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):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left. \frac{dP}{dt} \right\vert_{\mathrm {bath} } = \frac{P_0 - P}{\tau_P}}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P_0} is the reference pressure, i.e. the pressure of the external pressure "bath", and Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P} is the instantaneous pressure. Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu} is given by (Eq. 20):

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu = 1 - \frac{\kappa_T \Delta t}{3\tau_P} (P_0 -P)}

where Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \kappa_T} is the isothermal compressibility. The value of Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \kappa_T = 4.6 \times 10^{-5} \mathrm{bar}^{-1}} ).