Monte Carlo simulations in the isoenthalpic-isotension-isobaric ensemble

We discuss simulations using a recently derived Monte Carlo method which generates the isoenthalpic-isotension-isobaric ensemble or HtN ensemble of classical statistical physics. This method is the Monte Carlo counterpart of the Andersen-Parrinello-Rahman HtN form of molecular dynamics. As an example of the use of HtN Monte Carlo calculations we discuss the calculation of the adiabatic elastic constants and other related thermodynamic properties of a crystalline solid from fluctuation formulas specific to the HtN ensemble and compare with the HtN molecular-dynamics calculation of these same quantities. The agreement of the results with earlier calculations of these quantities using other ensembles supports the inference that our probability density generates the HtN ensemble. For the elastic constants, the HtN Monte Carlo calculations have better convergence properties than the HtN molecular-dynamics calculations but are slower, by at least an order of magnitude, than the ThN and EhN molecular-dynamics and Monte Carlo methods.