In this section, several simulation techniques (or algorithms) used in MPDyn are summarized. The user who wants to know the algorithm and theory in detail should refer to the books and the original papers listed.
General theory and algorithms for molecular simulation are found in Ref. [1].
| Integrator (MD) | Reversible RESPA [2] --- Multiple time step algorithm Three time steps; Δtlong:Fkspace, Δtmiddle:Frspace, Δtshort:Fintramolecule, are used in the case of bulk systems under the periodic boundary condition. In the case of extended systems, time evolution of additional degrees of freedom (themostats or barostat) are solved with Δtlong using the higher order Trotter factorization form. |
| Integrator (DPD) | 1. Velocity Verlet-like algorithm [3] 2. Self-consistent velocity Verlet algorithm [4] 3. Lowe-Andersen algorithm [5] 4. Peters algorithm |
| Ensemble | NVE, NVT, NPT, NPnAT, NtT |
| Thermostat | Nose-Hoover [6], Nose-Hoover chain [6], massive Nose-Hoover chain [8], Velocity scaling |
| Barostat (Pressure control) |
Andersen [9], Parrinello-Rahman [10] (modularly invariant momentum form [11]) |
| Force Field | CHARMm [12], OPLS-AA [13, 14], EAM [15], BKS (exp-6 type) [16] Coarse grained models |
| LJ interaction | Cut-off & correction, switching function (CHARMM) |
| Coulombic interaction | Ewald sum [1] , Particle mesh Ewald [1, 17] |
| Energy minimization | Steepest descent |
| Holonomic constraints | SHAKE/RATTLE (ROLL:pressure control) [18,19,2], Reversible rigid-body approximation [20,21] |
| Path integral simulation | Normal-mode Hamiltonian [22] |
| Free energy calculation | Cavity insertion (particle insertion) [23], Thermodynamic integration [1], Perturbation method [1,24] |
| Parallelization | MPI, atom-decomposition |
[1] M. P. Allen and D. J. Tildesley, "Computer simulation of liquids",
Clarendon Press, Oxford, U.K.., 1987; D. Frenkel and B. Smit, "Understanding
Molecular Simulation", 2nd. Ed., Academic Press, San Diego, 2002;
T. Schlick, "Molecular Modeling and Simulation", Springer-Verlag,
New York, 2002.
[2] M. E. Tuckerman et al. J. Chem. Phys. 97 1990 (1992); G. J. Martyna
et al., Mol. Phys. 87, 1117 (1996).
[3] S. Nose, J. Chem. Phys. 81, 511 (1984); S. Nose, Mol. Phys. 52, 269
(1984); W. G. Hoover, Phys. Rev. A 31, 1695 (1985).
[4] R. D. Groot and P. B. Warren, J. Chem. Phys. 107, 4423 (1997).
[5] I. Vattulainen, M. Karttunen, G. Besold, and J. M. Polson, J. Chem.
Phys. 116, 3967 (2002).
[6] C. P. Lowe, Europhys. Lett. 47, 145 (1999).
[7] G. J. Martyna et al., J. Chem. Phys. 97, 2635 (1992).
[8] M. T. Tuckerman et al., J. Chem. Phys. 99, 2796 (1993).
[9] H. C. Andersen, J. Chem. Phys. 72, 2384 (1980).
[10] M. Parrinello and A. Rahman, Phys. Rev. Lett. 45, 1196 (1980); M.
Parrinello and A. Rahman, J. Appl. Phys. 52, 7182 (1981); J. R. Ray, Comput.
Phys. Rep. 8, 109 (1988).
[11] G. J. Martyna et al., J. Chem. Phys. 101, 4177 (1994); W. Shinoda
et al., Phys. Rev. B 69, 134103 (2004).
[12] B. R. Brooks et al., J. Comput. Chem. 4, 187 (1983); A. D. MacKerell et al. J. Phys. Chem. B 102, 3586 (1998); S. E. Feller and A. D. MacKerell, J. Phys. Chem. B 104 7510 (1999).
[13] W. L.. Jorgensen et al., J. Am. Chem. Soc. 117, 11225 (1996); W. L.
Jorgensen and J. Tiradorives, J. Am. Chem. Soc. 110, 1657 (1988); W. L.
Jorgensen, "BOSS - Biochemical and Organic Simulation System",
The Encyclopedia of Computational Chemistry, P. v. R. Schleyer (editor-in-chief),John
Wiley & Sons Ltd, Athens, USA, 1998, 5, 3281-3285.
[14] W. D. Cornell et al., J. Am. Chem. Soc. 117, 5179 (1995).
[15] M. S. Daw and M. I. Baskes, Phys. Rev. Lett. 50, 1285 (1983); Phys. Rev. B 29, 6443 (1984); J. E. Angelo et al., Model. Simul. Mater. Sci. Eng. 3, 289 (1995); M. I. Baskes et al., Model. Simul. Mater. Sci. Eng. 5, 651 (1997).
[16] B. W. H. van Beest, G. J. Kramer, and R. A. van Santen, Phys. Rev.
Lett. 64 1955 (1990).
[17] T. Darden et al., J. Chem. Phys. 98, 10089 (1993); U. Essmann et al.,
J. Chem. Phys. 103, 8577 (1995).
[18] J. P. Ryckaert et al., J. Comput. Phys. 23 327 (1977).
[19] H. C. Andersen, J. Comput. Phys. 52, 24 (1983).
[20] N. Matubayasi and M. Nakahara, J. Chem. Phys. 110, 3291 (1999).
[21] W. Shinoda and M. Mikami, J. Comput. Chem. 24, 920 (2003).
[22] M. E. Tuckerman and A. Hughes, in Classical and Quantum Dynamics in
Condensed Phase Simulations, B. J. Berne, G. Ciccotti, and D. F. Coker
eds., p.311, World Scientific, Singapore, 1998; J. Cao and G. J. Martyna,
J. Chem. Phys. 104, 2028 (1996).
[23] P. Jedlovszky and M. Mezei, J. Am. Chem. Soc. 122, 5125 (2000); W.
Shinoda et al. J. Phys. Chem. B 108 9346 (2004).
[24] M. Zacharias et al., J. Chem. Phys. 100, 9025 (1994); T. C. Beutler
et al., Chem. Phys. Lett. 222, 529 (1994).