NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

Resumé

An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to “entropic drift” of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid.
OriginalsprogEngelsk
TidsskriftJournal of Chemical Physics
Vol/bind135
Udgave nummer10
Antal sider9
ISSN0021-9606
DOI
StatusUdgivet - 2011

Citer dette

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title = "NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface",
abstract = "An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to “entropic drift” of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid.",
keywords = "differential geometry, entropy, Lennard-Jones potential, molecular dynamics method, numerical stability, potential energy surfaces",
author = "Trond Ingebrigtsen and S{\o}ren Toxv{\ae}rd and Ole Heilmann and Thomas Schr{\o}der and Dyre, {J. C.}",
year = "2011",
doi = "10.1063/1.3623585",
language = "English",
volume = "135",
journal = "Journal of Chemical Physics",
issn = "0021-9606",
publisher = "American Institute of Physics",
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NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface. / Ingebrigtsen, Trond; Toxværd, Søren; Heilmann, Ole; Schrøder, Thomas; Dyre, J. C.

I: Journal of Chemical Physics, Bind 135, Nr. 10, 2011.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface

AU - Ingebrigtsen, Trond

AU - Toxværd, Søren

AU - Heilmann, Ole

AU - Schrøder, Thomas

AU - Dyre, J. C.

PY - 2011

Y1 - 2011

N2 - An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to “entropic drift” of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid.

AB - An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to “entropic drift” of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid.

KW - differential geometry

KW - entropy

KW - Lennard-Jones potential

KW - molecular dynamics method

KW - numerical stability

KW - potential energy surfaces

U2 - 10.1063/1.3623585

DO - 10.1063/1.3623585

M3 - Journal article

VL - 135

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

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ER -