Multipolar electrostatic sums in numerical simulations with wall boundary conditions

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Abstract
In order to cope with numerical simulations of charged periodic systems bounded by an infinite wall, the planewise summation method is discussed. The equations needed to evaluate, in this quasi-two-dimensional geometry, the lattice sums of arbitrary derivatives of 1/r at any field point of a general lattice, are given. The relationship with the Ewald method is discussed and it is found that, roughly speaking, the computational time required is comparable for both methods.