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

Abstract

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.

Reply to “Comment on ‘High-pressure phases of group-II difluorides: Polymorphism and superionicity’ ”

“…We also remark that in the QHA, the free energy surfaces of the γ and P 62m phases are almost parallel ( Fig. 6 of [1]), which introduces uncertainty in calculating their high-T intersections [7].…”

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

“…To obtain the phase diagrams of Lennard-Jones spheres using full molecular dynamics, we used the Successive Interpolation of Multistate Reweighting (SIMR) method. 13 This method combines the reduced free energy difference values between temperature and pressure states within a polymorph, defined as βG, and a reference Gibbs free energy difference between polymorphs at the same temperature, which can then be combined to obtain the Gibbs free energy difference between polymorphs at all temperatures and pressures in the region of interest.…”

“…The uncertainty in the coexistence points using this method is found in equation 3 where δd is the magnitude of the uncertainty in the coexistence line perpendicular to the line, and δ∆G is the uncertainty in the free energy at a point along the coexistence line. Full details of this method can be found in Schieber et al 13 In theory, reweighting can be used to refine estimates in between coexistence points rather than direct interpolation but this is less reliable in the case of configuration mapping, as described below.…”

“…One requirement for simulations used for the SIMR method is that simulations adjacent in temperature or pressure have a non-negligible amount of phase space overlap, 13 as defined in equation 4. Conceptually this means that simulations have some set of configurations that they both sample.…”

“…11,12 We have previously introduced the Successive Interpolation of Multistate Reweighting (SIMR) method to predict solid-solid phase diagrams. 13 This methodology does not rely on lattice dynamics, and thus is applicable in systems that are far from harmonic. It calculates the phase diagram from direct calculation of the relative Gibbs free energy using a series of direct molecular dynamics or Monte Carlo simulations without any specialized sampling techniques.…”