Skip to main content
SpringerLink
Log in

Molecular Dynamics in Systems with Multiple Time Scales: Reference System Propagator Algorithms

  • Conference paper
Book cover Computational Molecular Dynamics: Challenges, Methods, Ideas

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 4))

Abstract

Systems with multiple time scales, and with forces which can be subdivided into long and short range components are frequently encountered in computational chemistry. In recent years, new, powerful and efficient methods have been developed to reduce the computational overhead in treating these problems in molecular dynamics simulations. Numerical reversible integrators for dealing with these problems called r-RESPA (Reversible Reference System Propagator Algorithms) are reviewed in this article. r-RESPA leads to considerable speedups in generating molecular dynamics trajectories with no loss of accuracy. When combined with the Hybrid Monte Carlo (HMC) method and used in the Jump-Walking and the Smart-Walking algorithms, r-RESPA is very useful for the enhanced sampling of rough energy landscapes in biomolecules.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B. J. Alder and T. E. Wainwright. J. Chem. Phys., 27: 1208–9, 1957.

    Article  Google Scholar 

  2. B. J. Alder and T. E. Wainwright. J. Chem. Phys., 31: 459–56, 1959.

    Article  MathSciNet  Google Scholar 

  3. A. Rahman. Phys. Rev., 136A: 405–11, 1964.

    Article  Google Scholar 

  4. G. D. Harp and B. J. Berne. J. Chem. Phys., 49: 1249–54, 1968.

    Article  Google Scholar 

  5. G. D. Harp and B. J. Berne. Phys. Rev., A2: 975–96, 1970.

    Google Scholar 

  6. A. Rahman and F. H. Stillinger. J. Chem. Phys., 55: 3336–59, 1971.

    Article  Google Scholar 

  7. M. P. Allen and D. J. Tildesley. Computer Simulation of Liquids. Oxford University Press, Oxford, 1987.

    MATH  Google Scholar 

  8. J. A. McCammon and S. C. Harvey. Dynamics of Proteins and Nucleic Acids. Cambridge University Press, Cambridge, 1987.

    Book  Google Scholar 

  9. J. M. Haille. Molecular Dynamics Simulation: Elementary Methods. John Wiley & Sons, USA, 1992.

    Google Scholar 

  10. D. Frenkel and B. Smit. Understanding Molecular Simulation. Academic Press, 1996.

    Google Scholar 

  11. J. P. Ryckaert and G. Ciccotti and H. J. C. Berendsen. J. Comp. Phys., 23: 327, 1977.

    Article  Google Scholar 

  12. S. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth. Phys. Rev. Lett. B, 195: 216–222, 1987.

    Google Scholar 

  13. M. E. Tuckerman, G. J. Martyna, and B. J. Berne. J. Chem. Phys., 93: 1287–1291, (1990).

    Article  Google Scholar 

  14. M. Tuckerman, B. J. Berne, and A. Rossi. J. Chem. Phys., 94: 1465–1469, (1991).

    Article  Google Scholar 

  15. B. J. Berne M. Tuckerman and G. Martyna. J. Chem. Phys., 94: 6811–6815, (1991).

    Article  Google Scholar 

  16. M. Tuckerman and B. J. Berne. J. Chem. Phys., 95: 8362–8364, (1991).

    Article  Google Scholar 

  17. M. E. Tuckerman, B. J. Berne, and G.J. Martyna. J. Chem. Phys., 97: 1990–2001, (1992).

    Article  Google Scholar 

  18. S. J. Stuart, R. Zhou, and B. J. Berne. J. Chem. Phys., 105: 1426–1436, (1996).

    Article  Google Scholar 

  19. M.E. Tuckerman and M. Parrinello. J. Chem. Phys., 101: 1302–1315, (1994).

    Article  Google Scholar 

  20. M. E. Tuckerman and G. J. Martyna and B. J. Berne. J. Chem. Phys., 93: 1287, 1990.

    Article  Google Scholar 

  21. J. Hutter, M.E. Tuckerman, and M. Parrinello. J. Chem. Phys., (1995).

    Google Scholar 

  22. D. Humphreys, R. A. Friesner, and B.J. Berne. J. Phys. Chem., 98: 6885–6892, (1994).

    Article  Google Scholar 

  23. D. Humphreys, R. A. Friesner, and B. J. Berne. J. Phys. Chem., 99: 10674–10685, (1995).

    Article  Google Scholar 

  24. R. Zhou and B.J. Berne. J. Chem. Phys., 103: 9444–9458, (1995).

    Article  Google Scholar 

  25. M. Watanabe and M. Karplus. J. Chem. Phys., 99: 8063–8074, 1993.

    Article  Google Scholar 

  26. F. Figueirido, R. Zhou, B. J. Berne, and R. M. Levy. J. Chem. Phys., 106: 9835–9849, (1997).

    Article  Google Scholar 

  27. L. Verlet. Phys. Rev., 159: 98–103, 1967.

    Article  Google Scholar 

  28. T. A. Andrea, W. C. Swope, and H. C. Andersen. J. Chem. Phys., 79: 4576–4584, 1983.

    Article  Google Scholar 

  29. H. Goldstein. Classical Mechanics. Addison Wesley Publishing Company, Inc., 1980.

    Google Scholar 

  30. Haruo Yoshida. Phys. Lett A., 150: 262–268, (1990).

    Article  MathSciNet  Google Scholar 

  31. J. J. Biesiadecki and R. D. Skeel. J. Comp. Phys., 109: 318–328, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  32. S. K. Gray, D. W. Noid, and B. G. Sumpter. J. Chem. Phys., 101: 4062–4072, 1994.

    Article  Google Scholar 

  33. S. Auerbach and A. Friedman. J. Comp. Phys., 93: 189, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  34. M.E. Tuckerman and B. J. Berne. J. Chem. Phys., 98: 7301–7318, (1993).

    Article  Google Scholar 

  35. P. Procacci and B.J. Berne. J. Chem. Phys., 101: 2421, (1994).

    Article  Google Scholar 

  36. H. Grubmuller, H. Heller, A. Windemuth, and K. Schulten. Molecular Simulation, 6: 121–142, (1991).

    Article  Google Scholar 

  37. G.J. Martyna and M.E. Tuckerman. J. Chem. Phys., 102: 8071–8077, (1996).

    Article  Google Scholar 

  38. F. Mohamadi and N. G. J. Richards and W. C. Guida and R. Liskamp and M. Lipton and C. Caufield and G. Chang and T. Hendrickson and W. C. Still. J. Comp. Chem., 11: 440, 1990.

    Article  Google Scholar 

  39. S. J. Weiner and P. A. Kollman and D. T. Nguyen and D. A. Case. J. Comp. Chem., 7: 230, 1986.

    Article  Google Scholar 

  40. W. L. Jorgensen and J. Tirado-Rives. J. Am. Chem. Soc, 110: 1657, 1988.

    Article  Google Scholar 

  41. B. R. Brooks and R. E. Bruccoeri and B. D. Olafson and D. J. States and S. Swaminathan and M. Karplus. J. Comp. Chem., 4: 187–217, 1983.

    Article  Google Scholar 

  42. P. Procacci and M. Marchi. J. Chem. Phys., 104: 3003–3012, 1996.

    Article  Google Scholar 

  43. L. Greengard. The Rapid Evaluation of Potential Fields in Particle Systems. The MIT Press, Cambridge, Massachusetts, 1988.

    MATH  Google Scholar 

  44. L. Greengard and V. Rokhlin. J. Comp. Phys., 73: 325, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  45. C. A. White and M. Head-Gordon. J. Chem. Phys., 101: 6593–6605, 1994.

    Article  Google Scholar 

  46. J. Shimada and H. Kaneko and T. Takada. J. Comp. Chem., 15: 28, 1994.

    Article  Google Scholar 

  47. H.-Q. Ding and N. Karasawa and W. A. Goddard III. J. Chem. Phys., 97: 4309, 1992.

    Article  Google Scholar 

  48. M. Saito. Molecular Simulations, 8: 321–333, 1992.

    Article  Google Scholar 

  49. C. Niedermeier and P. Tavan. Molecular Simulation., 17: 57–66, (1996).

    Article  Google Scholar 

  50. K. E. Schmidt and M. A. Lee. J. Stat. Phys., 63: 1223–1235, 1991.

    Article  Google Scholar 

  51. T. Darden, D. M. York, and L. G. Pedersen. Particle mesh Ewald: An Nlog(N) method for Ewald sums in large systems. J. Chem. Phys., 98: 10089–10092, 1993.

    Article  Google Scholar 

  52. H. G. Petersen. J. Chem. Phys., 103: 3668–3679, 1995.

    Article  Google Scholar 

  53. U. Essman, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen. J. Chem. Phys., 103: 8577–8593, 1995.

    Article  Google Scholar 

  54. R. W. Hockney and J. W. Eastwood. Computer Simulation Using Particles. Adam Hilger, Bristol-New York, 1989.

    Google Scholar 

  55. P. Procacci and T. Darden and M. Marchi. J. Phys. Chem., 100: 10464–10468, 1996.

    Article  Google Scholar 

  56. B. J. Berne and John E. Straub. Current Topics in Structural Biology, 7 No 2: 181–189, (1997).

    Article  Google Scholar 

  57. D. D. Prantz, D. L. Freeman, and J. D. Doll. J. Chem. Phys., 93: 2769–2784, 1990.

    Article  Google Scholar 

  58. R. Zhou and B. J. Berne. J. Chem. Phys., 107: 9185–9196, (1997).

    Article  Google Scholar 

  59. Z. Liu and B. J. Berne. J. Chem. Phys., 99: 6071, (1993).

    Article  Google Scholar 

  60. U. H. E. Hansmann, Y. Okamoto, and F. Eisenmenger. Chem. Phys. Lett., 259: 321–330, 1996.

    Article  Google Scholar 

  61. R. M. Neal. J. Comp. Phys., 111: 194–203, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  62. S. Gupta, A. Irback, F. Karsch, and B. Petersson. Phys. Lett. B, 242: 437–443, 1990.

    Article  Google Scholar 

  63. P. B. Markenzie. Phys. Lett. B, 226: 369–371, 1989.

    Article  Google Scholar 

  64. M. Tuckerman, B. J. Berne, G. Martyna, and M. Klein. J. Chem. Phys., 99: 2796–2784, (1993).

    Article  Google Scholar 

  65. S. Nosé. J. Chem. Phys., 81: 511–519, 1984.

    Article  Google Scholar 

  66. G.J. Martyna, M.E. Tuckerman, D.J. Tobias, and M.L. Klein. Mol Phys., 87: 1117–1157, (1996).

    Article  Google Scholar 

  67. D. L. Freeman, D. D. Frantz, and J. D. Doll. J. Chem. Phys., 97: 5713, 1992.

    Article  Google Scholar 

  68. A. Matro, D. L. Freeman, and R. Q. Topper. J. Chem. Phys., 104: 8690, 1996.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Chemistry, Columbia University, New York, NY, 10027, USA

    Bruce J. Berne

Authors
  1. Bruce J. Berne
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Konrad-Zuse-Zentrum Berlin (ZIB), Takustrasse 7, D-14195, Berlin-Dahlem, Germany

    Peter Deuflhard

  2. Department of Biochemistry and Biophysics, University of North Carolina, Chapel Hill, NC, 27599-7260, USA

    Jan Hermans

  3. Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, KS, 66045, USA

    Benedict Leimkuhler

  4. Laboratorium für Physikalische Chemie ETH Zentrum, CH-8092, Zürich, Switzerland

    Alan E. Mark

  5. Department of Mathematics and Statistics, University of Surrey, Guildford, Surrey, GU2 5XH, UK

    Sebastian Reich

  6. Department of Computer Science, University of Illinois, 1304 West Springfield Avenue, Urbana, IL, 61801-6631, USA

    Robert D. Skeel

Rights and permissions

Reprints and permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Berne, B.J. (1999). Molecular Dynamics in Systems with Multiple Time Scales: Reference System Propagator Algorithms. In: Deuflhard, P., Hermans, J., Leimkuhler, B., Mark, A.E., Reich, S., Skeel, R.D. (eds) Computational Molecular Dynamics: Challenges, Methods, Ideas. Lecture Notes in Computational Science and Engineering, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58360-5_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-58360-5_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63242-9

  • Online ISBN: 978-3-642-58360-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation