Berendsen barostat
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The Berendsen barostat [1] 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 (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.{\frac {dP}{dt}}\right\vert _{\mathrm {bath} }={\frac {P_{0}-P}{\tau _{P}}}}
where Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\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 so-many steps. 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}} ).