*see also*Atomic structure

Madelung constant (Wikipedia)

J M Borwein, M L Glasser, R C McPhedran, J G Wan, I J Zucker, Lattice Sums Then and Now (CUP, 2013)

R E Crandall, Unified algorithms for polylogarithm, L-series, and zeta variants (preprint, 2012)

M Mazars, Long ranged interactions in computer simulations and for quasi-2D systems, PR 500, 43 (2011)

M Karttunen, J Rottler, I Vattulainen, C Sagui, Electrostatics in biomolecular simulations: Where are we now and where are we heading?, Computational Modeling of Membrane Bilayers 60, 49 (Academic Press, 2008)

A Arnold, C Holm, Efficient methods to compute long-range interactions for soft matter systems, Adv Polym Sci 185, 59 (2005)

E V Kholopov, Convergence problems of Coulomb and multipole sums in crystals, Phys Usp 47, 965 (2004)

M P Tosi, Cohesion of ionic solids in the Born model, Solid State Physics 16, 1 (1964)

C M Linton, I Thompson, One- and two-dimensional lattice sums for the three-dimensional Helmholtz equation, J Comput Phys 228, 1815 (2009)

C J Fennell, J D Gezelter, Is the Ewald summation still necessary? Pairwise alternatives to the accepted standard for long-range electrostatics, JCP 124, 234104 (2006)

W A Harrison, Simple calculation of Madelung constants, PRB 73, 212103 (2006)

S Tyagi, Logarithmic interaction under periodic boundary conditions: closed form formulas for energy and forces, Mol Phys 104, 359 (2006)

S Tyagi, Coulomb potentials in two and three dimensions under periodic boundary conditions, JCP 122, 014101 (2005)

M A Stremler, Evaluation of phase-modulated lattice sums, JMP 45, 3584 (2004)

R Strebel, R Sperb, An alternative to Ewald sums. Part 3: Implementation and results, Molecular Simulation 27, 61 (2001)

R Strebel, Pieces of software for the Coulombic m body problem, PhD thesis (ETH Zurich, 2000)

S L Marshall, A periodic Green function for calculation of coloumbic lattice potentials, JPC 12, 4575 (2000)

D Wolf, P Keblinski, S R Phillpot, J Eggebrecht, Exact method for the simulation of Coulombic systems by spherically truncated, pairwise r-1 summation, JCP 110, 8254 (1999)

R Sperb, An alternative to Ewald sums. Part 2: The Coulomb potential in a periodic system, Molecular Simulation 22, 199 (1999)

R Sperb, An alternative to Ewald sums. Part 1: Identities for sums, Molecular Simulation 20, 179 (1998)

J Lekner, Coulomb forces and potentials in systems with an orthorhombic unit cell, Molecular Simulation 20, 357 (1998)

R Sperb, Extension and simple proof of Lekner's summation formula for Coulomb forces, Molecular Simulation 13, 189 (1994)

E Johnson, The calculation of electrostatic potentials for periodic charge distributions, JCP 105, 13 (1996)

J Lekner, Summation of Coulomb fields in computer-simulated disordered systems, PA 176, 485 (1991)

R E Crandall, J F Delord, The potential within a crystal lattice, JPA 20, 2279 (1987)

F E Harris, H J Monkhorst, Electronic-structure studies of solids. I. Fourier representation method for Madelung sums, PRB 2, 4400 (1970)

C A Sholl, The calculation of electrostatic energies of metals by plane-wise summation, Proc Phys Soc 92, 434 (1967)

R Hoppe, Madelung constants, Angew Chem Int Ed 5, 95 (1966)

A Sabry, M Ayadi, A Chouikh, Simulation of ionic crystals and calculation of electrostatic potentials, Comput Mater Sci 18, 345 (2000)

M M Mestechkin, Electrostatic parameters of ionic crystals, J Phys Chem Ref Data 29, 571 (2000)

Q C Johnson, D H Templeton, Madelung constants for several structures, JCP 34, 2004 (1961)