Monte Carlo simulations at constant chemical potential and pressure

The usual way of carrying out Monte Carlo simulations of open systems is by using the grand canonical ensemble. In the grand canonical (TVμ) ensemble a system of fixed volume V is in contact with a temperature reservoir having temperature T, and a particle reservoir having chemical potential μ. In order to obtain values for thermodynamic functions for a given pressure in TVμ Monte Carlo simulations a series of simulations at fixed T and V and different chemical potentials is carried out to determine P(μ), and then an extrapolation to the desired pressure must be carried out. Here we discuss Monte Carlo simulations of open systems in the RPμ ensemble in which an energy R, the chemical potential μ, and the pressure are held fixed during the simulation. Thus each RPμ ensemble simulation replaces a set of TVμ simulations. Simulations of an embedded atom model of liquid palladium are discussed using the new method.