Collective Variables for Conformational Polymorphism in Molecular Crystals

Toward On-Demand Polymorphic Transitions of Organic Crystals via Side Chain and Lattice Dynamics Engineering

Controlling polymorphism, namely, the occurrence of multiple crystal forms for a given compound, is still an open technological challenge that needs to be addressed for the reliable manufacturing of crystalline functional materials. Here, we devised a series of 13 organic crystals engineered to embody molecular fragments undergoing specific nanoscale motion anticipated to drive cooperative order-disorder phase transitions. By combining polarized optical microscopy coupled with a heating/cooling stage, differential scanning calorimetry, X-ray diffraction, low-frequency Raman spectroscopy, and calculations (density functional theory and molecular dynamics), we proved the occurrence of cooperative transitions in all the crystalline systems, and we demonstrated how both the molecular structure and lattice dynamics play crucial roles in these peculiar solid-to-solid transformations. These results introduce an efficient strategy to design polymorphic molecular crystalline materials endowed with specific molecular-scale lattice and macroscopic dynamics.

Theoretical Investigation into Polymorphic Transformation between β-HMX and δ-HMX by Finite Temperature String

Polymorphic transformation is important in chemical industries, in particular, in those involving explosive molecular crystals. However, due to simulating challenges in the rare event method and collective variables, understanding the transformation mechanism of molecular crystals with a complex structure at the molecular level is poor. In this work, with the constructed order parameters (OPs) and K-means clustering algorithm, the potential of mean force (PMF) along the minimum free-energy path connecting β-HMX and δ-HMX was calculated by the finite temperature string method in the collective variables (SMCV), the free-energy profile and nucleation kinetics were obtained by Markovian milestoning with Voronoi tessellations, and the temperature effect on nucleation was also clarified. The barriers of transformation were affected by the finite-size effects. The configuration with the lower potential barrier in the PMF corresponded to the critical nucleus. The time and free-energy barrier of the polymorphic transformation were reduced as the temperature increased, which was explained by the pre-exponential factor and nucleation rate. Thus, the polymorphic transformation of HMX could be controlled by the temperatures, as is consistent with previous experimental results. Finally, the HMX polymorph dependency of the impact sensitivity was discussed. This work provides an effective way to reveal the polymorphic transformation of the molecular crystal with a cyclic molecular structure, and further to prepare the desired explosive by controlling the transformation temperature.

Buckets Instead of Umbrellas for Enhanced Sampling and Free Energy Calculations

Umbrella sampling has been a workhorse for free energy calculations in molecular simulations for several decades. In conventional umbrella sampling, restraining bias potentials are strategically applied along one or several collective variables. Major drawbacks associated with this method are the requirement of a large number of bias windows and the poor sampling of the transverse coordinates. In this work, we propose an alternate formalism that departs from the traditional umbrella sampling to mitigate these issues, where we replace umbrella-type restraining bias potentials with bucket-type wall potentials. This modification permits one to formulate an efficient computational strategy leveraging wall potentials and metadynamics sampling. This new method, called "bucket sampling", can significantly reduce the computational cost of obtaining converged high-dimensional free energy surfaces. Extensions of the proposed method with temperature acceleration and replica exchange solute tempering are also demonstrated.

Enhanced Sampling of Crystal Nucleation with Graph Representation Learnt Variables

In this study, we present a graph neural network (GNN)-based learning approach using an autoencoder setup to derive low-dimensional variables from features observed in experimental crystal structures. These variables are then biased in enhanced sampling to observe state-to-state transitions and reliable thermodynamic weights. In our approach, we used simple convolution and pooling methods. To verify the effectiveness of our protocol, we examined the nucleation of various allotropes and polymorphs of iron and glycine in their molten states. Our graph latent variables, when biased in well-tempered metadynamics, consistently show transitions between states and achieve accurate thermodynamic rankings in agreement with experiments, both of which are indicators of dependable sampling. This underscores the strength and promise of our GNN variables for improved sampling. The protocol shown here should be applicable for other systems and other sampling methods.

Finite temperature string by K-means clustering sampling with order parameters as collective variables for molecular crystals: application to polymorphic transformation between β-CL-20 and ε-CL-20

Polymorphic transformation of molecular crystals is a fundamental phase transition process, and it is important practically in the chemical, material, biopharmaceutical, and energy storage industries. However, understanding of the transformation mechanism at the molecular level is poor due to the extreme simulating challenges in enhanced sampling and formulating order parameters (OPs) as the collective variables that can distinguish polymorphs with quite similar and complicated structures so as to describe the reaction coordinate. In this work, two kinds of OPs for CL-20 were constructed by the bond distances, bond orientations and relative orientations. A K-means clustering algorithm based on the Euclidean distance and sample weight was used to smooth the initial finite temperature string (FTS), and the minimum free energy path connecting β-CL-20 and ε-CL-20 was sketched by the string method in collective variables, and the free energy profile along the path and the nucleation kinetics were obtained by Markovian milestoning with Voronoi tessellations. In comparison with the average-based sampling, the K-means clustering algorithm provided an improved convergence rate of FTS. The simulation of transformation was independent of OP types but was affected greatly by finite-size effects. A surface-mediated local nucleation mechanism was confirmed and the configuration located at the shoulder of potential of mean force, rather than overall maximum, was confirmed to be the critical nucleus formed by the cooperative effect of the intermolecular interactions. This work provides an effective way to explore the polymorphic transformation of caged molecular crystals at the molecular level.