Accurate calculation of Coulomb sums: Efficacy of Pade-like methods
- Computer Centre, The University of Burdwan, Burdwan 713 104 (India)
- Department of Chemistry, The University of Burdwan, Burdwan 713 104 (India)
The adequacy of numerical sequence accelerative transforms in providing accurate estimates of Coulomb sums is considered, referring particularly to distorted lattices. Performance of diagonal Pade approximants (DPA) in this context is critically assessed. Failure in the case of lattice vacancies is also demonstrated. The method of multiple-point Pade approximants (MPA) has been introduced for slowly convergent sequences 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 distortions owing to vacancies, a strategy of obtaining reliable results by separate 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 lattices follow.
- OSTI ID:
- 6274680
- Journal Information:
- Physical Review, B: Condensed Matter; (United States), Vol. 48:10; ISSN 0163-1829
- Country of Publication:
- United States
- Language:
- English
Similar Records
Asymptotic expansion of two-electron integrals and its application to Coulomb and exchange lattice sums in metallic, semimetallic, and nonmetallic crystals
On uniform approximation of elliptic functions by Pade approximants
Related Subjects
SUPERCONDUCTIVITY AND SUPERFLUIDITY
IONIC CRYSTALS
COULOMB ENERGY
CALCULATION METHODS
CONVERGENCE
CUBIC LATTICES
ERRORS
IMPURITIES
PADE APPROXIMATION
VACANCIES
CRYSTAL DEFECTS
CRYSTAL LATTICES
CRYSTAL STRUCTURE
CRYSTALS
ENERGY
POINT DEFECTS
665000* - Physics of Condensed Matter- (1992-)