Supplementary Information s84
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 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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