Interfacial ion solvation: Obtaining the thermodynamic limit from molecular simulations

Abstract

Inferring properties of macroscopic solutions from molecular simulations is complicated by the limited size of systems that can be feasibly examined with a computer. When long-ranged electrostatic interactions are involved, the resulting finite size effects can be substantial and may attenuate very slowly with increasing system size, as shown by previous work on dilute ions in bulk aqueous solution. Here we examine corrections for such effects, with an emphasis on solvation near interfaces. Our central assumption follows the perspective of Hünenberger and McCammon [J. Chem. Phys. 110, 1856 (1999)]: Long-wavelength solvent response underlying finite size effects should be well described by reduced models like dielectric continuum theory, whose size dependence can be calculated straightforwardly. Applied to an ion in a periodic slab of liquid coexisting with vapor, this approach yields a finite size correction for solvation free energies that differs in important ways from results previously derived for bulk solution. For a model polar solvent, we show that this new correction quantitatively accounts for the variation of solvation free energy with volume and aspect ratio of the simulation cell. Correcting periodic slab results for an aqueous system requires an additional accounting for the solvent's intrinsic charge asymmetry, which shifts electric potentials in a size-dependent manner. The accuracy of these finite size corrections establishes a simple method for a posteriori extrapolation to the thermodynamic limit and also underscores the realism of dielectric continuum theory down to the nanometer scale.

The Influence of Distant Boundaries on the Solvation of Charged Particles

“…Both cases are shown in Figure 2b, which shows that inclusion of distant boundaries, both Bethe and physical boundaries, oppose the usual charge hydration asymmetry in the case of SPC/E-like water models because both ∆v q C and (∆v q C + ∆v q D ) are negative. This is in agreement with recent results from Cox and Geissler, who computed ionic charging free energies in systems with and without an explicit water-vapor interface, and showed that proper inclusion of the boundary potentials, as well as important system size and geometry-dependent dielectric response corrections, bring the two sets of free energies into agreement 57 .…”

“…Periodic boundaries result in an ionic charging free energy that arises purely from local structural perturbations, both charging induced, ∆G c IS , and from any local core contributions to ρ q 0 (r) that may contribute to ∆G c PB . Note that PBCs may lead to additional finite size effects on ∆G c IS that have been discussed throughout the literature 50,53,56,57 , and we ignore these well understood corrections.…”

Computational optimization of electric fields for better catalysis design

“…Even so, Cox and Geissler have shown that dielectric continuum descriptions can provide highly accurate finite size corrections for ion solvation at planar interfaces. 57 Together these results make clear that the key is to unravel the local and non-linear electrostatic effects through explicit atomistic or variable density representations, that is then embedded in or corrected by a continuum model for the long-range electrostatic effects. This is likely why modified Poisson Boltzmann treatments/DFT 58 and classical/quantum DFT approaches 56 and recent hybrid and double hybrid functionals which incorporate some percentage of exact exchange, are addressing better QM accuracy 61 , and new approaches have been introduced that incorporate true many-body polarization effects across the QM/MM boundary.…”

Assessing long-range contributions to the charge asymmetry of ion adsorption at the air–water interface

“…Contrary to Born's result, computer simulations indicate that the sign of the charge of small ions can signicantly inuence their charging free energy F chg (q, R), i.e., the work involved in reversibly introducing the solute's charge q. [30][31][32][33][34][35][36][37][38][39] This dependence is most easily scrutinized for simple point charge (SPC) models of molecular interactions, where an ion's charge can be varied independently of its other properties. In SPC/E water, 40 for instance, charging a solute roughly the size of uoride (R F z 0.317 nm) has an asymmetry, F chg (e, R F ) À F chg (Àe, R F ) z 16 kcal mol À1 , almost 30 times larger than thermal energy k B T. Here, e is the magnitude of an electron's charge.…”