Ewald summation for confined fluids

Having understood the concepts of Ew ald summation techniques for three-dimensional bulk systems, we now turn to systems that are finite in at least one spatial dimension. We focus on a slab-like geometry where the fluid is confined by two plane parallel and structureless solid surfaces separated by a distance s along the 2-axis of the coordinate system and of infinite extent in the x-y plane (see also Section 1.3.2). Hence, for the time being, we shall be 

Not surprisingly, the reduction of spatial symmetry renders the treatment of long-range fluid fluid interactions significantly more involved than in the three-dimensional case. This concerns not only the derivation of appropriate (Ewald or other) expressions for energies, forces, and torques, but also the computational effort needed in actual calculations. 

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