On the calculation of the lattice energy of ionic crystals using the detailed electron-density distribution. I. Treatment of spherical atomic distributions and application to NaF

Ewald's method of accelerated convergence [Ewald (1921). Ann. Phys. (Leipzig), 64, 253–287] is generalized to calculate the electrostatic potential of a crystal in which the atoms have overlapping spherical densities. The algorithm is applied to the cubic NaF crystal. The potentials at the Na and F nuclei are calculated for the free-ion model and for the results from a κ refinement of the experimental data of Howard & Jones [Acta Cryst. (1977), A33, 776–783]. The κ refinement indicates an incomplete charge transfer but gives an electrostatic energy close to that of the point-charge model with full charge transfer and a lattice energy that is in good agreement with the experimental value.