Reliability of the slab-adapted Ewald method

To demonstrate the reliability of the slab-adapted Ewald method introduced in the preceding Section 6.3.2, we present in the following results from lattice calculations [257]. Specifically, we consider a slab composed of dipolar spheres of diameter a located at the sites of a face-centered cubic (fee) lattice. The lattice vectors are r = (f/2) (IxJyJz) where ( is the lattice constant (fixed such that the reduced density = 4a fi = 1.0), and / (o = x,y,z) arc integers with + ly 1 Iz even. An infinibdy extendexi slab is then realized by setting -oo lx,ly oc and = 0. n — 1 with n being the number of fee layers in -direction. 

We evaluate the system s total dipolar energy for the following situations  

The latter, somewhat unphysical situation has been included to investigate the importance of the correction term given in Eq. (6.43). Clearly, the correction is irrelevant for case 1. 

For both situations, we calculate the (dimensionless) dipolar energy per particle, a Ux)/fj, N, via the slab-adapted three-dimensional Ewald sum [see Eq. (6.44)] and with the rigorous Ewald method for dipolar slab systems 

Also shown in Figs. 6.2 are results obtained via direct summation of the dipolar interactions. Using the fact that particles within a given layer contribute equally, the total configurational potential energy for case 2 can 

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Having established the accuracy and reliability of the slab-adapted three-dimensional Ewald method, we present in this paragraph numerical results from GCEMC simulations (see Section 5.2.2) for a confined Stockmaycr fluid. The particles then interact with each other via both the long-range. 

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