Berendsen thermostat: Difference between revisions
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Carl McBride (talk | contribs) (New page: ==References== #[http://dx.doi.org/10.1063/1.448118 H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak "Molecular dynamics with coupling to an external...) |
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The '''Berendsen thermostat''' <ref>[http://dx.doi.org/10.1063/1.448118 H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak "Molecular dynamics with coupling to an external bath", Journal of Chemical Physics '''81''' pp. 3684-3690 (1984)]</ref> is a method for controlling the [[temperature]] in a [[molecular dynamics]] simulation. | |||
The Berendsen [[thermostats |thermostat]] uses a weak coupling <math>(\gamma_i)</math> to an external heat bath of temperature <math>T_0</math>. This results in the modified equation of motion (Ref. 1 Eq. 8): | |||
:<math>m_i \frac{{\mathrm d} {\mathbf {v}}_i}{{\mathrm d} t} = {\mathbf {F}}_i + m_i \gamma \left( \frac{T_0}{T} -1\right){\mathbf {v}}_i </math>. | |||
This represents a proportional scaling of the velocities per [[time step]] from <math>{\mathbf {v}}</math> to <math>\lambda {\mathbf {v}}</math>, where (Ref. 1 Eq. 11) | |||
:<math>\lambda = \left[1 + \frac{\Delta t}{\tau_T} \left( \frac{T_0}{T} -1\right)\right]^{1/2}</math> | |||
where <math>\tau_T</math> is a time constant associated with the coupling. | |||
==See also== | |||
*[[Bussi-Donadio-Parrinello thermostat]] | |||
==References== | ==References== | ||
<references/> | |||
[[category: molecular dynamics]] | [[category: molecular dynamics]] | ||
Latest revision as of 13:30, 16 February 2010
The Berendsen thermostat [1] is a method for controlling the temperature in a molecular dynamics simulation. The Berendsen thermostat uses a weak coupling to an external heat bath of temperature . This results in the modified equation of motion (Ref. 1 Eq. 8):
- .
This represents a proportional scaling of the velocities per time step from to , where (Ref. 1 Eq. 11)
![{\displaystyle \lambda =\left[1+{\frac {\Delta t}{\tau _{T}}}\left({\frac {T_{0}}{T}}-1\right)\right]^{1/2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4e10e2a6ec32315d6b131754e7a0c6b3b5f8e281)
where is a time constant associated with the coupling.
