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We have already seen in Monte
Carlo
, that isobaric simulations
should involve volume changes. So constant pressure MD naturally
involves the volume changes and its implementation requires the
equation of motion to describe its evolution. The technique described
below was proposed by Andersen in 1980, and involves coordinates
scaling, similar to *NPT* Monte Carlo, described previously.
^{}

First we introduce the constant pressure analog of the microcanonical
ensemble--*iso-enthalpic* ensemble. We already know, how to make
it work at a constant temperature. Now we will show how to make *P*
constant.

Constant pressure is realized by the virtual ``piston'' of mass *M*
(which actually has units of ),
which is under constant force, that corresponds to the applied
pressure *P _{0}*. Piston motion changes the volume of the system.
Additional kinetic and potential

(10) |

(11) |

Coupling this method to the Hoover thermostat by introducing another
variable (and ), we can make the whole thing
reproduce the *NPT* ensemble. This can be again shown using Liouville
equation for the probability density distribution. *NPT*-MD
equations are:

(12) |

Again a non-rigorous, but practical scheme, similar to the
van Gunstern-Berendsen thermostat exists. It is called
*Berendsen barostat.* It rescales the particle coordinates at
every step by the factor

(13) |

© 1997

Tue Dec 2 20:24:47 EST 1997