Chapter 3.4 Accelerated convergence treatment of Rn lattice sums

Reciprocal space

First Online Edition (2006)

Part 3. Dual bases in crystallographic computing

  1. D. E. Williams

Published Online: 1 JAN 2006

DOI: 10.1107/97809553602060000562

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Williams, D. E. 2006. Accelerated convergence treatment of Rn lattice sums. International Tables for Crystallography. B:3:3.4:385–397.

Author Information

  1. Department of Chemistry, University of Louisville, Louisville, Kentucky 40292, USA

Publication History

  1. Published Online: 1 JAN 2006


Accelerated-convergence treatment of the Coulombic lattice sum of ionic crystals and the dispersion-energy sum of ionic or molecular crystals is described. The Coulombic energy is very long-range and convergence of the Coulombic lattice-energy sum is extremely slow. Accelerated-convergence treatment is indispensable to achieve accuracy with a reasonable amount of computational effort. The dispersion-energy sum has somewhat better convergence properties than the Coulombic sum, but accelerated-convergence treatment of the dispersion sum is also strongly recommended since its use can yield at least an order of magnitude improvement in accuracy for a given calculation effort.


  • accelerated convergence;
  • lattice sums;
  • direct-space sums;
  • Coulombic lattice energy;
  • dispersion energy;
  • composite lattices;
  • incomplete gamma function;
  • intramolecular energy terms