(86c) An Atomistic Lattice Dynamics Approach for Free Energy Calculations within Crystal Structure Prediction Studies

A plethora of organic molecules exhibit polymorphism, which refers to the ability of chemical compounds to pack into different crystalline motifs. This phenomenon is of special importance both to industry and academia since physical and chemical properties, such as solubility, bioavailability and mechanical strength may vary tremendously between polymorphs. From a thermodynamic standpoint, polymorphs can be identified as minima on the free energy (FE) landscape, with the most stable form corresponding to the global minimum and other forms corresponding to local minima (metastable structures). This thermodynamic understanding has motivated the development of crystal structure prediction (CSP) tools that are designed to determine all polymorphs for a given compound with the correct order of stability based on minimal information, such as the chemical connectivity diagram¹.

Recent advances in CSP were highlighted in the last blind test organised by Cambridge Crystallographic Data Centre². It is worth noting that only 7 out of the 25 groups participating in the last test have incorporated FE calculations within their workflow, while the remaining groups used only lattice energy in their predictions, thus neglecting temperature and vibrational effects. Lattice dynamics (LD) theory was deployed successfully for the evaluation of vibrational free energies, utilizing either dispersion-corrected periodic density functional theory^3,4 (DFT-d) or force field methods based on distributed multipoles expansion^5,6,7 (DMA). DFT-d can provide very accurate results at a high computational cost, whereas the DMA-based approach provides a good trade-off between accuracy and efficiency but cannot account for internal modes arising from intramolecular vibrations. A limitation of both methods is that they rely on the construction of supercells, which increases computational demands and results in some ambiguity in the generation of dispersion curves.

In this work, we present a recently-developed methodology⁸ for performing atomistic lattice dynamics calculations, which is suitable for conducting FE calculations for a large number (>100) of structures generated in CSP studies. This methodology is based on LD theory within the harmonic approximation, with intramolecular interactions quantified by isolated quantum mechanical calculations⁹. The intermolecular interactions are partitioned into electrostatics and repulsion/dispersion interactions and are modelled using ab initio distributed multipoles and a semi empirical potential, respectively. To illustrate the approach, we apply a multistage CSP methodology to tetracyanoethylene (C₆N₄), a small planar molecule. The global search stage is performed using the CrystalPredictorII^10,11 for the generation of candidate structures. The lowest energy structures, within 20kJ/mol from the global minimum in lattice energy, are minimised atomistically using CrystalOptimizer¹² yielding 837 unique structures after clustering. We evaluate the vibrational free energy of the 200 most promising structures, using our in-house LD algorithm⁸, for the determination of polymorphic stability, entropy, heat capacity and thermal energy in a temperature range between 0 and 400K.

References:

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(12) Kazantsev, A. V.; Karamertzanis, P. G.; Adjiman, C. S.; Pantelides, C. C. Efficient Handling of Molecular Flexibility in Lattice Energy Minimization of Organic Crystals. J. Chem. Theory Comput. 2011, 7, 1998–2016.