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):

$\left.{\frac {dP}{dt}}\right\vert _{\mathrm {bath} }={\frac {P_{0}-P}{\tau _{P}}}$

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):

$\mu =1-{\frac {\kappa _{T}\Delta t}{3\tau _{P}}}(P_{0}-P)$

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 $\kappa _{T}=4.6\times 10^{-5}\mathrm {bar} ^{-1}$).