Multiscale Molecular Dynamics and the Reverse Mapping Problem

Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 9)


Multiscale techniques are becoming increasingly important for molecular simulation as a result of interest in increasingly complex problems involving events occurring over multiple time and length scales. Here, inspired by the success of the multiscale quantum mechanics/molecular mechanics (QM/MM) methods, we introduce a hybrid, adaptive resolution, multiscale molecular dynamics method that combines accurate, atomistic, modeling of key regions of the system with a coarse-grained modeling of the remainder of the system. Hybrid multiscale methods must solve the interfacial hand-shaking problem of coupling together different levels of description in different spatial regions of the system; in addition, to implement an adaptive resolution algorithm to correctly model diffusive systems, one must have a procedure in place to dynamically change the representation of a molecule, either from a finer to a coarser level or vice versa. We propose a solution to these problems through a detailed energy analysis and the use of a rotational dynamics to align molecular fragments. The algorithms we propose significantly advance the state-of-the-art and should serve to spur significant advances in our ability to model complex chemical systems.


Multiscale Adaptive resolution Coarse-graining Molecular dynamics Reverse mapping Rotational dynamics 



We are very grateful to Preston B. Moore, Peter G. Bolhuis, Michael L. Klein and Michele Parrinello for helpful discussions.


  1. 1.
    Wesolowski, T. A., Warshel, A., J. Phys. Chem. 1993, 97, 8050.CrossRefGoogle Scholar
  2. 2.
    Jacob, C., Neugebauer, J., Visscher, L., J. Comput. Chem. 2008, 29, 1011.CrossRefGoogle Scholar
  3. 3.
    Cramer, C. J., Truhlar, D. G., Chem. Rev. 1999, 99, 2161.CrossRefGoogle Scholar
  4. 4.
    Tomasi, J., Mennucci, B., Cammi, R., Chem. Rev. 2005, 105, 2999.CrossRefGoogle Scholar
  5. 5.
    Tomasi, J., Persico, M., Chem. Rev. 1994, 94, 2027.CrossRefGoogle Scholar
  6. 6.
    Gao, J., in Reviews in Computational Chemistry, edited by Lipkowitz, K., Boyd, D., Volume 7, pp. 119–185, 119, VCH, New York, 1992.Google Scholar
  7. 7.
    Ensing, B., Nielsen, S. O., Moore, P. B., Klein, M. L., Parrinello, M., J. Chem. Theory Comput. 2007, 3, 1100.CrossRefGoogle Scholar
  8. 8.
    Praprotnik, M., Site, L. D., Kremer, K., J. Chem. Phys. 2005, 123, 224106.CrossRefGoogle Scholar
  9. 9.
    Heyden, A., Truhlar, D. G., J. Chem. Theory Comput. 2008, 4, 217.CrossRefGoogle Scholar
  10. 10.
    Shi, Q., Izvekov, S., Voth, G. A., J. Phys. Chem. B 2006, 110, 15045.CrossRefGoogle Scholar
  11. 11.
    Neri, M., Anselmi, C., Cascella, M., Maritan, A., Carloni, P., Phys. Rev. Lett. 2005, 95, 218102.CrossRefGoogle Scholar
  12. 12.
    Villa, E., Balaeff, A., Mahadevan, L., Schulten, K., Multiscale Model. Simul. 2004, 2, 527.CrossRefGoogle Scholar
  13. 13.
    Dupuy, L. M., Tadmor, E. B., Miller, R., Phillips, R., Phys. Rev. Lett. 2005, 95, 060202.CrossRefGoogle Scholar
  14. 14.
    Diestler, D. J., Zhou, H., Feng, R., Zeng, X. C., J. Chem. Phys. 2006, 125, 064705.CrossRefGoogle Scholar
  15. 15.
    Rudd, R. E., Broughton, J. Q., Phys. Stat. Sol. B 2000, 217, 251.CrossRefGoogle Scholar
  16. 16.
    Izvekov, S., Voth, G. A., J. Phys. Chem. B 2005, 109, 2469.CrossRefGoogle Scholar
  17. 17.
    Liu, P., Izvekov, S., Voth, G. A., J. Phys. Chem. B 2007, 111, 11566.CrossRefGoogle Scholar
  18. 18.
    Lyman, E., Ytreberg, F., Zuckerman, D., Phys. Rev. Lett. 2006, 96, 028105.CrossRefGoogle Scholar
  19. 19.
    Lyman, E., Zuckerman, D. M., J. Chem. Theory Comput. 2006, 2, 656.CrossRefGoogle Scholar
  20. 20.
    Christen, M., van Gunsteren, W., J. Chem. Phys. 2006, 124, 154106.CrossRefGoogle Scholar
  21. 21.
    Liu, P., Voth, G. A., J. Chem. Phys. 2007, 126, 045106.CrossRefGoogle Scholar
  22. 22.
    Csányi, G., Albaret, T., Payne, M. C., DeVita, A., Phys. Rev. Lett. 2004, 93, 175503.CrossRefGoogle Scholar
  23. 23.
    Hoogerbrugge, P. J., Koelman, J. M. V. A., Europhys. Lett. 1992, 19, 155.CrossRefGoogle Scholar
  24. 24.
    Smith, D. E., Harris, C. B., J. Chem. Phys. 1990, 92, 1304.CrossRefGoogle Scholar
  25. 25.
    Turq, P., Lantelme, F., Friedman, H. L., J. Chem. Phys. 1977, 66, 3039.CrossRefGoogle Scholar
  26. 26.
    Laio, A., Parrinello, M., Proc. Natl. Acad. Sci. USA 2002, 99, 12562.CrossRefGoogle Scholar
  27. 27.
    Ensing, B., Vivo, M. D., Liu, Z. W., Moore, P. B., Klein, M. L., Acc. Chem. Res. 2006, 39, 73.CrossRefGoogle Scholar
  28. 28.
    Nielsen, S. O., Lopez, C. F., Srinivas, G., Klein, M. L., J. Phys. Condens. Mater. 2004, 16, R481.CrossRefGoogle Scholar
  29. 29.
    Henderson, R. L., Phys. Lett. A 1974, 49A, 197.CrossRefGoogle Scholar
  30. 30.
    Lyubartsev, A. P., Laaksonen, A., Phys. Rev. E 1995, 52, 3730.CrossRefGoogle Scholar
  31. 31.
    Soper, A. K., Chem. Phys. 1996, 202, 295.CrossRefGoogle Scholar
  32. 32.
    Akkermans, R., Briels, W., J. Chem . Phys. 2001, 114, 1020.CrossRefGoogle Scholar
  33. 33.
    Jain, S., Garde, S., Kumar, S. K., Ind. Eng. Chem. Res. 2006, 45, 5614.CrossRefGoogle Scholar
  34. 34.
    Njo, S. L., van Gunsteren, W. F., Mueller-Plathe, F., J. Chem. Phys. 1995, 102, 6199.CrossRefGoogle Scholar
  35. 35.
    Ercolessi, F., Adams, J. B., Europhys. Lett. 1994, 26, 583.CrossRefGoogle Scholar
  36. 36.
    Izvekov, S., Parrinello, M., Burnham, C. J., Voth, G. A., J. Chem. Phys. 2004, 120, 10896.CrossRefGoogle Scholar
  37. 37.
    Maurer, P., Laio, A., Hugosson, H. W., Colombo, M. C., Rothlisberger, U., J. Chem. Theory Comput. 2007, 3, 628.CrossRefGoogle Scholar
  38. 38.
    de Pablo, J. J., Curtin, W. A., MRS Bull. 2007, 32, 905.Google Scholar
  39. 39.
    Nosé, S. J., J. Chem. Phys. 1984, 81, 511.CrossRefGoogle Scholar
  40. 40.
    Hoover, W. G., Phys. Rev. A 1985, 31, 1695.CrossRefGoogle Scholar
  41. 41.
    Parrinello, M., Rahman, A., Phys. Rev. Lett. 1980, 45, 1196.CrossRefGoogle Scholar
  42. 42.
    Bussi, G., Donadio, D., Parrinello, M., J. Chem. Phys. 2007, 126, 014101.CrossRefGoogle Scholar
  43. 43.
    MacKerel Jr., A., Brooks III, C., Nilsson, L., Roux, B., Won, Y., Karplus, M., CHARMM: The energy function and its parameterization with an overview of the program, in The Encyclopedia of Computational Chemistry, edited by v. R. Schleyer et al., P., Volume 1, pp. 271–277, John Wiley & Sons: Chichester, 1998.Google Scholar
  44. 44.
    Jorgensen, W., Madura, J., Swenson, C., J. Am. Chem. Soc. 1984, 106, 6638.CrossRefGoogle Scholar
  45. 45.
    Abrams, C. F., J. Chem. Phys. 2005, 123, 234101.CrossRefGoogle Scholar
  46. 46.
    Praprotnik, M., Kremer, K., Site, L. D., J. Phys. A Math. Theor. 2007, 40, F281.CrossRefGoogle Scholar
  47. 47.
    Praprotnik, M., Kremer, K., Site, L. D., Phys. Rev. E 2007, 75, 017701.CrossRefGoogle Scholar
  48. 48.
    Heyden, A., Lin, H., Truhlar, D. G., J. Phys. Chem. B 2007, 111, 2231.CrossRefGoogle Scholar
  49. 49.
    Taylor, C. J., Kriegman, D. J., IEEE Trans. Rob. Autom. 1998, 14, 417.CrossRefGoogle Scholar
  50. 50.
    Press, W. H., Teukolsky, S. A., Vetterling, W. T., Flannery, B. P., Numerical Recipes, Cambridge University Press: New York, 1992.Google Scholar
  51. 51.
    Nielsen, S. O., Ensing, B., Moore, P. B., Klein, M. L., Coarse grained to atomistic mapping algorithm: a tool for multiscale simulations, in Multiscale simulation methods for nanomaterials, edited by Ross, R., Mohanty, S., pp. 73–88, John Wiley and Sons, Inc.; Hoboken, NJ, 2008.Google Scholar
  52. 52.
    Krysl, P., Endres, L., Int. J. Numer. Methods Eng. 2005, 62, 2154.CrossRefGoogle Scholar
  53. 53.
    Nielsen, S. O., Lopez, C. F., Srinivas, G., Klein, M. L., J. Chem. Phys. 2003, 119, 7043.CrossRefGoogle Scholar
  54. 54.
    Praprotnik, M., Matysiak, S., Site, L. D., Kremer, K., Clementi, C., J. Phys. Condens. Mater. 2007, 19, 292201.CrossRefGoogle Scholar
  55. 55.
    Matysiak, S., Clementi, C., Praprotnik, M., Kremer, K., Site, L. D., J. Chem. Phys. 2008, 128, 024503.CrossRefGoogle Scholar
  56. 56.
    Praprotnik, M., Site, L. D., Kremer, K., Phys. Rev. E 2006, 73, 066701.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Van’t Hoff Institute for Molecular SciencesUniversity of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of ChemistryUniversity of Texas at DallasRichardsonUSA

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