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Long Time Step MD Simulations Using Split Integration Symplectic Method

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

Abstract

The design and analysis of an explicit Split Integration Symplectic Method (SISM) for molecular dynamics (MD) simulations is described. SISM uses an analytical treatment of high frequency motions within a second order generalized leapfrog scheme. SISM is up to an order of magnitude faster than the commonly used leapfrog-Verlet (LFV) algorithm which is of the same order and complexity as SISM. The main restriction on time step in the general MD simulations, which stems from the high-frequency motion is, to a large extent, overcome in this approach. The simulation results for selected examples show that SISM posses long term stability and the ability to use long time steps. This should significantly extend the scope of the presently used algorithms and thus contribute to the general applicability of MD algorithms.

This work was supported by the Ministry of Science and Technology of Slovenia under grant No. J1-7346-104-97.

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References

  1. Brooks, B. R., Janežič, D., Karplus, M.: Harmonic Analysis of Large Systems: I. Methodology. J. Comput. Chem. 16 (1995) 1522–1542

    Article  Google Scholar 

  2. Janežič, D., Brooks, B. R.: Harmonic Analysis of Large Systems: II. Comparison of Different Protein Models. J. Comput. Chem. 16 (1995) 1543–1553

    Article  Google Scholar 

  3. Janežič, D., Venable, R. M., Brooks, B. R.: Harmonic Analysis of Large Systems. III. Comparison with Molecular Dynamics. J. Comput. Chem. 16 (1995) 1554–1566

    Article  Google Scholar 

  4. Allen, M. P., Tildesley, D. J.: Computer Simulation of Liquids. Clarendon Press: Oxford (1987)

    MATH  Google Scholar 

  5. Sanz-Serna, J. M. Symplectic Integrators for Hamiltonian Problems: An Overview. Acta Numerica (1991) 243–286

    Google Scholar 

  6. Sanz-Serna, J. M., Calvo, M. P.: Numerical Hamiltonian Problems. Chapman and Hall: London (1994)

    MATH  Google Scholar 

  7. Janežič, D., Orel, B.: Implicit Runge-Kutta Method for Molecular Dynamics Integration. J. Chem. Inf. Comput. Sci. 33 (1993) 252–257

    Article  Google Scholar 

  8. Janežič, D., Orel, B.: Improvement of Methods for Molecular Dynamics Integration. Int. J. Quant. Chem. 51 (1994) 407–415

    Article  Google Scholar 

  9. Trobec, R.; Jerebic, L; D.Janežič, D. Parallel Algorithm for Molecular Dynamics Integration. Parallel Computing 19 (1993) 1029–1039

    Article  Google Scholar 

  10. Janezič, D.; Trobec, R. Parallelization of an Implicit Runge-Kutta Method for Molecular Dynamics Integration. J. Chem. Inf. Comput. Sci. 34 (1994) 641–646

    Article  Google Scholar 

  11. R. Trobec and D. Janezic; Comparison of Parallel Verlet and Implicit Runge-Kutta Method for Molecular Dynamics Integration. J. Chem. Inf. Comp. Sci., 35 (1995) 100–105

    Article  Google Scholar 

  12. Janežič, D., Merzel, F.: An Efficient Symplectic Integration Algorithm for Molecular Dynamics Simulations. J. Chem. Inf. Comput. Sci. 35 (1995) 321–326

    Article  Google Scholar 

  13. Verlet, L.: Computer “Experiments ” on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules. Physical Review 159 (1967) 98–103

    Article  Google Scholar 

  14. Janežič, D., Merzel, F.: Split Integration Symplectic Method for Molecular Dynamics Integration. J. Chem. Inf. Comput. Sci. 37 (1997) 1048–1054

    Article  Google Scholar 

  15. McLachlan, R. I.: On the Numerical Integration of Ordinary Differential Equations by Symplectic Composition Methods. SIAM J. Sci. Comput. 16 (1995) 151–168

    Article  MathSciNet  MATH  Google Scholar 

  16. Wisdom, J.; Holman, M. Symplectic Maps for the N-body Problem. Astron. J. 102 (1991) 1528–1538

    Article  Google Scholar 

  17. Wisdom, J. The Origin of the Kirkwood Gaps: A Mapping for Asteroidal Motion Near the 3/1 Commensurability. Astron. J. 87 (1982) 577–593

    Article  MathSciNet  Google Scholar 

  18. Tuckerman, M., Martyna, G. J., Berne, J.: Reversible Multiple Time Scale Molecular Dynamics. J. Chem. Phys. 97 (1992) 1990–2001

    Article  Google Scholar 

  19. Tuckerman, M., Berne, J.: Vibrational Relaxation in Simple Fluids: Comparison of Theory and Simulation. J. Chem. Phys. 98 (1993) 7301–7318

    Article  Google Scholar 

  20. Humphreys, D. D., Friesner, R. A., Berne, B. J.: A Multiple-Time Step Molecular Dynamics Algorithm for Macromolecules. J. Chem. Phys. 98 (1994) 6885–6892

    Article  Google Scholar 

  21. Tuckerman, M., Martyna, G. J., Berne, J.: Molecular Dynamics Algorithm for Condensed Systems with Multiple Time Scales. J. Chem. Phys. 93 (1990) 1287–1291

    Article  Google Scholar 

  22. Watanabe, M., Karplus, M.: Dynamics of Molecules with Internal Degrees of Freedom by Multiple Time-Step Methods. J. Chem. Phys. 99 (1995) 8063–8074

    Article  Google Scholar 

  23. Figueirido, F., Levy, R. M., Zhou, R., Berne, B. J.: Large Scale Simulation of Macromolecules in Solution: Combining the Periodic Fast Multiple Method with Multiple Time Step Integrators. J. Chem. Phys. 106 (1997) 9835–9849

    Article  Google Scholar 

  24. Derreumaux, P., Zhang, G., Schlick, T, Brooks, B.R.: A Truncated Newton Minimizer Adapted for CHARMM and Biomolecular Applications. J. Comp. Chem. 15 (1994) 532–555

    Article  Google Scholar 

  25. Arnold, V. I.: Mathematical Methods of Classical Mechanics. Springer: New York (1978)

    MATH  Google Scholar 

  26. Goldstein, H.: Classical Mechanics. Addison-Wesley: Reading (1965)

    Google Scholar 

  27. Forest, E., Ruth, R. D.: Fourth-Order Symplectic Integration. Phys. D 43 (1990) 105–117

    Article  MathSciNet  MATH  Google Scholar 

  28. Yoshida, H.: Recent Progress in the Theory and Application of Symplectic Integrators. Celestial Mechanics and Dynamical Astronomy 56 (1993) 27–43

    Article  MathSciNet  MATH  Google Scholar 

  29. Trobec, R., Merzel, F., Janežič, D.: On the Complexity of Parallel Symplectic Molecular Dynamics Algorithms. J. Chem. Inf. Comput. Sci. 37 (1997) 1055–1062

    Article  Google Scholar 

  30. Janežič, D., Merzel, F.: An Efficient Split Integration Symplectic Method for Molecular Dynamics Simulations of Complex Systems. In: Proceedings of the 15th IMACS World Congress on Scientific Computation, Modelling and Applied Mathematics, Ed. Sydow, A., Wissenschaft und Technik Verlag, Berlin 1 (1997) 493–498

    Google Scholar 

  31. Jorgensen, W.L., Chandrasekar, J., Madura, J.D., Impey, W., Klein, M.L.: J. Chem. Phys. 79 (1983) 926

    Article  Google Scholar 

  32. Grubmüller, EL, Heller, H., Windemuth, A., Schulten, K.: Generalized Verlet Algorithm for Efficient Molecular Dynamics Simulations with Long-range Interactions. Molecular Simulation 6 (1991) 121–142

    Article  Google Scholar 

  33. Garcia-Archilla, B., Sanz-Serna, J.M., Skeel, R.D.: Long-Time-Steps Methods for Oscillatory Differential Equations. SIAM J. Sci. Comput. (to appear)

    Google Scholar 

  34. Leimkuhler, B. J., Reich, S., Skeel, R. D.: Integration Methods for Molecular Dynamics. In: IMA Volumes in Mathematics and its Applications. Eds. Mesirov, J., Schulten, K., Springer-Verlag, Berlin 82 (1995)

    Google Scholar 

  35. Wisdom, J., Holman, M.: Symplectic Maps for the n-Body Problem: Stability Analysis. Astron. J. 104 (1992) 2022–2029

    Article  Google Scholar 

  36. Schlick, T., Barth, E., Mandziuk M.: Biomolecular Dynamics at Long Timesteps: Bridging the Timescale Gap Between Simulation and Experimentation. Ann. Rev. Biophy. Biomol. Struct. 26 (1997) 181–222

    Article  Google Scholar 

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© 1999 Springer-Verlag Berlin Heidelberg

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Janežič, D., Merzel, F. (1999). Long Time Step MD Simulations Using Split Integration Symplectic Method. 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_18

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  • DOI: https://doi.org/10.1007/978-3-642-58360-5_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63242-9

  • Online ISBN: 978-3-642-58360-5

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