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Supplementary Information:
In order to accurately simulate interface structure with shifted-force electrostatics, it is necessary to
include a correction, along the interface normal, to the force calculation. This is needed due to the anisotropic
charge distribution that results at the interface. Corrective procedure is based on treating areas of net charge
along the interface normal like flat sheets of charge which generate constant, long-range forces.
Electrostatic force correction begins by dividing the simulation box into 0.005 nm thick slices along the
interface normal (i.e. the z-axis). Each atom feels an individual corrective force along the interface normal which
is determined by summing the electric field corrections associated with each slice surrounding the atom and then
multiplying by that atom's charge. To determine a field correction for a slice, ions inside the slice are counted.
Only ions are counted in this correction due to a) the intention to specifically correct for charge anisotropy which
is at long-range a function of the ions and b) the assumption that shifted-force electrostatics handle the electric
field created by solvent molecules sufficiently. Next, the field correction is determined by taking the difference
between the long-range electric field created by a 2D sheet with charge density equal to that in the slice (using
formal electrostatic theory) and the reduced field felt when applying shifted-force treatment (determined prior to
simulation with our MD code by moving an ion toward a fine sheet of charge). This field difference is
determined during MD simulation by applying a polynomial fit for the atom-slice distance along the z-axis, and
it has the following terms: a0.5 = -0.01419216, a1 = 0.1434716, a1.5 = -0.004965239, a2 = -0.003602752 (each
coefficient represents the power of the polynomial term; distance in Å) [46]. At zero distance from the atom, the
field correction is zero. Beyond the electrostatic cutoff, the field correction is the full field itself. Note that this
approach is based around the isotropic charge distribution expected within each slice.
Testing of this technique has been performed by (1) calculating the force on an ion approaching a sheet
of ions, (2) comparing cesium ion packing results under various field strengths with an electrostatic cutoff of 10
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vs 15.5 Å, and (3) analyzing the structure of bulk solution in a zero-field simulation with and without the above
corrective procedure applied. All structural results suggest that the technique is accurate and does not cause
noticeable artifacts. There seems to be low sensitivity of results to the electrostatic cutoff used, which is not the
case when instead using explicit electrode charge and no field correction (i.e. just shifted-force electrostatics).
The overall electrostatic technique used in this study was motivated out of a desire for efficiency, but
highly quantitative work should certainly consider using Ewald-based techniques [47] or other approaches [48].
The outlined approach is only intended for obtaining accurate structural results, and it has not been considered
for more sensitive applications.
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