Could anyone provide me some materials on the derivation of Ewald's generalized theta function (in English)? The original paper was written in German :-( 


Die Berechnung optischer und elektrostatischer Gitterpotentiale


P. P. Ewald


Annalen der Physik


Volume 369, pages 253–287, 1921


<http://onlinelibrary.wiley.com/doi/10.1002/andp.19213690304/abstract>


(DOI: 10.1002/andp.19213690304)



Ewald's generalized theta function
A step by step derivation of Ewald summation can be found in:


Williams, D. E. (1971). Accelerated convergence of crystal-lattice potential sums. Acta Crystallographica Section A, 27(5), 452–455. doi:10.1107/S0567739471000998


There's also an expanded version of the above paper:


Williams, D. E. (2006). Accelerated convergence treatment of $R^{-n}$ lattice sums. In U. Shmueli (Ed.), International Tables for Crystallography. Volume B. (pp. 385–397). Kluwer Academic Publishers.


Some additional material that might help you:


De Leeuw, S. W., Perram, J. W., & Smith, E. R. (1980). Simulation of Electrostatic Systems in Periodic Boundary Conditions. I. Lattice Sums and Dielectric Constants. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 373(1752), 27–56. doi:10.1098/rspa.1980.0135


Nijboer, B. R. A., & De Wette, F. W. (1957). On the calculation of lattice sums. Physica, 23(1-5), 309–321. doi:10.1016/S0031-8914(57)92124-9


I think between the papers of Williams and the appendices in Nijboer and De Wette, it is possible to fill all the gaps (at least in the case where there's no dipole moment).


