Rapid calculation of individual ion Madelung constants and their convergence to bulk values Available to Purchase

The distinction between the single Madelung constant that characterizes bulk materials and the range of Madelung constants that exists for real (finite) materials is emphasized. Madelung constants are calculated using a fast algorithm to compute Coulomb sums. The weighted averages of the specific ion Madelung constants provide a measure of the electrostatic potential for any cluster of ions. The central ions’ Madelung constants in a succession of progressively larger structures with the same symmetry as the bulk converge rapidly to the bulk Madelung constant if all the precursors to the bulk are electrically neutral. If this condition is satisfied, convergence is faster than other methods and is simpler to implement than the classical Ewald method. Applications to surface science and to the conformations and energies of nanostructures are made possible by this approach.