf) evaluates the electrostatic energy of a finite unit cell inside an infinitely periodic supercell. Although it has been used as a de facto standard treatment of electrostatics for simulations of extended polar or charged interfaces, the finite-size effect on simulated properties has yet to be fully understood. There is, however, an intuitive way to quantify the average effect arising from the difference between the e3dtf and Coulomb potentials on the response of mobile charges to contact surfaces with fixed charges and/or to an applied external electric field. While any charged interface formed by mobile countercharges that compensate the fixed charges slips upon the change of the acting electric field, the distance between a pair of oppositely charged interfaces is found to be nearly stationary, which allows an analytic finite-size correction to the amount of countercharges. Application of the theory to solvated electric double layers (insulator/electrolyte interfaces) predicts that the state of complete charge compensation is invariant with respect to solvent permittivities, which is confirmed by a proper analysis of simulation data in the literature.

Dielectric response with short-ranged electrostatics

“…Crucial to what follows is that LMFT also gives the correct average polarization in the presence of a uniform field, which is also shown in Fig. 4 sults from previous studies [61][62][63][64][65] suggest the fluctuations will also be affected, and establishing how they are affected is likely to provide useful physical insight. To set about tackling this issue, let us consider a continuum model in which a uniform dielectric slab with thickness w is centered at z = 0 such that its boundaries occur at z ± = ±w/2.…”

“…30,67 It is also clear that the polarization fluctuations of inhomogeneous systems will also be affected, which could have been anticipated from previous studies. In particular, symmetry-preserving mean-field theory (an extension of LMFT) [61][62][63][64] likely provides a means to recover the fluctuations by capturing both equilibrium and dynamical effects of interfaces with high symmetry (see also Ref. 65).…”

Short solvent model for ion correlations and hydrophobic association

“…It has been shown that LMF theory can very accurately describe drying near a hydrophobic solute in water, overcharging near a highly charged colloid, dielectric screening of a charged ion, and the induced water structure near hydrophobic or charged walls. A recent extension of LMF theory, the symmetry-preserving mean-field theory, has been proved to be able to capture both the equilibrium and dynamical effects of electrostatics at interfaces with high symmetry (78)(79)(80)(81).…”

Dielectric response with short-ranged electrostatics

“…It is clear that LMFT provides a means to correct for the effects of neglecting LR electrostatics on the average dielectric response in inhomogeneous systems. Results from previous studies (60)(61)(62)(63)(64) suggest the fluctuations will also be affected, and establishing how they are affected is likely to provide useful physical insight. To set about tackling this issue, let us consider a continuum model in which a uniform dielectric slab with thickness w is centered at z = 0 such that its boundaries occur at z± = ±w /2.…”