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Energy conservation in molecular dynamics simulations of classical systems
Søren Toxvaerd1, Ole J Heilmann, Jeppe C Dyre
1DNRF centre Glass and Time, IMFUFA, Department of Sciences, Roskilde University, Postbox 260, DK-4000 Roskilde, Denmark.
The Journal of Chemical Physics
|June 21, 2012
Summary
Molecular dynamics simulations using the Verlet algorithm show energy fluctuations. Incorporating a shadow Hamiltonian significantly reduces these fluctuations, improving energy conservation in simulations.
Area of Science:
- Computational physics
- Chemical physics
- Molecular dynamics
Background:
- Classical Newtonian dynamics conserves energy in isolated systems.
- Discrete numerical methods like the Verlet algorithm introduce energy fluctuations in simulations.
- The concept of a shadow Hamiltonian explains mean energy conservation in discrete simulations.
Purpose of the Study:
- To improve energy conservation in molecular dynamics simulations.
- To investigate the impact of the shadow Hamiltonian's first non-trivial term on energy fluctuations.
- To analyze the long-term energy conservation and sensitivity to numerical errors.
Main Methods:
- Utilized the Verlet algorithm for molecular dynamics simulations.
- Applied an asymptotic expansion to derive the shadow Hamiltonian.
- Investigated a system with Lennard-Jones pair interactions.
- Performed analytical and numerical analyses of energy conservation.
Main Results:
- Inclusion of the shadow Hamiltonian term reduced energy fluctuation standard deviation by 100x.
- Energy was conserved for over 100 million time steps under specific conditions.
- Energy conservation demonstrated robustness against round-off errors.
Conclusions:
- The shadow Hamiltonian provides a more accurate discrete energy estimate.
- Improved energy conservation is achievable in molecular dynamics simulations.
- Numerical stability of energy conservation is high, even with potential discontinuities.
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