Simulating Charged Systems with ESPResSo

  • A. Arnold
  • B.A.F. Mann
  • Christian Holm
Part of the Lecture Notes in Physics book series (LNP, volume 703)


We give an introduction into the topic of how to compute efficiently long range interactions. We start with reviewing the traditional Ewald sum for 3D Coulomb systems, discuss then in some detail the P3M method of Hockney and Eastwood. We continue with explaining some strategies to perform the sum under partially periodic boundary conditions, where we present two recently developed methods, namely MMM2D and the ELC method for two dimensionally periodic boundary conditions, and the MMM1D method for systems with only one periodic coordinate. After this, we briefly mention alternative ways of dealing with the Coulomb sum, such as the MEMD method of Maggs. In the second part we present our recently developed MD simulation package, ESPResSo, that includes most of the introduced algorithms. We give a short introduction into the capabilities of ESPResSo and its usage. Finally we present some recent simulation results for polymer networks which were obtained by using ESPResSo.


Periodic Boundary Condition Radial Distribution Function Fast Multipole Method Charge Fraction Image Layer 
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  1. 1.
    A. Arnold and C. Holm (2005) Efficient methods to compute long range interactions for soft matter systems. In C. Holm and K. Kremer, editors, Advanced Computer Simulation Approaches for Soft Matter Sciences II volume II of, pp. 59–109, Advances in Polymer Sciences, Springer Berlin HeidelbergGoogle Scholar
  2. 2.
    R. W. Hockney and J. W. Eastwood (1988) Computer Simulation Using Particles IOP, LondonzbMATHCrossRefGoogle Scholar
  3. 3.
    ESPResSo (2004) Homepage. http://www.espresso.mpg.deGoogle Scholar
  4. 4.
    A. Arnold, B. A. Mann, H.-J. Limbach, and C. Holm (2004) ESPResSo – An Extensible Simulation Package for Research on Soft Matter Systems. In Kurt Kremer and Volker Macho, editors, Forschung und wissenschaftliches Rechnen 2003 volume 63 of GWDG-Bericht, pp. 43–59. Gesellschaft für wissenschaftliche Datenverarbeitung mbh, Göttingen, GermanyGoogle Scholar
  5. 5.
    H.-J. Limbach, A. Arnold, B. A. Mann, and C. Holm (2006) Espresso – an extensible simulation package for research on soft matter systems. Comp. Phys. Comm. 174, pp. 704–727CrossRefADSGoogle Scholar
  6. 6.
    P. P. Ewald (1921) Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. 64, pp. 253–287CrossRefGoogle Scholar
  7. 7.
    J. Perram, H. G. Petersen, and S. de Leeuw (1988) An algorithm for the simulation of condensed matter which grows as the 3/2 power of the number of particles. Mol. Phys. 65, p. 875CrossRefADSGoogle Scholar
  8. 8.
    M. Deserno and C. Holm (1998) How to mesh up Ewald sums. I. A theoretical and numerical comparison of various particle mesh routines. J. Chem. Phys. 109, p. 7678CrossRefADSGoogle Scholar
  9. 9.
    S. W. de Leeuw, J. W. Perram, and E. R. Smith (1980) Simulation of electrostatic systems in periodic boundary conditions. i. lattice sums and dielectric constants. Proc. R. Soc. Lond. A 373, pp. 27–56ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    D. M. Heyes (1981) Electrostatic potentials and fields in infinite point charge lattices. J. Chem. Phys. 74(3), pp. 1924–1929CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    H. J. C. Berendsen (1993) In Wilfred F. van Gunsteren, P. K. Weiner, and A. J. Wilkinson, editors, Computer Simulation of Biomolecular Systems 2, pp. 161–81, The Netherlands, ESCOMGoogle Scholar
  12. 12.
    P. H. Hünenberger (2000) Optimal charge-shaping functions for the particleparticle- particle-mesh (p3m) method for computing electrostatic interactions in molecular simulations. J. Chem. Phys. 113(23), pp. 10464–10476CrossRefGoogle Scholar
  13. 13.
    J. Kolafa and J. W. Perram (1992) Cutoff errors in the ewald summation formulae for point charge systems. Molecular Simulation 9(5), pp. 351–68CrossRefGoogle Scholar
  14. 14.
    M. Deserno and C. Holm (1998) How to mesh up Ewald sums. II. An accurate error estimate for the particle-particle-particle-mesh algorithm. J. Chem. Phys. 109, p. 7694CrossRefADSGoogle Scholar
  15. 15.
    R. Strebel (1999) Pieces of software for the Coulombic m body problem. Dissertation 13504, ETH ZuerichGoogle Scholar
  16. 16.
    E. R. Smith (1981) Electrostatic energy in ionic crystals. Proc. R. Soc. Lond. A 375, pp. 475–505zbMATHADSCrossRefGoogle Scholar
  17. 17.
    A. Arnold and C. Holm (2002) MMM2D: A fast and accurate summation method for electrostatic interactions in 2D slab geometries. Comp. Phys. Comm. 148(3), pp. 327–348CrossRefADSGoogle Scholar
  18. 18.
    A. Arnold and C. Holm (2005) MMM1D: A method for calculating electrostatic interactions in 1D periodic geometries. J. Chem. Phys. 123(14), p. 144103CrossRefADSGoogle Scholar
  19. 19.
    M. Abramowitz and I. Stegun (1970) Handbook of mathematical functions. Dover Publications Inc., New YorkGoogle Scholar
  20. 20.
    I.-C. Yeh and M. L. Berkowitz (1999) Ewald summation for systems with slab geometry. J. Chem. Phys. 111(7), pp. 3155–3162CrossRefADSGoogle Scholar
  21. 21.
    E. R. Smith (1988) Electrostatic potentials for thin layers. Mol. Phys. 65, pp. 1089–1104CrossRefADSGoogle Scholar
  22. 22.
    A. Arnold, J. de Joannis, and C. Holm (2002) Electrostatics in Periodic Slab Geometries I. J. Chem. Phys. 117, pp. 2496–2502CrossRefADSGoogle Scholar
  23. 23.
    J. Lekner (1989) Summation of dipolar fields in simulated liquid vapor interfaces. Physica A 157, p. 826CrossRefADSGoogle Scholar
  24. 24.
    A. G. Moreira and R. R. Netz (2001) Binding of similarly charged plates with counterions only. Phys. Rev. Lett. 87, p. 078301CrossRefADSGoogle Scholar
  25. 25.
    R. Sperb (1994) Extension and simple proof of lekner’s summation formula for coulomb forces. Molecular Simulation 13, pp. 189–193CrossRefGoogle Scholar
  26. 26.
    M. Mazars (2001) Lekner summations. J. Chem. Phys. 115(7), p. 2955CrossRefADSGoogle Scholar
  27. 27.
    L. Greengard and V. Rokhlin (1997) A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica 6, pp. 229–269MathSciNetCrossRefGoogle Scholar
  28. 28.
    I. Tsukermann (2006) A class of difference schemes with flexible local approximation. Journal of Computational Physics 211, pp. 659–699CrossRefADSMathSciNetGoogle Scholar
  29. 29.
    G. Sutmann and B. Steffen (2005) A particle–particle particle–multigrid method for long–range interactions in molecular simulations. Comp. Phys. Comm. 169, pp. 343–346CrossRefADSGoogle Scholar
  30. 30.
    A. C. Maggs and V. Rosseto (2002) Local simulation algorithms for coulombic interactions. Phys. Rev. Lett. 88, p. 196402CrossRefADSGoogle Scholar
  31. 31.
    I. Pasichnyk and B. Dünweg (2004) Coulomb interactions via local dynamics: A molecular-dynamics algorithm. Journal of Physics: Cond. Mat. 16(38), pp. 3999–4020CrossRefADSGoogle Scholar
  32. 32.
    Tcl/Tk (2003) Tool Command Language / ToolKit – HomepageGoogle Scholar
  33. 33.
    LAM/MPI (2004) Local Area Multicomputer Message Passing Interface –HomepageGoogle Scholar
  34. 34.
    MPICH (2004) Message Passing Interface CHameleon – HomepageGoogle Scholar
  35. 35.
    FFTW (2003) Fastest Fourier Transform in the West – HomepageGoogle Scholar
  36. 36.
    CVS (2003) Concurrent Versions System – HomepageGoogle Scholar
  37. 37.
    Doxygen (2005) Doxygen – A documentation generation systemGoogle Scholar
  38. 38.
    G. S. Grest and K. Kremer (1986) Molecular dynamics simulation for polymers in the presence of a heat bath. Phys. Rev. A 33(5), pp. 3628–31CrossRefADSGoogle Scholar
  39. 39.
    A. Kolb and B. Dünweg (1999) Optimized constant pressure stochastic dynamics. J. Chem. Phys. 111(10), pp. 4453–4459CrossRefADSGoogle Scholar
  40. 40.
    W. Humphrey, A. Dalke, and K. Schulten (1996) VMD: Visual molecular dynamics. Journal of Molecular Graphics 14, pp. 33–38CrossRefGoogle Scholar
  41. 41.
    B. A. Mann, C. Holm, and K. Kremer (2005) Swelling behaviour of polyelectrolyte networks. J. Chem. Phys. 122(15), p. 154903CrossRefADSGoogle Scholar
  42. 42.
    B. A. Mann, C. Holm, and K. Kremer (2006) Polyelectrolyte networks in poor solvent. in preparation Google Scholar
  43. 43.
    B. A. Mann, R. Everaers, C. Holm, and K. Kremer (2004) Scaling in polyelectrolyte networks. Europhys. Lett. 67(5), pp. 786–792CrossRefADSGoogle Scholar
  44. 44.
    H. Schiessel and P. Pincus (1998) Counterion-condensation-induced collapse of highly charged polyelectrolytes. Macromolecules 31, pp. 7953–7959CrossRefADSGoogle Scholar
  45. 45.
    H. J. Limbach and C. Holm (2003) Single-chain properties of polyelectrolytes in poor solvent. J. Phys. Chem. B 107(32), pp. 8041–8055CrossRefGoogle Scholar
  46. 46.
    H. J. Limbach, C. Holm, and K. Kremer (2002) Structure of polyelectrolytes in poor solvent. Europhys. Lett. 60(4), pp. 566–572CrossRefADSGoogle Scholar
  47. 47.
    Bernward A. Mann, Swelling Behaviour of Polyelectrolyte Networks, Ph.D. thesis, JoGu Universität Mainz, 2005Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • A. Arnold
    • 1
    • 2
  • B.A.F. Mann
    • 1
  • Christian Holm
    • 1
    • 2
  1. 1.Max-Planck-Institut für PolymerforschungMainzGermany
  2. 2.Frankfurt Institute for Advanced Studies (FIAS)Johann Wolfgang Goethe-UniversitätFrankfurt/MainGermany

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