Andersen thermostat: Difference between revisions
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The '''Andersen thermostat''' (Ref. 1, section IV) couples the system to a heat bath via stochastic forces that modify the kinetic energy of the atoms or molecules. | The '''Andersen thermostat''' was the first thermostat proposed for [[molecular dynamics]], thus permitting one to use the [[canonical ensemble]] (NVT) in simulations. The Andersen thermostat (Ref. <ref>[http://dx.doi.org/10.1063/1.439486 Hans C. Andersen "Molecular dynamics simulations at constant pressure and/or temperature", Journal of Chemical Physics '''72''' pp. 2384-2393 (1980)]</ref>, section IV) couples the system to a heat bath via stochastic forces that modify the kinetic energy of the atoms or molecules. | ||
The time between collisions, or the number of collisions in some (short) time interval is decided [[random numbers |randomly]], with the following [[Poisson distribution]] ( | The time between collisions, or the number of collisions in some (short) time interval is decided [[random numbers |randomly]], with the following [[Poisson distribution]] (Eq. 4.1): | ||
:<math>P(t) = \nu e^{-\nu t}.</math> | :<math>P(t) = \nu e^{-\nu t}.</math> | ||
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where <math>\nu</math> is the stochastic collision frequency. | where <math>\nu</math> is the stochastic collision frequency. | ||
Between collisions the system evolves at constant energy, i.e. business as usual. Upon a 'collision event' the new momentum of the lucky atom (or molecule) is chosen at random from a [[Boltzmann distribution]] at [[temperature]] <math>T</math>. | Between collisions the system evolves at constant energy, i.e. business as usual. Upon a 'collision event' the new momentum of the lucky atom (or molecule) is chosen at random from a [[Boltzmann distribution]] at [[temperature]] <math>T</math>. | ||
In principle <math>\nu</math> can adopt any value. However, there does exist an optimum choice ( | In principle <math>\nu</math> can adopt any value. However, there does exist an optimum choice (Eq. 4.9): | ||
:<math>\nu = \frac{2a \kappa V^{1/3}}{3 k_BN} = \frac{2a \kappa}{3 k_B\rho^{1/3}N^{2/3}}</math> | :<math>\nu = \frac{2a \kappa V^{1/3}}{3 k_BN} = \frac{2a \kappa}{3 k_B\rho^{1/3}N^{2/3}}</math> | ||
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where <math>a</math> is a dimensionless constant, <math>\kappa</math> is the [[thermal conductivity]], <math>V</math> is the volume, <math>k_B</math> is the [[Boltzmann constant]], and <math>\rho</math> is the [[number density]] of particles; <math>\rho:=N/V</math>. | where <math>a</math> is a dimensionless constant, <math>\kappa</math> is the [[thermal conductivity]], <math>V</math> is the volume, <math>k_B</math> is the [[Boltzmann constant]], and <math>\rho</math> is the [[number density]] of particles; <math>\rho:=N/V</math>. | ||
Note: the Andersen thermostat should only be used for time-independent properties. Dynamic properties, such as the [[diffusion]], should not be calculated if the system is thermostated using the Andersen algorithm ( | Note: the Andersen thermostat should only be used for time-independent properties. Dynamic properties, such as the [[diffusion]], should not be calculated if the system is thermostated using the Andersen algorithm <ref>[http://dx.doi.org/10.1063/1.445020 H. Tanaka, Koichiro Nakanishi, and Nobuatsu Watanabe "Constant temperature molecular dynamics calculation on Lennard-Jones fluid and its application to water", Journal of Chemical Physics '''78''' pp. 2626-2634 (1983)]</ref>. | ||
==See also== | ==See also== | ||
*[[Lowe-Andersen thermostat]] | *[[Lowe-Andersen thermostat]] | ||
==References== | ==References== | ||
<references/> | |||
;Related reading | |||
*[http://dx.doi.org/10.1002/cpa.20198 Weinan E and Dong Li "The Andersen thermostat in molecular dynamics", Communications on Pure and Applied Mathematics '''61''' pp. 96-136 (2008)] | |||
[[Category: Molecular dynamics]] | [[Category: Molecular dynamics]] | ||
Latest revision as of 15:43, 27 February 2014
The Andersen thermostat was the first thermostat proposed for molecular dynamics, thus permitting one to use the canonical ensemble (NVT) in simulations. The Andersen thermostat (Ref. [1], section IV) couples the system to a heat bath via stochastic forces that modify the kinetic energy of the atoms or molecules. The time between collisions, or the number of collisions in some (short) time interval is decided randomly, with the following Poisson distribution (Eq. 4.1):
where is the stochastic collision frequency. Between collisions the system evolves at constant energy, i.e. business as usual. Upon a 'collision event' the new momentum of the lucky atom (or molecule) is chosen at random from a Boltzmann distribution at temperature . In principle can adopt any value. However, there does exist an optimum choice (Eq. 4.9):
where is a dimensionless constant, is the thermal conductivity, is the volume, is the Boltzmann constant, and is the number density of particles; .
Note: the Andersen thermostat should only be used for time-independent properties. Dynamic properties, such as the diffusion, should not be calculated if the system is thermostated using the Andersen algorithm [2].
See also[edit]
References[edit]
- ↑ Hans C. Andersen "Molecular dynamics simulations at constant pressure and/or temperature", Journal of Chemical Physics 72 pp. 2384-2393 (1980)
- ↑ H. Tanaka, Koichiro Nakanishi, and Nobuatsu Watanabe "Constant temperature molecular dynamics calculation on Lennard-Jones fluid and its application to water", Journal of Chemical Physics 78 pp. 2626-2634 (1983)
- Related reading