+ Site Statistics
+ Search Articles
+ PDF Full Text Service
How our service works
Request PDF Full Text
+ Follow Us
Follow on Facebook
Follow on Twitter
Follow on LinkedIn
+ Subscribe to Site Feeds
Most Shared
PDF Full Text
+ Translate
+ Recently Requested

Effective way to sum over long-range Coulomb potentials in two and three dimensions



Effective way to sum over long-range Coulomb potentials in two and three dimensions



Physical Review. E Statistical Nonlinear and Soft Matter Physics 70(6 Pt 2): 066703



I propose a method to calculate the logarithmic interaction in two dimensions and the Coulomb interaction in three dimensions under periodic boundary conditions. This paper considers the case of a rectangular cell in two dimensions and an orthorhombic cell in three dimensions. Unlike the Ewald method, there is no parameter to be optimized, nor does the method involve error functions, thus leading to the accuracy obtained. This method is similar in approach to that of Mol. Simul. 22, 199 (1999)]], but the derivation is considerably simpler and physically appealing. An important aspect of the proposed method is the faster convergence of the Green's function for a particular case as compared to Sperb's work. The convergence of the sums for most parts of the unit cell is exponential, and hence requires the calculation of only a few dozen terms. In a very simple way, we also obtain expressions for the interaction for systems with slab geometries. Expressions for the Madelung constants of CsCl and NaCl are also obtained.

Please choose payment method:






(PDF emailed within 0-6 h: $19.90)

Accession: 048897460

Download citation: RISBibTeXText

PMID: 15697549

DOI: 10.1103/physreve.70.066703


Related references

Low-energy scattering theory for Coulomb plus long-range potentials. Physical Review. C Nuclear Physics 35(4): 1188-1200, 1987

Resolutions of the Coulomb Operator: VII. Evaluation of Long-Range Coulomb and Exchange Matrices. Journal of Chemical Theory and Computation 9(2): 863-867, 2013

Coulomb potentials in two and three dimensions under periodic boundary conditions. Journal of Chemical Physics 122(1): 14101, 2005

Nonadiabatic coefficients of long-range effective potentials and the Faraday effect. Physical Review. A Atomic Molecular and Optical Physics 53(4): 2289-2294, 1996

Unified Treatment of Screening Coulomb and Anharmonic Oscillator Potentials in Arbitrary Dimensions. Communications in Theoretical Physics 45(5): 807-812, 2006

Allowing for Coulomb effects in the effective range expansion for two coupled channels. Bulletin of the Russian Academy of Sciences: Physics 76(4): 425-428, 2012

Investigation of Coulomb Logarithm and Relaxation Processes in Dense Plasma on the Basis of Effective Potentials. Contributions to Plasma Physics 55(2-3): 271-276, 2015

Direct Monte Carlo sampling of the short-range screening potentials for classical Coulomb liquids. Physical Review. E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics 53(1): 1094-1099, 1996

Effective short-range Coulomb correction to model the aggregation behavior of ionic surfactants. Journal of Chemical Physics 144(23): 234904, 2016

Short-range screening potentials for classical Coulomb fluids: Monte Carlo sampling and cluster model studies. Physical Review. E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics 50(4): 2977-2985, 1994

Short-range screening potentials for classical Coulomb fluids: Reanalysis of Monte Carlo sampling and cluster model studies. Physical Review. E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics 53(2): 2000-2007, 1996

The surface Coulomb energy and proton Coulomb potentials of pyrophyllite 010, 110, 100, and 130 edges. Clays and Clay Minerals 41(3): 305-316, 1993

Use of Coulomb-Sturmian functions in calculating scattering quantities in Coulomb-like potentials. Physical Review. A Atomic Molecular and Optical Physics 46(7): 4437-4439, 1992

Long-range Coulomb interaction in bilayer graphene. Physical Review Letters 102(5): 056807, 2009

Long-range Coulomb forces and localized bonds. Acta Crystallographica. Section B Structural Science 55(Pt 5): 698-711, 1999