Chapter 3.4 Accelerated convergence treatment of Rn lattice sums

Reciprocal space

Second Online Edition (2010)

Part 3. Dual bases in crystallographic computing

  1. D. E. Williams

Published Online: 1 JUN 2010

DOI: 10.1107/97809553602060000771

International Tables for Crystallography

International Tables for Crystallography

How to Cite

Williams, D. E. 2010. Accelerated convergence treatment of Rn lattice sums. International Tables for Crystallography. B:3:3.4:449–457.

Author Information

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

Publication History

  1. Published Online: 1 JUN 2010



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