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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 P0. Piston motion changes the volume of the system. Additional kinetic and potential P0V energy terms, coupled to the particles' momenta, are added to the Hamiltonian (Hoover, 1985). The potential and kinetic energies of the particles are written in terms of scaled variables and
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:
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
© 1997 Boris Veytsman and Michael Kotelyanskii