Abstract
In molecular dynamics the highly oscillatory vibrations in the chemical bonds are often replaced by holonomic constraints that freeze the bond length/angle to its equilibrium value. In some cases this approach can be justified if the force constants of the bond vibrations are sufficiently large. However, for moderate values of the force constant, the constrained system might lead to a dynamical behavior that is too “rigid” compared to the flexible model. To compensate for this effect, the concept of soft constraints was introduced in [7,12,13]. However, its implementation is rather expensive. In this paper, we suggest an alternative approach that modifies the force field instead of the constraint functions. This leads to a more efficient method that avoids the resonance induced instabilities of multiple-time-stepping [5] and the above described effect of standard constrained dynamics.
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References
M.P. Allen and D.J. Tildesley, Computer Simulations of Liquids (Clarendon Press, Oxford, 1987).
G. Benettin, L. Galgani and A. Giorgilli, Realization of holonomic constraints and freezing of high frequency degrees of freedom in the light of classical perturbation theory. Part II, Commun. Math. Phys. 113 (1989) 557-601.
G. Benettin and A. Giorgilli, On the Hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms, J. Statist. Phys. 74 (1994) 1117- 1143.
J.J. Biesiadecki and R.D. Skeel, Dangers of multiple-time-step methods, J. Comput. Phys. 109 (1993) 318-328.
T. Bishop, R.D. Skeel and K. Schulten, Difficulties with multiple time-stepping and the fast multipole algorithm in molecular dynamics, J. Comput. Chem. 18 (1997) 1785-1791.
B.R. Brooks, R.E. Bruccoleri, B.D. Olafson, D.J. States, S. Swaminathan and M. Karplus, CHARMM: A program for macromolecular energy, minimization, and dynamics calculations, J. Comput. Chem. 4 (1983) 187-217.
B.R. Brooks, J. Zhou and S. Reich, Elastic molecular dynamics with flexible constraints (in preparation, 1998).
H. Grubmüller, H. Heller, A. Windemuth and K. Schulten, Generalized Verlet algorithm for efficient molecular dynamics simulations with long-range interactions, Molecular Simulations 6 (1991) 121-142.
E. Helfand, Flexible vs. rigid constraints in statistical mechanics, J. Chem. Phys. 71 (1979) 5000-5007.
B. Leimkuhler and R.D. Skeel, Symplectic numerical integrators in constrained Hamiltonian systems, J. Comput. Phys. 112 (1994) 117-125.
J.R. Marsden and T. Ratiu, An Introduction to Mechanics and Symmetry (Springer, New York, 1994).
S. Reich, Smoothed dynamics of highly oscillatory Hamiltonian systems, Physica D 89 (1995) 28-42.
S. Reich, Torsion dynamics of molecular systems, Phys. Rev. E 53 (1996) 4176-4181.
S. Reich, Dynamical systems, numerical integration, and exponentially small estimates, Habilitationsschrift, FU Berlin (1998).
H. Rubin and P. Ungar, Motion under a strong constraining force, Comm. Pure Appl. Math. 10 (1957) 65-87.
M. Tuckerman, B.J. Berne and G.J. Martyna, Reversible multiple time scale molecular dynamics, J. Chem. Phys. 97 (1992) 1990-2001.
L. Verlet, Computer experiments on classical fluids: I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev. 159 (1967) 1029-1039.
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Reich, S. Modified potential energy functions for constrained molecular dynamics. Numerical Algorithms 19, 213–221 (1998). https://doi.org/10.1023/A:1019198205349
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DOI: https://doi.org/10.1023/A:1019198205349