ACCURATE CALCULATION OF COULOMB SUMS - EFFICACY OF PADE-LIKE METHODS

The adequacy of numerical sequence accelerative transforms in providin g accurate estimates of Coulomb sums is considered, referring particul arly to distorted lattices. Performance of diagonal Pade approximants (DPA) in this context is critically assessed. Failure in the case of l attice vacancies is also demonstrated. The method of multiple-point Pa de approximants (MPA) has been introduced for slowly convergent sequen ces and is shown to work well for both regular and distorted lattices, the latter being due either to impurities or vacancies. Viability of the two methods is also compared. In divergent situations with distort ions owing to vacancies, a strategy of obtaining reliable results by s eparate applications of both DPA and MPA at appropriate places is also sketched. Representative calculations involve two basic cubic-lattice sums, one slowly convergent and the other divergent, from which very good quality estimates of Madelung constants for a number of common la ttices follow.