Extension of the Einstein molecule method for solid free energy calculation to non-periodic and semi-periodic systems

Abstract

Free energy calculations on solid phases are important for understanding the phase behavior of various systems. For periodic crystalline solids, the Einstein molecule method can be used to determine the free energy difference between the solid of interest and an ideal crystal for which the free energy can be found analytically. In this work, we show how this method is extensible to systems which are nonperiodic or periodic in some dimensions but not in others. This allows for the calculation of exact absolute free energies of finite-sized crystals having specific shapes and surface geometries. We demonstrate this using the fcc Lennard-Jones solid and also illustrate how surface contributions to free energies can easily be extracted from simulations of this solid in semi-infinite slab geometries. We have developed a software package which interfaces with the LAMMPS molecular dynamics code to perform these calculations.