### Resumé

and determine the relations between the energies and temperatures for the different ensembles, including the $(NVE_0(h))$ and $(NVT_0(h))$ ensembles.

The differences in the energies and temperatures are proportional with $h^2$ and they are of the order a few tenths of a percent for a traditional value of $h$.

The relations between $(NV\tilde{E}(h))$ and $(NVE)$, and $(NV\tilde{T}(h))$ and $(NVT)$ are easily determined for a given density and temperature, and allows for using larger time increments in MD. The accurate determinations of the energies are used to determine the kinetic degrees of freedom in a system of $N$ particles. It is $3N-3$ for a three dimensional system. The knowledge of the degrees of freedom is necessary when simulating small system, e.g. at nucleation.

Originalsprog | Engelsk |
---|---|

Artikelnummer | 139 |

Tidsskrift | Journal of Chemical Physics |

Vol/bind | 139 |

Udgave nummer | 22 |

Sider (fra-til) | 224106-1 |

Antal sider | 8 |

ISSN | 0021-9606 |

DOI | |

Status | Udgivet - 14 dec. 2013 |

### Emneord

- dynamik ved konstant temperatur

### Citer dette

*Journal of Chemical Physics*,

*139*(22), 224106-1. [139]. https://doi.org/10.1063/1.4836615

}

*Journal of Chemical Physics*, bind 139, nr. 22, 139, s. 224106-1. https://doi.org/10.1063/1.4836615

**Ensemble simulations with discrete classical dynamics.** / Toxværd, Søren.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

T1 - Ensemble simulations with discrete classical dynamics

AU - Toxværd, Søren

PY - 2013/12/14

Y1 - 2013/12/14

N2 - For discrete classical Molecular dynamics (MD) obtained by the "Verlet" algorithm (VA) with the time increment $h$ there exist a shadow Hamiltonian $\tilde{H}$ with energy $\tilde{E}(h)$, for which the discrete particle positions lie on the analytic trajectories for $\tilde{H}$. $\tilde{E}(h)$ is employed to determine the relation with the corresponding energy, $E$ for the analytic dynamics with $h=0$ and the zero-order estimate $E_0(h)$ of the energy for discrete dynamics, appearing in the literature for MD with VA. We derive a corresponding time reversible VA algorithm for canonical dynamics for the $(NV\tilde{T}(h))$ ensembleand determine the relations between the energies and temperatures for the different ensembles, including the $(NVE_0(h))$ and $(NVT_0(h))$ ensembles.The differences in the energies and temperatures are proportional with $h^2$ and they are of the order a few tenths of a percent for a traditional value of $h$.The relations between $(NV\tilde{E}(h))$ and $(NVE)$, and $(NV\tilde{T}(h))$ and $(NVT)$ are easily determined for a given density and temperature, and allows for using larger time increments in MD. The accurate determinations of the energies are used to determine the kinetic degrees of freedom in a system of $N$ particles. It is $3N-3$ for a three dimensional system. The knowledge of the degrees of freedom is necessary when simulating small system, e.g. at nucleation.

AB - For discrete classical Molecular dynamics (MD) obtained by the "Verlet" algorithm (VA) with the time increment $h$ there exist a shadow Hamiltonian $\tilde{H}$ with energy $\tilde{E}(h)$, for which the discrete particle positions lie on the analytic trajectories for $\tilde{H}$. $\tilde{E}(h)$ is employed to determine the relation with the corresponding energy, $E$ for the analytic dynamics with $h=0$ and the zero-order estimate $E_0(h)$ of the energy for discrete dynamics, appearing in the literature for MD with VA. We derive a corresponding time reversible VA algorithm for canonical dynamics for the $(NV\tilde{T}(h))$ ensembleand determine the relations between the energies and temperatures for the different ensembles, including the $(NVE_0(h))$ and $(NVT_0(h))$ ensembles.The differences in the energies and temperatures are proportional with $h^2$ and they are of the order a few tenths of a percent for a traditional value of $h$.The relations between $(NV\tilde{E}(h))$ and $(NVE)$, and $(NV\tilde{T}(h))$ and $(NVT)$ are easily determined for a given density and temperature, and allows for using larger time increments in MD. The accurate determinations of the energies are used to determine the kinetic degrees of freedom in a system of $N$ particles. It is $3N-3$ for a three dimensional system. The knowledge of the degrees of freedom is necessary when simulating small system, e.g. at nucleation.

KW - dynamik ved konstant temperatur

U2 - 10.1063/1.4836615

DO - 10.1063/1.4836615

M3 - Journal article

VL - 139

SP - 224106

EP - 224101

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 22

M1 - 139

ER -