Pablo M. Piaggi

Enhancing Entropy and Enthalpy Fluctuations to Drive Crystallization in Atomistic Simulations

Crystallization is a process of great practical relevance in which rare but crucial fluctuations lead to the formation of a solid phase starting from the liquid. As in all first order first transitions, there is an interplay between enthalpy and entropy. Based on this idea, in order to drive crystallization in molecular simulations, we introduce two collective variables, one enthalpic and the other entropic. Defined in this way, these collective variables do not prejudge the structure into which the system is going to crystallize. We show the usefulness of this approach by studying the cases of sodium and aluminum that crystallize in the bcc and fcc crystalline structures, respectively. Using these two generic collective variables, we perform variationally enhanced sampling and well tempered metadynamics simulations and find that the systems transform spontaneously and reversibly between the liquid and the solid phases.

Entropy based fingerprint for local crystalline order

We introduce a new fingerprint that allows distinguishing between liquid-like and solid-like atomic environments. This fingerprint is based on an approximate expression for the entropy projected on individual atoms. When combined with local enthalpy, this fingerprint acquires an even finer resolution and it is capable of discriminating between different crystal structures.

A Cannibalistic Approach to Grand Canonical Crystal Growth

Canonical molecular dynamics simulations of crystal growth from solution suffer from severe finite-size effects. As the crystal grows, the solute molecules are drawn from the solution to the crystal, leading to a continuous drop in the solution concentration. This is in contrast to experiments in which the crystal grows at an approximately constant supersaturation of a bulk solution. Recently, Perego et al. [ J. Chem. Phys. 2015, 142, 144113] showed that in a periodic setup in which the crystal is represented as a slab, the concentration in the vicinity of the two surfaces can be kept constant while the molecules are drawn from a part of the solution that acts as a molecular reservoir. This method is quite effective in studying crystallization under controlled supersaturation conditions. However, once the reservoir is depleted, the constant supersaturation conditions cannot be maintained. We propose a variant of this method to tackle this depletion problem by simultaneously dissolving one side of the crystal while letting the other side grow. A continuous supply of particles to the solution due to the crystal dissolution maintains a steady solution concentration and avoids reservoir depletion. In this way, a constant supersaturation condition can be maintained for as long as necessary. We have applied this method to study the growth and dissolution of urea crystal from water solution under constant supersaturation and undersaturation conditions, respectively. The computed growth and dissolution rates are in good agreement with those obtained in previous studies.

Predicting polymorphism in molecular crystals using orientational entropy

Significance Small organic molecules often exhibit an amazing polymorphism. Since most drugs are based on organic molecules, this has important practical consequences. Not only does the deliverability of the drugs depend on the crystal structure but also different polymorphs can be separately patented. We address this problem by appropriately designed enhanced sampling simulations that start from the liquid and let the system crystallize spontaneously at the freezing temperature. In such a way entropy effects are automatically included. We successfully apply the method to the cases of urea and naphthalene and discover that entropy plays an important role. We introduce a computational method to discover polymorphs in molecular crystals at finite temperature. The method is based on reproducing the crystallization process starting from the liquid and letting the system discover the relevant polymorphs. This idea, however, conflicts with the fact that crystallization has a timescale much longer than that of molecular simulations. To bring the process within affordable simulation time, we enhance the fluctuations of a collective variable by constructing a bias potential with well-tempered metadynamics. We use as a collective variable an entropy surrogate based on an extended pair correlation function that includes the correlation between the orientations of pairs of molecules. We also propose a similarity metric between configurations based on the extended pair correlation function and a generalized Kullback–Leibler divergence. In this way, we automatically classify the configurations as belonging to a given polymorph, using our metric and a hierarchical clustering algorithm. We apply our method to urea and naphthalene. We find different polymorphs for both substances, and one of them is stabilized at finite temperature by entropic effects.

Molecular dynamics simulations of liquid silica crystallization

Significance Silica is one of the most abundant minerals in Earth’s crust and since the dawn of civilization its use has accompanied mankind’s technological evolution. Understanding crystallization is crucial in many industrial processes as well as in geology. Although experiments and simulations are difficult, we are able to perform an atomistic simulation of the β-cristobalite crystallization using an enhanced sampling method that uses as input only the intensity of the highest X-ray diffraction peak of β-cristobalite. Silica is one of the most abundant minerals on Earth and is widely used in many fields. Investigating the crystallization of liquid silica by atomic simulations is of great importance to understand the crystallization mechanism; however, the high crystallization barrier and the tendency of silica to form glasses make such simulations very challenging. Here we have studied liquid silica crystallization to β-cristobalite with metadynamics, using X-ray diffraction (XRD) peak intensities as collective variables. The frequent transitions between solid and liquid of the biased runs demonstrate the highly successful use of the XRD peak intensities as collective variables, which leads to the convergence of the free-energy surface. By calculating the difference in free energy, we have estimated the melting temperature of β-cristobalite, which is in good agreement with the literature. The nucleation mechanism during the crystallization of liquid silica can be described by classical nucleation theory.