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):

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

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

$\lambda ={[1+\frac{\mathrm{\Delta }t}{{\tau }_T}(\frac{T_0}{T}-1)]}^{1/2}$

where ${\tau }_T$ is a time constant associated with the coupling.

See also

• Bussi-Donadio-Parrinello thermostat