### Abstract

We report results from molecular dynamics simulations for a bistable piecewise-harmonic potential. A new method for molecular dynamics-the Langevin/implicit-Euler scheme-is investigated here and compared to the common Verlet integration algorithm. The implicit scheme introduces new computational and physical features since it (1) does not restrict integration time step to a very small value, and (2) effectively damps vibrational modes ω≫ω_{c}, where ω_{c} is a chosen cutoff frequency. The main issue we explore in this study is how different choices of time steps and cutoff frequencies affect computed transition rates. The one-dimensional, double-well model offers a simple visual and computational opportunity for observing the two different damping forces introduced by the scheme-frictional and intrinsic-and for characterizing the dominating force at a given parameter combination. Another question we examine here is the choice of time step below which the Langevin/implicit-Euler scheme produces "correct" transition rates for a model potential whose energy distribution is "well-described" classically.

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

Pages (from-to) | 4986-4996 |

Number of pages | 11 |

Journal | The Journal of chemical physics |

Volume | 95 |

Issue number | 7 |

State | Published - 1991 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*The Journal of chemical physics*,

*95*(7), 4986-4996.

**A transition-rate investigation by molecular dynamics with the Langevin/implicit-Euler scheme.** / Nyberg, Anna M.; Schlick, Tamar.

Research output: Contribution to journal › Article

*The Journal of chemical physics*, vol. 95, no. 7, pp. 4986-4996.

}

TY - JOUR

T1 - A transition-rate investigation by molecular dynamics with the Langevin/implicit-Euler scheme

AU - Nyberg, Anna M.

AU - Schlick, Tamar

PY - 1991

Y1 - 1991

N2 - We report results from molecular dynamics simulations for a bistable piecewise-harmonic potential. A new method for molecular dynamics-the Langevin/implicit-Euler scheme-is investigated here and compared to the common Verlet integration algorithm. The implicit scheme introduces new computational and physical features since it (1) does not restrict integration time step to a very small value, and (2) effectively damps vibrational modes ω≫ωc, where ωc is a chosen cutoff frequency. The main issue we explore in this study is how different choices of time steps and cutoff frequencies affect computed transition rates. The one-dimensional, double-well model offers a simple visual and computational opportunity for observing the two different damping forces introduced by the scheme-frictional and intrinsic-and for characterizing the dominating force at a given parameter combination. Another question we examine here is the choice of time step below which the Langevin/implicit-Euler scheme produces "correct" transition rates for a model potential whose energy distribution is "well-described" classically.

AB - We report results from molecular dynamics simulations for a bistable piecewise-harmonic potential. A new method for molecular dynamics-the Langevin/implicit-Euler scheme-is investigated here and compared to the common Verlet integration algorithm. The implicit scheme introduces new computational and physical features since it (1) does not restrict integration time step to a very small value, and (2) effectively damps vibrational modes ω≫ωc, where ωc is a chosen cutoff frequency. The main issue we explore in this study is how different choices of time steps and cutoff frequencies affect computed transition rates. The one-dimensional, double-well model offers a simple visual and computational opportunity for observing the two different damping forces introduced by the scheme-frictional and intrinsic-and for characterizing the dominating force at a given parameter combination. Another question we examine here is the choice of time step below which the Langevin/implicit-Euler scheme produces "correct" transition rates for a model potential whose energy distribution is "well-described" classically.

UR - http://www.scopus.com/inward/record.url?scp=0040502154&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0040502154&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0040502154

VL - 95

SP - 4986

EP - 4996

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 7

ER -