Configurational mapping significantly increases the efficiency of solid-solid phase coexistence calculations via molecular dynamics: Determining the FCC-HCP coexistence line of Lennard-Jones particles.

In this study, we incorporate configuration mapping between simulation ensembles into the successive interpolation of multistate reweighting (SIMR) method in order to increase phase space overlap between neighboring simulation ensembles. This significantly increases computational efficiency over the original SIMR method in many situations. We use this approach to determine the coexistence curve of face-centered cubic-hexagonal close-packed Lennard-Jones spheres using direct molecular dynamics and SIMR. As previously noted, the coexistence curve is highly sensitive to the treatment of the van der Waals cutoff. Using a cutoff treatment, the chemical potential difference between phases is moderate and SIMR quickly finds the phase equilibrium lines with good statistical uncertainty. Using a smoothed cutoff results in nonphysical errors in the phase diagram, while the use of particle mesh Ewald for the dispersion term results in a phase equilibrium curve that is comparable with previous results. The drastically closer free energy surfaces for this case test the limits of this configuration mapping approach to phase diagram prediction.

Using reweighting and free energy surface interpolation to predict solid-solid phase diagrams.

Many physical properties of small organic molecules are dependent on the current crystal packing, or polymorph, of the material, including bioavailability of pharmaceuticals, optical properties of dyes, and charge transport properties of semiconductors. Predicting the most stable crystalline form at a given temperature and pressure requires determining the crystalline form with the lowest relative Gibbs free energy. Effective computational prediction of the most stable polymorph could save significant time and effort in the design of novel molecular crystalline solids or predict their behavior under new conditions. In this study, we introduce a new approach using multistate reweighting to address the problem of determining solid-solid phase diagrams and apply this approach to the phase diagram of solid benzene. For this approach, we perform sampling at a selection of temperature and pressure states in the region of interest. We use multistate reweighting methods to determine the reduced free energy differences between T and P states within a given polymorph and validate this phase diagram using several measures. The relative stability of the polymorphs at the sampled states can be successively interpolated from these points to create the phase diagram by combining these reduced free energy differences with a reference Gibbs free energy difference between polymorphs. The method also allows for straightforward estimation of uncertainties in the phase boundary. We also find that when properly implemented, multistate reweighting for phase diagram determination scales better with the size of the system than previously estimated.

Effects of a More Accurate Polarizable Hamiltonian on Polymorph Free Energies Computed Efficiently by Reweighting Point-Charge Potentials.

We examine the free energies of three benzene polymorphs as a function of temperature in the point-charge OPLS-AA and GROMOS54A7 potentials as well as the polarizable AMOEBA09 potential. For this system, using a polarizable Hamiltonian instead of the cheaper point-charge potentials is shown to have a significantly smaller effect on the stability at 250 K than on the lattice energy at 0 K. The benzene I polymorph is found to be the most stable crystal structure in all three potentials examined and at all temperatures examined. For each potential, we report the free energies over a range of temperatures and discuss the added value of using full free energy methods over the minimized lattice energy to determine the relative crystal stability at finite temperatures. The free energies in the polarizable Hamiltonian are efficiently calculated using samples collected in a cheaper point-charge potential. The polarizable free energies are estimated from the point-charge trajectories using Boltzmann reweighting with MBAR. The high configuration-space overlap necessary for efficient Boltzmann reweighting is achieved by designing point-charge potentials with intramolecular parameters matching those in the expensive polarizable Hamiltonian. Finally, we compare the computational cost of this indirect reweighted free energy estimate to the cost of simulating directly in the expensive polarizable Hamiltonian.