Application to the lattice energy of alkali halides

1 The Electrostatic Energy for the Point-Charge and Overlapping-Ion Models 

Sodium fluoride, NaF, is a favorable choice for X-ray analysis of the lattice energy of an ionic crystal. Both Na and F are relatively light atoms, and the Na 3s-radial distribution, though diffuse, is not quite as spread out as the Li 2s shell (single-C values are 0.8358 and 0.6396 au-1, respectively see appendix F), and therefore contributes to a larger number of reflections. 

With K in the convergence function of Eq. (9.18) equal to 0.4 A-1, the accelerated convergence method reaches an accuracy of nine significant figures with inclusion of only 1000 unit cells. By comparison, about 50,000 unit cells would be required for a summation performed exclusively in direct space. 

For the unit-point-charge crystal, the absolute value of the electrostatic energy is equal to the potential at the nuclear position. This potential will be equal for both ions in the alkali halide structure, as their positions are equivalent that is, 

For the crystal composed of ions, the equality given in Eq. (9.33) is no longer valid, because the two ionic charge distributions, which partly shield the nuclear charges, are different. For the free-ion crystal, the values of the potential at the nuclear positions in NaF, evaluated according to Section 9.3.2, are 

---