### Abstract

Molecular dynamics is one of the most commonly used approaches for studying the dynamics and statistical distributions of physical, chemical, and biological systems using atomistic or coarse-grained models. It is often the case, however, that the interparticle forces drive motion on many time scales, and the efficiency of a calculation is limited by the choice of time step, which must be sufficiently small that the fastest force components are accurately integrated. Multiple time-stepping algorithms partially alleviate this inefficiency by assigning to each time scale an appropriately chosen step-size. As the fast forces are often computationally cheaper to evaluate than the slow forces, this results in a significant gain in efficiency. However, such approaches are limited by resonance phenomena, wherein motion on the fastest time scales limits the step sizes associated with slower time scales. In atomistic models of biomolecular systems, for example, resonances limit the largest time step to around 5-6 fs. Stochastic processes promote mixing and ergodicity in dynamical systems and reduce the impact of resonant modes. In this paper, we introduce a set of stochastic isokinetic equations of motion that are shown to be rigorously ergodic, largely free of resonances, and can be integrated using a multiple time-stepping algorithm which is easily implemented in existing molecular dynamics codes. The technique is applied to a simple, illustrative problem and then to a more realistic system, namely, a flexible water model. Using this approach outer time steps as large as 100 fs are shown to be possible.

Original language | English (US) |
---|---|

Pages (from-to) | 3579-3594 |

Number of pages | 16 |

Journal | Molecular Physics |

Volume | 111 |

Issue number | 22-23 |

DOIs | |

State | Published - Dec 1 2013 |

### Fingerprint

### Keywords

- Flexible water
- Molecular dynamics
- Multiple time-stepping
- Resonance
- Stochastic isokinetic dynamics

### ASJC Scopus subject areas

- Physical and Theoretical Chemistry
- Condensed Matter Physics
- Biophysics
- Molecular Biology

### Cite this

*Molecular Physics*,

*111*(22-23), 3579-3594. https://doi.org/10.1080/00268976.2013.844369

**Stochastic, resonance-free multiple time-step algorithm for molecular dynamics with very large time steps.** / Leimkuhler, Ben; Margul, Daniel T.; Tuckerman, Mark.

Research output: Contribution to journal › Article

*Molecular Physics*, vol. 111, no. 22-23, pp. 3579-3594. https://doi.org/10.1080/00268976.2013.844369

}

TY - JOUR

T1 - Stochastic, resonance-free multiple time-step algorithm for molecular dynamics with very large time steps

AU - Leimkuhler, Ben

AU - Margul, Daniel T.

AU - Tuckerman, Mark

PY - 2013/12/1

Y1 - 2013/12/1

N2 - Molecular dynamics is one of the most commonly used approaches for studying the dynamics and statistical distributions of physical, chemical, and biological systems using atomistic or coarse-grained models. It is often the case, however, that the interparticle forces drive motion on many time scales, and the efficiency of a calculation is limited by the choice of time step, which must be sufficiently small that the fastest force components are accurately integrated. Multiple time-stepping algorithms partially alleviate this inefficiency by assigning to each time scale an appropriately chosen step-size. As the fast forces are often computationally cheaper to evaluate than the slow forces, this results in a significant gain in efficiency. However, such approaches are limited by resonance phenomena, wherein motion on the fastest time scales limits the step sizes associated with slower time scales. In atomistic models of biomolecular systems, for example, resonances limit the largest time step to around 5-6 fs. Stochastic processes promote mixing and ergodicity in dynamical systems and reduce the impact of resonant modes. In this paper, we introduce a set of stochastic isokinetic equations of motion that are shown to be rigorously ergodic, largely free of resonances, and can be integrated using a multiple time-stepping algorithm which is easily implemented in existing molecular dynamics codes. The technique is applied to a simple, illustrative problem and then to a more realistic system, namely, a flexible water model. Using this approach outer time steps as large as 100 fs are shown to be possible.

AB - Molecular dynamics is one of the most commonly used approaches for studying the dynamics and statistical distributions of physical, chemical, and biological systems using atomistic or coarse-grained models. It is often the case, however, that the interparticle forces drive motion on many time scales, and the efficiency of a calculation is limited by the choice of time step, which must be sufficiently small that the fastest force components are accurately integrated. Multiple time-stepping algorithms partially alleviate this inefficiency by assigning to each time scale an appropriately chosen step-size. As the fast forces are often computationally cheaper to evaluate than the slow forces, this results in a significant gain in efficiency. However, such approaches are limited by resonance phenomena, wherein motion on the fastest time scales limits the step sizes associated with slower time scales. In atomistic models of biomolecular systems, for example, resonances limit the largest time step to around 5-6 fs. Stochastic processes promote mixing and ergodicity in dynamical systems and reduce the impact of resonant modes. In this paper, we introduce a set of stochastic isokinetic equations of motion that are shown to be rigorously ergodic, largely free of resonances, and can be integrated using a multiple time-stepping algorithm which is easily implemented in existing molecular dynamics codes. The technique is applied to a simple, illustrative problem and then to a more realistic system, namely, a flexible water model. Using this approach outer time steps as large as 100 fs are shown to be possible.

KW - Flexible water

KW - Molecular dynamics

KW - Multiple time-stepping

KW - Resonance

KW - Stochastic isokinetic dynamics

UR - http://www.scopus.com/inward/record.url?scp=84889568848&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84889568848&partnerID=8YFLogxK

U2 - 10.1080/00268976.2013.844369

DO - 10.1080/00268976.2013.844369

M3 - Article

AN - SCOPUS:84889568848

VL - 111

SP - 3579

EP - 3594

JO - Molecular Physics

JF - Molecular Physics

SN - 0026-8976

IS - 22-23

ER -