Berendsen thermostat

The Berendsen thermostat is a method for controlling the temperature in a molecular dynamics simulation. The Berendsen thermostat uses a weak coupling Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle (\gamma _{i})} to an external heat bath of temperature $T_{0}$. This results in the modified equation of motion (Ref. 1 Eq. 8):

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle 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)

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \lambda =\left[1+{\frac {\Delta t}{\tau _{T}}}\left({\frac {T_{0}}{T}}-1\right)\right]^{1/2}}

where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \tau _{T}} is a time constant associated with the coupling.

See also

• Bussi-Donadio-Parrinello thermostat