Editing Berendsen barostat

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The '''Berendsen barostat''' <ref>[http://dx.doi.org/10.1063/1.448118     H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, and J. R. Haak "Molecular dynamics with coupling to an external bath", Journal of Chemical Physics '''81''' pp. 3684-3690 (1984)]</ref> is a method for controlling the [[pressure]] in a [[molecular dynamics]] simulation.
The Berendsen [[barostats | barostat]] adds an extra term to to the equations of motion which effects the pressure change (Eq. 12):

:<math>\left. \frac{dP}{dt} \right\vert_{\mathrm {bath} }  = \frac{P_0 - P}{\tau_P}</math>

where <math>P_0</math> is the reference pressure, i.e. the pressure of the external pressure "bath", and <math>P</math> is the instantaneous pressure.
<math>\tau_P</math> is a time constant.
Within this scheme the coordinates and the box sides are rescaled every so-many steps. Assuming the system is isotropic and within a cubic box the scaling factor <math>\mu</math> is given by (Eq. 20):

:<math> \mu = 1 - \frac{\kappa_T \Delta t}{3\tau_P} (P_0 -P)</math>

where <math>\kappa_T</math> is the [[Compressibility#Isothermal compressibility | isothermal compressibility]]. The value of <math>\kappa_T</math> 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 
<math>\kappa_T = 4.6 \times 10^{-5} \mathrm{bar}^{-1}</math>). 
==References==
<references/>
[[category: molecular dynamics]]