Concurrent coupling of realistic and ideal models of liquids and solids in Hamiltonian adaptive resolution simulations

  • Maziar Heidari
  • Robinson Cortes-Huerto
  • Kurt Kremer
  • Raffaello PotestioEmail author
Open Access
Regular Article
Part of the following topical collections:
  1. Advances in Computational Methods for Soft Matter Systems


To understand the properties of a complex system it is often illuminating to perform a comparison with a simpler, even idealised one. A prototypical application of this approach is the calculation of free energies and chemical potentials in liquids, which can be decomposed in the sum of ideal and excess contributions. In the same spirit, in computer simulations it is possible to extract useful information on a given system making use of setups where two models, an accurate one and a simpler one, are concurrently employed and directly coupled. Here, we tackle the issue of coupling atomistic or, more in general, interacting models of a system with the corresponding idealised representations: for a liquid, this is the ideal gas, i.e. a collection of non-interacting particles; for a solid, we employ the ideal Einstein crystal, a construct in which particles are decoupled from one another and restrained by a harmonic, exactly integrable potential. We describe in detail the practical and technical aspects of these simulations, and suggest that the concurrent usage and coupling of realistic and ideal models represents a promising strategy to investigate liquids and solids in silico.

Graphical abstract


Topical issue: Advances in Computational Methods for Soft Matter Systems 



Open Access funding provided by Max Planck Society.


  1. 1.
    R.P. Feynman, Int. J. Theor. Phys. 21, 467 (1982)CrossRefGoogle Scholar
  2. 2.
    D. Frenkel, J.-P. Hansen, Phys. World 9, 35 (1996)CrossRefGoogle Scholar
  3. 3.
    W.F. van Gunsteren, A.E. Mark, J. Chem. Phys. 108, 6109 (1998)CrossRefADSGoogle Scholar
  4. 4.
    W.G. Hoover, 50 Years of Computer Simulation -- a Personal View, arXiv:0812.2086v2 (2008)Google Scholar
  5. 5.
    M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids (Clarendon Press, Oxford, 1987)Google Scholar
  6. 6.
    D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to Applications (Elsevier, 2001)Google Scholar
  7. 7.
    M. Praprotnik, L. Delle Site, K. Kremer, Annu. Rev. Phys. Chem. 59, 545 (2008)CrossRefADSGoogle Scholar
  8. 8.
    K. Kremer, Soft and fragile matter non equilibrium dynamics, metastability and flow, in SUSSP Proceedings Vol. 53 (IOP Publishing Ltd., 2000) pp. 145--184Google Scholar
  9. 9.
    A. Mulero (Editor), Theory and Simulation of Hard-Sphere Fluids and Related Systems (Springer, Berlin, Heidelberg, 2008)Google Scholar
  10. 10.
    K. Kremer, F. Müller-Plathe, MRS Bull. 26, 205 (2001)CrossRefGoogle Scholar
  11. 11.
    R.E. Caflisch, G. Ceder, K. Kremer, T. Pollock, M. Scheffler, E.G. Wang (Editors), Focus on Novel Materials Discovery, New J. Phys. (IOP, 2013 and 2014)Google Scholar
  12. 12.
    C. Micheletti, P. Carloni, A. Maritan, Proteins 55, 635 (2004)CrossRefGoogle Scholar
  13. 13.
    W.G. Noid, J. Chem. Phys. 139, 090901 (2013)CrossRefADSGoogle Scholar
  14. 14.
    F. Pontiggia, A. Zen, C. Micheletti, Biophys. J. 95, 5901 (2008)CrossRefADSGoogle Scholar
  15. 15.
    M. Karplus, J. McCammon, Nature 277, 578 (1979)CrossRefADSGoogle Scholar
  16. 16.
    M. Karplus, Acc. Chem. Res. 35, 321 (2002)CrossRefGoogle Scholar
  17. 17.
    A. Pérez, F.J. Luque, M. Orozco, Acc. Chem. Res. 45, 196 (2012)CrossRefGoogle Scholar
  18. 18.
    P. Ballone, Entropy 16, 322 (2014)CrossRefADSGoogle Scholar
  19. 19.
    J. Kirkwood, J. Chem. Phys. 3, 300 (1935)CrossRefADSGoogle Scholar
  20. 20.
    P. Raiteri, A. Laio, F.L. Gervasio, C. Micheletti, M. Parrinello, J. Phys. Chem. B 110, 3533 (2006)CrossRefGoogle Scholar
  21. 21.
    M.E. Tuckerman, Statistical Mechanics: Theory and Molecular Simulation (Oxford University Press, 2010)Google Scholar
  22. 22.
    M. Praprotnik, L. Delle Site, K. Kremer, Phys. Rev. E 73, 066701 (2006)CrossRefADSGoogle Scholar
  23. 23.
    M. Praprotnik, L. Delle Site, K. Kremer, J. Chem. Phys. 126, 134902 (2007)CrossRefADSGoogle Scholar
  24. 24.
    S. Fritsch, S. Poblete, C. Junghans, G. Ciccotti, L. Delle Site, K. Kremer, Phys. Rev. Lett. 108, 170602 (2012)CrossRefADSGoogle Scholar
  25. 25.
    P. Español, R. Delgado-Buscalioni, R. Everaers, R. Potestio, D. Donadio, K. Kremer, J. Chem. Phys. 142, 064115 (2015)CrossRefADSGoogle Scholar
  26. 26.
    A.C. Fogarty, R. Potestio, K. Kremer, J. Chem. Phys. 142, 195101 (2015)CrossRefADSGoogle Scholar
  27. 27.
    A.C. Fogarty, R. Potestio, K. Kremer, Proteins 84, 1902 (2016)CrossRefGoogle Scholar
  28. 28.
    R. Fiorentini, K. Kremer, R. Potestio, A.C. Fogarty, J. Chem. Phys. 146, 244113 (2017)CrossRefADSGoogle Scholar
  29. 29.
    T. Tarenzi, V. Calandrini, R. Potestio, A. Giorgetti, P. Carloni, J. Chem. Theory Comput. 13, 5647 (2017)CrossRefGoogle Scholar
  30. 30.
    R. Potestio, S. Fritsch, P. Español, R. Delgado-Buscalioni, K. Kremer, R. Everaers, D. Donadio, Phys. Rev. Lett. 110, 108301 (2013)CrossRefADSGoogle Scholar
  31. 31.
    R. Potestio, P. Español, R. Delgado-Buscalioni, R. Everaers, K. Kremer, D. Donadio, Phys. Rev. Lett. 111, 060601 (2013)CrossRefADSGoogle Scholar
  32. 32.
    M. Heidari, K. Kremer, R. Cortes-Huerto, R. Potestio, Spatially resolved thermodynamic integration: An efficient method to compute chemical potentials of dense fluids, arXiv:1802.08045, submitted to J. Chem. Theory ComputGoogle Scholar
  33. 33.
    K. Kreis, A.C. Fogarty, K. Kremer, R. Potestio, Eur. Phys. J. ST 224, 2289 (2015)CrossRefGoogle Scholar
  34. 34.
    M. Praprotnik, L. Delle Site, K. Kremer, J. Chem. Phys. 123, 224106 (2005)CrossRefADSGoogle Scholar
  35. 35.
    J. Zavadlav, R. Podgornik, M. Melo, S. Marrink, M. Praprotnik, Eur. Phys. J. ST 225, 1595 (2016)CrossRefGoogle Scholar
  36. 36.
    K. Kreis, R. Potestio, K. Kremer, A.C. Fogarty, J. Chem. Theory Comput. 12, 4067 (2016)CrossRefGoogle Scholar
  37. 37.
    M. Heidari, R. Cortes-Huerto, D. Donadio, R. Potestio, Eur. Phys. J. ST 225, 1505 (2016)CrossRefGoogle Scholar
  38. 38.
    D. Wolf, P. Keblinski, S.R. Phillpot, J. Eggebrecht, J. Chem. Phys. 110, 8254 (1999)CrossRefADSGoogle Scholar
  39. 39.
    C.J. Fennell, J.D. Gezelter, J. Chem. Phys. 124, 234104 (2006)CrossRefADSGoogle Scholar
  40. 40.
    H.J.C. Berendsen, J.R. Grigera, T.P. Straatsma, J. Phys. Chem. 91, 6269 (1987)CrossRefGoogle Scholar
  41. 41.
    L.X. Dang, B.M. Pettitt, J. Phys. Chem. 91, 3349 (1987)CrossRefGoogle Scholar
  42. 42.
    Y. Wu, H.L. Tepper, G.A. Voth, J. Chem. Phys. 124, 024503 (2006)CrossRefADSGoogle Scholar
  43. 43.
    S. Plimpton, J. Comput. Phys. 117, 1 (1995)CrossRefADSGoogle Scholar
  44. 44.
    J.D. Halverson, T. Brandes, O. Lenz, A. Arnold, S. Bevc, V. Starchenko, K. Kremer, T. Stuehn, D. Reith, Comput. Phys. Commun. 184, 1129 (2013)CrossRefADSGoogle Scholar
  45. 45.
    K. Kreis, A.C. Fogarty, K. Kremer, R. Potestio, Eur. Phys. J. ST 224, 2289 (2015)CrossRefGoogle Scholar
  46. 46.
    J. Kohanoff, Comput. Mater. Sci. 2, 221 (1994)CrossRefGoogle Scholar
  47. 47.
    F. Pavia, W.A. Curtin, Model. Simul. Mater. Sci. Eng. 23, 055002 (2015)CrossRefADSGoogle Scholar
  48. 48.
    R. Rudd, J. Broughton, Phys. Status Solidi B: Basic Res. 217, 251 (2000)CrossRefADSGoogle Scholar
  49. 49.
    J. Rottler, S. Barsky, M.O. Robbins, Phys. Rev. Lett. 89, 148304 (2002)CrossRefADSGoogle Scholar
  50. 50.
    G. Csanyi, T. Albaret, M.C. Payne, A.D. Vita, Phys. Rev. Lett. 93, 175503 (2004)CrossRefADSGoogle Scholar
  51. 51.
    D. Jiang, E.A. Carter, Acta Mater. 52, 4801 (2004)CrossRefGoogle Scholar
  52. 52.
    G. Lu, E.B. Tadmor, E. Kaxiras, Phys. Rev. B 73, 024108 (2006)CrossRefADSGoogle Scholar
  53. 53.
    D. Frenkel, A.J.C. Ladd, J. Chem. Phys. 81, 3188 (1984)CrossRefADSGoogle Scholar
  54. 54.
    J.M. Polson, E. Trizac, S. Pronk, D. Frenkel, J. Chem. Phys. 112, 5339 (2000)CrossRefADSGoogle Scholar
  55. 55.
    M.A. van der Hoef, J. Chem. Phys. 113, 8142 (2000)CrossRefADSGoogle Scholar
  56. 56.
    C. Vega, E.G. Noya, J. Chem. Phys. 127, 154113 (2007)CrossRefADSGoogle Scholar

Copyright information

© The Author(s) 2018

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  • Maziar Heidari
    • 1
  • Robinson Cortes-Huerto
    • 1
  • Kurt Kremer
    • 1
  • Raffaello Potestio
    • 1
    • 2
    • 3
  1. 1.Max Planck Institute for Polymer ResearchMainzGermany
  2. 2.Physics DepartmentUniversity of TrentoTrentoItaly
  3. 3.INFN-TIFPATrento Institute for Fundamental Physics and ApplicationsTrentoItaly

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