Slab-adapted Ewald summation

Equation (6.40) is our final expression for the energy of a charged system between insulating walls within the slab-adapted three-dimensional Ewald summation method. On the right side, the contribution f/ le =oo is defined by Eqs. (6.15), (6.16), and (6.17b). The reader should also realize that, for the current system, the volume V appearing in the Fourier pjurt of the energy [see Eq. (6.16b)] includes the vacuum space that is, V = = 7S -... 

Figure 6.2 Dimensionless energy per particle for dipolar crystalline (fee) slabs as a function of the number of lattice layers, assuming perfect order along the ar-axis (a) and along the z-axis (b). Included are results from direct summation (O), the rigorous Ewald sum for slab systems (A) (sec Appendix F.3.1.2], and the slab-adapted three-dimensional Ewald sum (x) [see Eq. (6.44)j. Part (b) additionally includes results from the latter method when the correction term [see Eq. (6.43)) is neglected ( ).

Similar expressions are obteiined for case 1. Data plotted in Figs. 6.2 have been obtained by truncating the sums over Z and ly at 5000, which yields convergent results as long as n, < 4. Comparing these results with those from the two Ewald methods, we conclude that not only the rigorous Ewald summation, but also the slab-adapted three-dimensional version provide quasi-exact results for th( dipolar energy. 

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