Stochastic sampling of the isothermal-isobaric ensemble: phase diagram of crystalline solids from molecular dynamics simulation

A methodology to sample the isothermal-isobaric ensemble using Langevin dynamics is proposed, which combines novel features of geometric integrators for the equations of motion. By employing the Trotter expansion, the methodology generates a robust, symmetric and accurate numerical algorithm. In order to show that the proposed method correctly samples the phase-space, simulations in the isotropic NPT ensemble were carried out for two analytical examples. Also this method permits to study a solid-solid phase transition, by conducting a fully flexible-cell molecular dynamics simulation. Additionally, we present an efficient method to determine the Gibbs free energy in a wide interval of pressure along an isothermal path, which allows us to determine the transition pressure in a driven by pressure solid-solid phase transition. Our calculations show that the methodology is highly suitable for the study of phase diagram of crystalline solids.