Mapping coexistence lines via free-energy extrapolation: Application to order-disorder phase transitions of hard-core mixtures

In recent years, several relatively similar empirical models of titanium dioxide have been proposed as reparameterisations of the potential of Matsui and Akaogi, with the Buckingham interaction replaced by a Lennard-Jones interaction. However, because of the steepness of the repulsive region of the Lennard-Jones potential, such reparameterised models result in rather different mechanical and thermodynamic properties compared to the original potential. Here, we use free-energy calculations based on the Einstein crystal method to compute the phase diagram of both the Matsui-Akaogi potential and one of its Lennard-Jones-based reparameterisations. Both potentials are able to support a large number of distinct crystalline polymorphs of titanium dioxide that have been observed in experiment, but the regions of thermodynamic stability of the individual phases are significantly different from one another. Moreover, neither potential results in phase behaviour that is fully consistent with the available experimental evidence. arXiv:1908.03497v1 [cond-mat.stat-mech]

Section: Phase Diagrams and Free-energy Calculationsmentioning

confidence: 99%

Phase behavior of empirical potentials of titanium dioxide

Reinhardt

2019

“…The principles behind such an expansion are hardly new, especially in the canonical ensemble, 15,19 and similar concepts have been applied to estimate fluid phase coexistence from grand canonical and Gibbs ensemble Monte Carlo simulations in the past. 20–25 However, these efforts have focused on extrapolating unbiased simulations which only sample the phase space relatively near to the most likely macrostates at a given condition; consequently, these approaches only yield reasonable predictions relatively close to the original simulation’s state point. By invoking flat-histogram methods to explore a broad range of predefined macrostates, we anticipate that these principles can be used to make predictions over an even more broad range of conditions.…”

Section: Introductionmentioning

confidence: 99%

Multivariable extrapolation of grand canonical free energy landscapes

Mahynski

Errington

Shen

2017

We derive an approach for extrapolating the free energy landscape of multicomponent systems in the grand canonical ensemble, obtained from flat-histogram Monte Carlo simulations, from one set of temperature and chemical potentials to another. This is accomplished by expanding the landscape in a Taylor series at each value of the order parameter which defines its macrostate phase space. The coefficients in each Taylor polynomial are known exactly from fluctuation formulas, which may be computed by measuring the appropriate moments of extensive variables that fluctuate in this ensemble. Here we derive the expressions necessary to define these coefficients up to arbitrary order. In principle, this enables a single flat-histogram simulation to provide complete thermodynamic information over a broad range of temperatures and chemical potentials. Using this, we also show how to combine a small number of simulations, each performed at different conditions, in a thermodynamically consistent fashion to accurately compute properties at arbitrary temperatures and chemical potentials. This method may significantly increase the computational efficiency of biased grand canonical Monte Carlo simulations, especially for multicomponent mixtures. Although approximate, this approach is amenable to high-throughput and data-intensive investigations where it is preferable to have a large quantity of reasonably accurate simulation data, rather than a smaller amount with a higher accuracy.

“…Another existing phase diagram prediction method, free energy extrapolation 33 , finds the slope of the free energy surface and extrapolates it to nearby points to find coexistence points. In this method, the probability of a configuration in a simulation having a certain volume and energy is assumed to be a Gaussian.…”

Section: Introductionmentioning

confidence: 99%

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

Schieber

Dybeck

Shirts

2018

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.