Berendsen barostat: Difference between revisions
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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 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): | The Berendsen [[barostats | barostat]] adds an extra term to to the equations of motion which effects the pressure change (Eq. 12): | ||
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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. | 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. | <math>\tau_P</math> is a time constant. | ||
Within this scheme the coordinates and the box sides are rescaled every | 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 <math>\mu</math> is given by (Eq. 20): | ||
:<math> \mu = 1 - \frac{\kappa_T \Delta t}{3\tau_P} (P_0 -P)</math> | :<math> \mu = 1 - \frac{\kappa_T \Delta t}{3\tau_P} (P_0 -P)</math> | ||
Latest revision as of 13:15, 24 January 2014
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 (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}} ).