Berendsen barostat

The Berendsen barostat is a method for controlling the pressure in a molecular dynamics simulation. The Berendsen barostat adds an extra term to to the equations of motion which effects the pressure change (Eq. 12):

${\frac{dP}{dt}|}_{\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{h}}=\frac{P_0-P}{{\tau }_P}$

where $P_0$ is the reference pressure, i.e. the pressure of the external pressure "bath", and $P$ is the instantaneous pressure. ${\tau }_P$ is a time constant. Within this scheme the coordinates and the box sides are rescaled every step. Assuming the system is isotropic and within a cubic box the scaling factor $\mu$ is given by (Eq. 20):

$\mu =1-\frac{{\kappa }_T\mathrm{\Delta }t}{3{\tau }_P}(P_0-P)$

where ${\kappa }_T$ is the isothermal compressibility. The value of ${\kappa }_T$ only has to be reasonable; for example, both DL POLY and GROMACS use the value of the compressibility of water (at 1 atm and 300K, leading to ${\kappa }_T=4.6\times 10^{-5}{\mathrm{b}\mathrm{a}\mathrm{r}}^{-1}$).