Lattice Summations in STR

Calculating the structure constants (6.7,8.23) involves the time-consuming evaluation of the lattice sum 

4 the summation may be performed directly in real space, but for ,4 the long-range part must be evaluated separately by Fourier transformation. In the standard technique, from Ewald, the terms in the reciprocal sum behave like e +G 5 where X is a splitting parameter. The terms in 

N is an arbitrary splitting parameter and the functions G will be specified below. 

The separation of L into real and reciprocal lattice sums is performed as follows  

With (9.4-6) and using X of the order of ten times the inverse lattice constant together with N specified by (9.7), the structure constants may be evaluated with an accuracy of a few per cent by summation over 3 shells in the direct lattice plus less than ten points of the reciprocal lattice. For an accuracy exceeding one part per thousand the summations must include 6-8 shells of both lattices. 

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