Predicting polymorphism in molecular crystals using orientational entropy (1806.06006v1)

Abstract: 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 time scale much longer than that of molecular simulations. In order 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 collective variable an entropy surrogate based on an extended pair correlation function that includes the correlation between the orientation 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 find all relevant polymorphs for both substances and we predict new polymorphs. One of them is stabilized at finite temperature by entropic effects.

• The paper presents a novel computational method using orientational entropy and well-tempered metadynamics to predict molecular crystal polymorphs from liquid phase simulations.
• The methodology successfully identified known polymorphs and predicted a new entropically stabilized form (form B) for urea, demonstrating the crucial role of entropy at finite temperatures.
• This approach offers a computationally feasible strategy with significant implications for pharmaceuticals and potential extension to more complex molecular systems.

Predicting Polymorphism in Molecular Crystals Using Orientational Entropy

Polymorphism in molecular crystals, the ability of a substance to crystallize into multiple structures, presents fascinating challenges and opportunities both from theoretical and practical perspectives. The paper by Pablo M. Piaggi and Michele Parrinello addresses the complexities of predicting polymorphic outcomes in molecular crystallization through a novel computational approach driven by orientational entropy.

Study Focus and Methodology

The central aim of this paper is to develop a methodology for predicting polymorphic forms of molecular crystals at finite temperatures—a task traditionally constrained by the enormously long timescales associated with crystallization processes, which far exceed those typical of molecular simulations. Leveraging the concept of orientational entropy through the introduction of well-tempered metadynamics, the authors employ an entropy surrogate collective variable to enhance sampling and facilitate the discovery of polymorphic structures directly from the liquid phase.

Key to this approach is the use of an extended pair correlation function, $g(r, \theta)$, which incorporates both positional and orientational correlations among molecules in the crystal. This enables a measure of orientational entropy, $S_{\theta}$, that serves as a collective variable driving the metadynamic simulations. A novel similarity metric based on generalized Kullback-Leibler divergence complements this framework by enabling the automatic classification and comparison of different polymorphic forms through hierarchical clustering.

Numerical and Theoretical Insights

The simulations conducted using this methodology successfully identified all relevant polymorphs of the molecules studied, including urea and naphthalene. Remarkably, for urea, the paper predicted a new polymorph, form B, stabilized by entropic contributions at finite temperature—a promising demonstration of the model's capability to uncover entropically governed structures that might be overlooked by traditional zero-temperature approaches augmented with harmonic corrections. Particularly, form B was distinguished by a significant entropic stabilization, highlighting the critical role of entropy in polymorphic stability.

The investigation of these molecular systems indicates substantial orientation-related entropic effects that the model captures effectively, underscoring the importance of capturing both entropic and enthalpic contributions in polymorph prediction. The methodology can detect, classify, and provide insights into the free energy landscapes of different polymorphs, which is instrumental in guiding experimental screening processes.

Implications and Future Directions

The integration of orientational entropy in polymorph prediction holds notable implications for sectors such as pharmaceuticals, where the understanding and control of polymorphic forms are crucial to the development and patentability of drugs. This paper's approach alleviates some of the limitations intrinsic to conventional crystallization models, offering a computationally feasible and theoretically sound strategy to predict polymorphism in complex molecular systems.

Looking forward, further advancements could envisage extending these methods to molecular systems with more complex arrangements, including hydrogen-bonded networks or flexible molecules with internal degrees of freedom. This broader application could provide profound insights into the intricate interplay of forces that govern polymorph stability and transformation under diverse conditions. Moreover, refinement of computational efficiency and accuracy will certainly be pivotal as these models scale towards increasingly varying and larger system sizes in practical applications.

Overall, this paper contributes significantly to the computational toolkit available for polymorph prediction, marrying theoretical innovation with practical application in the predictive modeling of crystalline systems.