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Communication: On the origin of the surface term in the Ewald formula
2. P. H. Hünenberger, in Simulation and Theory of Electrostatic Interactions in Solution: Computational Chemistry, Biophysics, and Aqueous Solutions, edited by L. R. Pratt and G. Hummer (AIP, New York, 1999), pp. 17–83.
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21.No non-analytic can survive in (17) because the summand in (16) is absolutely convergent.
22.The electric neutrality of the simulation cell is often invoked as the reason for the exclusion of the term in (18), but neutrality alone is not sufficient because that term would still be plagued by an indeterminacy of the form 0 × ∞. That indeterminacy is intimately linked to how the long-range contributions in the lattice sum (1) are handled and it is resolved only by an adequate treatment of those contributions, performed here via the splitting (2).
23.One can show indeed that no term arises in (19), in the limit V → ∞, from the difference between the volume V and the crenelated volume made up of an integer number of cells.
24. J. A. Stratton, Electromagnetic Theory (IEEE Press, 2007).
29. V. Ballenegger, “On the electrostatic surface contributions to the Ewald potential in periodic charged systems” (unpublished).
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A transparent derivation of the Ewald formula for the electrostatic energy of a periodic three-dimensional system of point charges is presented. The problem of the conditional convergence of the lattice sum is dealt with by separating off, in a physically natural and mathematically simple way, long-range non-absolutely integrable contributions in the series. The general expression, for any summation order, of the surface (or dipole) term emerges very directly from those long-range contributions.
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