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

G Bauer and J Gross, JOURNAL OF CHEMICAL THEORY AND COMPUTATION, 15, 3778-3792 (2019).

DOI: 10.1021/acs.jctc.8b01023

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.

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