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# Difference between revisions of "Berendsen thermostat"

The Berendsen thermostat is a method for controlling the temperature in a molecular dynamics simulation. The Berendsen thermostat uses a weak coupling $(\gamma_i)$ to an external heat bath of temperature $T_0$. This results in the modified equation of motion (Ref. 1 Eq. 8):

$m_i \frac{{\mathrm d} {\mathbf {v}}_i}{{\mathrm d} t} = {\mathbf {F}}_i + m_i \gamma \left( \frac{T_0}{T} -1\right){\mathbf {v}}_i$.

This represents a proportional scaling of the velocities per time step from ${\mathbf {v}}$ to $\lambda {\mathbf {v}}$, where (Ref. 1 Eq. 11)

$\lambda = \left[1 + \frac{\Delta t}{\tau_T} \left( \frac{T_0}{T} -1\right)\right]^{1/2}$

where $\tau_T$ is a time constant associated with the coupling.

## References

1. 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)