Tables for
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2006). Vol. B, ch. 3.4, pp. 385-397   | 1 | 2 |
doi: 10.1107/97809553602060000562

Chapter 3.4. Accelerated convergence treatment of R−n lattice sums

D. E. Williamsa

aDepartment of Chemistry, University of Louisville, Louisville, Kentucky 40292, USA


Arfken, G. (1970). Mathematical methods for physicists, 2nd ed. New York: Academic Press.
Bertaut, E. F. (1952). L'énergie électrostatique de réseaux ioniques. J. Phys. (Paris), 13, 499–505.
Bertaut, E. F. (1978). The equivalent charge concept and its application to the electrostatic energy of charges and multipoles. J. Phys. (Paris), 39, 1331–1348.
Busing, W. R. (1981). WMIN, a computer program to model molecules and crystals in terms of potential energy functions. Oak Ridge National Laboratory Report ORNL-5747. Oak Ridge, Tennessee 37830, USA.
Cummins, P. G., Dunmur, D. A., Munn, R. W. & Newham, R. J. (1976). Applications of the Ewald method. I. Calculation of multipole lattice sums. Acta Cryst. A32, 847–853.
Davis, P. J. (1972). Gamma function and related functions. Handbook of mathematical functions with formulas, graphs, and mathematical tables, edited by M. Abramowitz & I. A. Stegun, pp. 260–262. London, New York: John Wiley. [Reprint, with corrections of 1964 Natl Bur. Stand. publication.]
DeWette, F. W. & Schacher, G. E. (1964). Internal field in general dipole lattices. Phys. Rev. 137, A78–A91.
Evjen, H. M. (1932). The stability of certain heteropolar crystals. Phys. Rev. 39, 675–694.
Ewald, P. P. (1921). Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. (Leipzig), 64, 253–287.
Fortuin, C. M. (1977). Note on the calculation of electrostatic lattice potentials. Physica (Utrecht), 86A, 574–586.
Glasser, M. L. & Zucker, I. J. (1980). Lattice sums. Theor. Chem. Adv. Perspect. 5, 67–139.
Hastings, C. Jr (1955). Approximations for digital computers. New Jersey: Princeton University Press.
Madelung, E. (1918). Das elektrische Feld in Systemen von regelmässig angeordneten Punktladungen. Phys. Z. 19, 524–532.
Massidda, V. (1978). Electrostatic energy in ionic crystals by the planewise summation method. Physica (Utrecht), 95B, 317–334.
Nijboer, B. R. A. & DeWette, F. W. (1957). On the calculation of lattice sums. Physica (Utrecht), 23, 309–321.
Pietila, L.-O. & Rasmussen, K. (1984). A program for calculation of crystal conformations of flexible molecules using convergence acceleration. J. Comput. Chem. 5, 252–260.
Widder, D. V. (1961). Advanced calculus, 2nd ed. New York: Prentice-Hall.
Williams, D. E. (1971). Accelerated convergence of crystal lattice potential sums. Acta Cryst. A27, 452–455.
Williams, D. E. (1984). PCK83, a crystal molecular packing analysis program. Quantum Chemistry Program Exchange, Department of Chemistry, Indiana University, Bloomington, Indiana 47405, USA.
Williams, D. E. (1989). Accelerated convergence treatment of [{\bi R}^{-n}] lattice sums. Crystallogr. Rev. 2, 3–23. Corrections: Crystallogr. Rev. 2, 163–166.