Phase Equilibria of Solid and Fluid Phases from Molecular Dynamics Simulations with Equilibrium and Nonequilibrium Free Energy Methods

In this work, we
present a methodology to determine phase coexistence
lines for atomic and rigid molecular systems with an emphasis on solid–fluid
and on solid–solid equilibria. Phase coexistence points are
found by computing the absolute free energy for each candidate phase
separately. For solid phases, a combination of the extended Einstein
crystal and the Einstein molecule method is presented which constitutes
a convenient way to compute the absolute free energy with fixed center
of mass. We compare results from equilibrium methodsthermodynamic
integration and reweighting using the multistate Bennett acceptance
ratio estimator (MBAR)with simulations using a nonequilibrium
method and discuss their advantages and disadvantages. Once absolute
free energies of different phases are available, they are combined
with simulations performed in the isothermal isobaric ensemble and
MBAR, which enables efficient, iterative tracing of coexistence lines.
The method is applicable to both liquid–solid as well as solid–solid
transitions and is comparably simple and convenient to apply since
the same method (MBAR) is used to compute free energies and to trace
the coexistence line. Furthermore, statistical uncertainties can readily
be computed in a transparent manner. We apply the method to an atomic
solid (fcc argon) as well as small molecular systems (methanol and
water) using the LAMMPS simulation package. Our study shows that all
methods can be used to reliably compute the absolute free energy of
solid phases, while MBAR is the most flexible method with high statistical
efficiency. We find the nonequilibrium method is an attractive choice
since it is simple to set up and to postprocess and is, hence, less
prone to errors. The presented workflow provides a flexible, efficient,
and robust way to compute phase diagrams using openly available software.