### Abstract

A frequently encountered problem in molecular dynamics is how to treat the long times that are required to simulate condensed systems consisting of particles interacting through long range forces. Standard methods require the calculation of the forces at every time step. Because each particle interacts with all particles within the interaction range of the potential the longer the range of the potential the larger the number forces that must be calculated at each time step. In this note we present a variant of the RESPA (reference system propagator algorithm), which we developed for handling systems with multiple time scales like disparate mass mixtures. This version of RESPA greatly reduces the number of forces that must be computed at each time step and thereby leads to a dramatic acceleration of such simulations. The RESPA method uses ideas similar to NAPA, an algorithm we invented to treat high frequency oscillators interacting with low frequency bath. The method is based on a choice of a reference system in which the particles interact through short range forces. The reference system is numerically integrated for n time steps σt and the error incurred by using short range forces is corrected by solving a rigorous set of equations once every Δt=nσt. This method reduces the cpu time dramatically. It is shown that this approach and suitable generalizations should be very useful for future simulations of quantum and classical condensed matter systems.

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

Pages (from-to) | 6811-6815 |

Number of pages | 5 |

Journal | The Journal of chemical physics |

Volume | 94 |

Issue number | 10 |

State | Published - 1991 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of chemical physics*,

*94*(10), 6811-6815.

**Molecular dynamics algorithm for multiple time scales : Systems with long range forces.** / Tuckerman, Mark; Berne, Bruce J.; Martyna, Glenn J.

Research output: Contribution to journal › Article

*The Journal of chemical physics*, vol. 94, no. 10, pp. 6811-6815.

}

TY - JOUR

T1 - Molecular dynamics algorithm for multiple time scales

T2 - Systems with long range forces

AU - Tuckerman, Mark

AU - Berne, Bruce J.

AU - Martyna, Glenn J.

PY - 1991

Y1 - 1991

N2 - A frequently encountered problem in molecular dynamics is how to treat the long times that are required to simulate condensed systems consisting of particles interacting through long range forces. Standard methods require the calculation of the forces at every time step. Because each particle interacts with all particles within the interaction range of the potential the longer the range of the potential the larger the number forces that must be calculated at each time step. In this note we present a variant of the RESPA (reference system propagator algorithm), which we developed for handling systems with multiple time scales like disparate mass mixtures. This version of RESPA greatly reduces the number of forces that must be computed at each time step and thereby leads to a dramatic acceleration of such simulations. The RESPA method uses ideas similar to NAPA, an algorithm we invented to treat high frequency oscillators interacting with low frequency bath. The method is based on a choice of a reference system in which the particles interact through short range forces. The reference system is numerically integrated for n time steps σt and the error incurred by using short range forces is corrected by solving a rigorous set of equations once every Δt=nσt. This method reduces the cpu time dramatically. It is shown that this approach and suitable generalizations should be very useful for future simulations of quantum and classical condensed matter systems.

AB - A frequently encountered problem in molecular dynamics is how to treat the long times that are required to simulate condensed systems consisting of particles interacting through long range forces. Standard methods require the calculation of the forces at every time step. Because each particle interacts with all particles within the interaction range of the potential the longer the range of the potential the larger the number forces that must be calculated at each time step. In this note we present a variant of the RESPA (reference system propagator algorithm), which we developed for handling systems with multiple time scales like disparate mass mixtures. This version of RESPA greatly reduces the number of forces that must be computed at each time step and thereby leads to a dramatic acceleration of such simulations. The RESPA method uses ideas similar to NAPA, an algorithm we invented to treat high frequency oscillators interacting with low frequency bath. The method is based on a choice of a reference system in which the particles interact through short range forces. The reference system is numerically integrated for n time steps σt and the error incurred by using short range forces is corrected by solving a rigorous set of equations once every Δt=nσt. This method reduces the cpu time dramatically. It is shown that this approach and suitable generalizations should be very useful for future simulations of quantum and classical condensed matter systems.

UR - http://www.scopus.com/inward/record.url?scp=36449001478&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36449001478&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:36449001478

VL - 94

SP - 6811

EP - 6815

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 10

ER -