The European Physical Journal Special Topics

, Volume 225, Issue 8–9, pp 1483–1503 | Cite as

Thermodynamic translational invariance in concurrent multiscale simulations of liquids

  • R. EveraersEmail author
Regular Article Hybrid and Adaptive Coarse Graining Methods
Part of the following topical collections:
  1. Modern Simulation Approaches in Soft Matter Science: From Fundamental Understanding to Industrial Applications


AdResS multi scale simulations of liquid systems allow for a free exchange of particles between regions, where their interactions are described by different models. The desired “model coexistence” is somewhat reminiscent of phase-coexistence. But while the latter describes heterogeneous systems with position-independent interactions, AdResS is meant to generate homogeneous systems with position-dependent interactions. Here we formulate the bulk equilibrium conditions for model coexistence, discuss the connection between the Hamiltonian H-AdResS scheme and widely used free energy methods based on the Kirkwood coupling parameter method of thermodynamic integration, and point out the relation between thermodynamic corrections in AdResS simulations and tail corrections for truncated long-range potentials. In particular, we use the analogy to derive expressions for the form of the correction profiles in narrow transition zones, which cannot be fully described by the local coupling parameter approximation. Finally, we illustrate how to treat transient mergers of small, diffusing all atom zones attached to reference particles in dynamic AdResS simulations without additional calibrations beyond the initial parameterization of the correction profile for individual all atom zones.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material


  1. 1.
    R.E. Rudd, J.Q. Broughton, Phys. Stat. Solidi B-basic Res. 217, 251 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    J. Rottler, S. Barsky, M.O. Robbins, Phys. Rev. Lett. 89, 148304 (2002)ADSCrossRefGoogle Scholar
  3. 3.
    A. Warshel, M. Levitt, J. Mol. Biol. 103, 227 (1976)CrossRefGoogle Scholar
  4. 4.
    M. Svensson, S. Humbel, R.D.J. Froese, T. Matsubara, S. Sieber, K. Morokuma, J. Phys. Chem. 100, 19357 (1996)CrossRefGoogle Scholar
  5. 5.
    G. Csanyi, T. Albaret, M.C. Payne, A.D. Vita, Phys. Rev. Lett. 93, 175503 (2004)ADSCrossRefGoogle Scholar
  6. 6.
    G. Lu, E.B. Tadmor, E. Kaxiras, Phys. Rev. B 73, 024108 (2006)ADSCrossRefGoogle Scholar
  7. 7.
    M. Praprotnik, L.D. Site, K. Kremer, J. Chem. Phys. 123, 224106 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    M. Praprotnik, L.D. Site, K. Kremer, Phys. Rev. E 73, 066701 (2006)ADSCrossRefGoogle Scholar
  9. 9.
    M. Praprotnik, L.D. Site, K. Kremer, J. Chem. Phys. 126, 134902 (2007)ADSCrossRefGoogle Scholar
  10. 10.
    B. Ensing, S.O. Nielsen, P.B. Moore, M.L. Klein, M. Parrinello, J. Chem. Theo. Comput. 3, 1100 (2007)CrossRefGoogle Scholar
  11. 11.
    R. Potestio, S. Fritsch, P. Espanol, R. Delgado-Buscalioni, K. Kremer, R. Everaers, D. Donadio, Phys. Rev. Lett. 110, 108301 (2013)ADSCrossRefGoogle Scholar
  12. 12.
    R. Potestio, P. Espanol, R. Delgado-Buscalioni, R. Everaers, K. Kremer, D. Donadio, Phys. Rev. Lett. 111, 060601 (2013)ADSCrossRefGoogle Scholar
  13. 13.
    D. Ruelle, Thermodynamic Formalism: The Mathematical Structures of Equilibrium Statistical Mechanics, 2nd edn. (Cambridge University Press, Cambridge, UK, 2004)Google Scholar
  14. 14.
    J.G. Kirkwood, J. Chem. Phys. 3, 300 (1935)ADSCrossRefGoogle Scholar
  15. 15.
    H.B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd edn. (John Wiley & Sons, US, 1985)Google Scholar
  16. 16.
    P. Espanol, R. Delgado-Buscalioni, R. Everaers, R. Potestio, D. Donadio, K. Kremer, J. Chem. Phys. 142, 064115 (2015)ADSCrossRefGoogle Scholar
  17. 17.
    S. Fritsch, S. Poblete, C. Junghans, G. Ciccotti, L.D. Site, K. Kremer, Phys. Rev. Lett. 108, 170602 (2012)ADSCrossRefGoogle Scholar
  18. 18.
    F. Ercolessi, J.B. Adams, Europhysics Lett. 26, 583 (1994)ADSCrossRefGoogle Scholar
  19. 19.
    A.P. Lyubartsev, A. Laaksonen, Phys. Rev. E 52, 3730 (1995)ADSCrossRefGoogle Scholar
  20. 20.
    D. Reith, M. Putz, F. Muller-Plathe, J. Computational Chem. 24, 1624 (2003)CrossRefGoogle Scholar
  21. 21.
    W.G. Noid, J.W. Chu, G.S. Ayton, V. Krishna, S. Izvekov, G.A. Voth, A. Das, H.C. Andersen, J. Chem. Phys. 128, 244114 (2008)ADSCrossRefGoogle Scholar
  22. 22.
    V. Ruhle, C. Junghans, A. Lukyanov, K. Kremer, D. Andrienko, J. Chem. Theo. Comput. 5, 3211 (2009)CrossRefGoogle Scholar
  23. 23.
    J.-P. Hansen, I.R. McDonald (ed.), Theory of Simple Liquids, 3rd edn. (Academic Press, London, 2006)Google Scholar
  24. 24.
    D. Frenkel, B. Smit (ed.), Understanding Molecular Simulation, 2nd edn. (Academic Press, San Diego, 2002)Google Scholar
  25. 25.
    M. Allen, D. Tildesley, Computer Simulation of Liquids (Oxford: Clarendon Pr, 1987)Google Scholar
  26. 26.
    C. Chipot, A.P. Edts (ed.), Free Energy Calculations: Theory and Applications in Chemistry and Biology (Springer, Berlin Heidelberg, 2007)Google Scholar
  27. 27.
    L.A. Rowley, D. Nicholson, N.G. Parsonage, J. Computational Phys. 26, 66 (1978)ADSCrossRefGoogle Scholar
  28. 28.
    H. Wang, C. Hartmann, C. Schutte, L.D. Site, Phys. Rev. X 3, 011018 (2013)Google Scholar
  29. 29.
    A. Agarwal, J.L. Zhu, C. Hartmann, H. Wang, L.D. Site, New J. Phys. 17, 083042 (2015)ADSCrossRefGoogle Scholar
  30. 30.
    L.D. Site, Phys. Rev. E 93, 022130 (2016)ADSCrossRefGoogle Scholar
  31. 31.
    U.H.E. Hansmann, Chem. Phys. Lett. 281, 140 (1997)ADSCrossRefGoogle Scholar
  32. 32.
    Y. Sugita, Y. Okamoto, Chem. Phys. Lett. 314, 141 (1999)ADSCrossRefGoogle Scholar
  33. 33.
    Y. Sugita, A. Kitao, Y. Okamoto, J. Chem. Phys. 113, 6042 (2000)ADSCrossRefGoogle Scholar
  34. 34.
    H. Fukunishi, O. Watanabe, S. Takada, J. Chem. Phys. 116, 9058 (2002)ADSCrossRefGoogle Scholar
  35. 35.
    C.J. Woods, J.W. Essex, M.A. King, J. Phys. Chem. B 107, 13703 (2003)CrossRefGoogle Scholar
  36. 36.
    T. Okabe, M. Kawata, Y. Okamoto, M. Mikami, Chem. Phys. Lett. 335, 435 (2001)ADSCrossRefGoogle Scholar
  37. 37.
    Q.L. Yan, J.J. de Pablo, J. Chem. Phys. 111, 9509 (1999)ADSCrossRefGoogle Scholar
  38. 38.
    L.D. Site, Phys. Rev. E 76, 047701 (2007)ADSCrossRefGoogle Scholar
  39. 39.
    S. Poblete, M. Praprotnik, K. Kremer, L.D. Site, J. Chem. Phys. 132, 114101 (2010)ADSCrossRefGoogle Scholar
  40. 40.
    E.M. Blokhuis, D. Bedeaux, C.D. Holcomb, J.A. Zollweg, Mol. Phys. 85, 665 (1995)ADSCrossRefGoogle Scholar
  41. 41.
    M.X. Guo, B.C.Y. Lu, J. Chem. Phys. 106, 3688 (1997)ADSCrossRefGoogle Scholar
  42. 42.
    F. Siperstein, A.L. Myers, O. Talu, Mol. Phys. 100, 2025 (2002)ADSCrossRefGoogle Scholar
  43. 43.
    K.C. Daoulas, V.A. Harmandaris, V.G. Mavrantzas, Macromolecules 38, 5780 (2005)ADSCrossRefGoogle Scholar
  44. 44.
    J. Janecek, J. Phys. Chem. B. 110, 6264 (2006)CrossRefGoogle Scholar
  45. 45.
    J.M. Miguez, M.M. Pineiro, F.J. Blas, J. Chem. Phys. 138, 034707 (2013)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.Univ. Lyon, ENS de Lyon, Univ Claude Bernard Lyon 1, CNRS, Laboratoire de Physique and Centre Blaise PascalLyonFrance

Personalised recommendations