Accurate energy conservation in molecular dynamics simulation
Abstract
In molecular dynamics, Hamiltonian systems of differential equations are numerically integrated using some symplectic method. Symplectic integrators are simple algorithms that appear to be wellsuited for large scale simulations. One feature of these simulations is that there is an unphysical drift in the energy of the system over long integration periods. A drift in the energy is more obvious when a relatively long time step is used. In this article, a special approach, based on symplectic discretization and momenta corrections, is presented. The proposed method conserves the total energy of the system over the interval of simulation for any acceptable time step. A new approach to perform a constanttemperature molecular dynamics simulation is also presented. Numerical experiments illustrating these approaches are described.
About the Authors
O. A. ZolotovRussian Federation
79 Svobodny Prospect, Krasnoyarsk 6
V. E. Zalizniak
Russian Federation
79 Svobodny Prospect, Krasnoyarsk 660041
References
1. C.J. Budd, M.D. Piggott. Geometric integration and its applications. Handbook of Numerical Analysis, XI, NorthHolland, Amsterdam, P. 35–139 (2003).
2. E. Hairer, C. Lubich, G. Wanner. Geometric Numerical Integration. Springer, Berlin, 2002, 644 p.
3. J.M. SanzSerna, M.P. Calvo. Numerical Hamiltonian Problems. Chapman and Hall, London, 1994, 207 p.
4. L. Verlet. Computer ‘experiments’ on classical fluids. I. Thermodynamical properties of LennardJones molecules. Phys. Rev., 159, P. 98–103 (1967).
5. G. Rowlands. A numerical algorithm for Hamiltonian systems. J. Comput. Phys., 97, P. 235–239 (1991).
6. J. Gans, D. Shalloway. Shadow mass and the relationship between velocity and momentum in symplectic numerical integration. Phys. Rev. E, 61, P. 4587–4592 (2000).
7. S. Toxvaerd, O.J. Heilmann, J.C. Dyre. Energy conservation in molecular dynamics simulations of classical systems. J. Chem. Phys., 136, P. 224106(8) (2012).
8. R.W. Hockney, J.W. Eastwood. Computer Simulation Using Particles. Adam Hilger, Bristol and New York, 1988, 523 p.
9. M.P. Allen, D.J. Tildesley. Computer Simulation of Liquids. Clarendon Press, Oxford, 1989, 385 p.
10. L.D. Landau, E.M. Lifshitz. Statistical Physics, Part 1 (Course of Theoretical Physics, Volume 5), Third Edition, Elsevier Butterworth Heinemann, Oxford, 1980, 544 p.
11. R.E. Nettleton. On the relation between thermodynamic temperature and kinetic energy per particle. Canadian Journal of Physics, 72(3–4), P. 106–112 (1994).
Review
For citations:
Zolotov O.A., Zalizniak V.E. Accurate energy conservation in molecular dynamics simulation. Nanosystems: Physics, Chemistry, Mathematics. 2013;4(5):657–669.