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# Difference between revisions of "Berendsen thermostat"

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+ | The '''Berendsen thermostat''' 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): | ||

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+ | :<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>. | ||

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+ | 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) | ||

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+ | :<math>\lambda = \left[1 + \frac{\Delta t}{\tau_T} \left( \frac{T_0}{T} -1\right)\right]^{1/2}</math> | ||

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+ | where <math>\tau_T</math> is a time constant associated with the coupling. | ||

==References== | ==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 bath", Journal of Chemical Physics '''81''' pp. 3684-3690 (1984)] | #[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)] | ||

[[category: molecular dynamics]] | [[category: molecular dynamics]] |

## Revision as of 18:16, 26 March 2008

The **Berendsen thermostat** 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)

where is a time constant associated with the coupling.