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Berendsen Thermostat

In the Berendsen algorithm the instantaneous temperature is pushed towards the desired temperature by scaling the velocities at each step:


$\displaystyle \chi$ $\textstyle \leftarrow$ $\displaystyle \left[ 1+ {\Delta t\over \tau_T}\left({T_{\rm ext}\over {\cal T}}-1\right)
\right]^{1/2}$
$\displaystyle \mbox{$\underline{v}$}(t + {1\over 2} \Delta t)$ $\textstyle \leftarrow$ $\displaystyle \left[ \mbox{$\underline{v}$}(t-{1\over 2} \Delta t) +
\Delta t {\mbox{$\underline{f}$}(t)\over m}\right]\chi$
$\displaystyle \mbox{$\underline{v}$}(t)$ $\textstyle \leftarrow$ $\displaystyle {1\over 2} \left[\mbox{$\underline{v}$}(t-{1\over 2}\Delta t)
+\mbox{$\underline{v}$}(t+{1\over 2}\Delta t)\right]$
$\displaystyle \mbox{$\underline{r}$}(t+\Delta t)$ $\textstyle \leftarrow$ $\displaystyle \mbox{$\underline{r}$}(t) + \Delta t \; \mbox{$\underline{v}$}(t+{1\over 2}\Delta t)$ (2.185)


As with the Nosé-Hoover thermostat iteration is required to obtain self consistency of $\chi$, $\mbox{$\underline{v}$}(t)$ and ${\cal T}$, although it should be noted $\chi$ has different roles in the two thermostats. The Berendsen algorithm conserves total momentum but not energy.

As with the Nosé-Hoover algorithm the presence of constraint bonds requires an additional iteration with one application of SHAKE corrections. The algorithm is implemented in the DL_POLY routines NVT_B0 and NVT_B1, the latter being for systems with bond constraints.



W Smith 2003-05-12