The type of sum that arises when the electrostatic energy of an ionic crystal is calculated. As the convergence of this type of sum is very slow, several methods have been used to speed it up. The Madelung constant is an important quantity in the calculation of lattice sums. The discussion of these sums is simplest when the ions are regarded as point charges, but this idealized assumption applies only when the electron distribution of an ion is spherical; in other cases, more complicated calculations must be performed.