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Computational Prediction of Effects of Pressure on Organic Crystal Structure

Andrei V. Kazantsev1, Panagiotis G. Karamertzanis1, Claire S. Adjiman1, and Constantinos C. Pantelides2. (1) Department of Chemical Engineering, Imperial College London, Centre for Process Systems Engineering, London, SW7 2AZ, United Kingdom, (2) Imperial College London / Process Systems Enterprise Ltd, Centre for Process Systems Engineering, London, SW7 2AZ, UK

The importance of polymorphism in crystal structures of organic molecules has been well recognized for many years. Interestingly, recent experimental studies1 have provided indications of the effectiveness of high pressure as an additional means for exploring this polymorphism. The present paper represents an examination of the extent to which state-of-the-art crystal structure prediction methods can be used to complement the experimental investigations.

We focus our study on a molecule of pharmaceutical interest, namely piracetam (2-oxo-1-pyrrolidine acetamide). Five distinct polymorphs have been identified experimentally for this molecule, two of which have been observed only at high pressure1. One of the polymorphs (Form V) is produced by the application of pressure to the most stable form at ambient conditions (Form II); this results in a direct reversible single-crystal to single-crystal transformation, a major characteristic of which is the shearing of the unit cell by ~10o.

A previous theoretical study2 of the crystal structure of piracetam pre-dated the experimental discovery of the high pressure Form V. Although piracetam possesses significant conformational flexibility, at the time of the previous study there were no reliable energy minimisation algorithms that could address flexibility directly. Instead, 400 rigid conformers were generated by sampling exhaustively all possible molecular conformations that the molecule could undertake around selected torsions at 0K and 0Pa. A crystal energy minimization was then undertaken for each of these “rigid” conformers. The intra-molecular energy contribution to the crystal energy was evaluated via a quantum mechanical calculation, whilst the inter-molecular interactions were computed using a distributed multipole expansion of the isolated-molecule charge density. The resulting structures obtained from the 400 separate calculations were then ranked together according to their total crystal energy. We further refined (and re-ranked) the most stable structures using DMAFlex3, an advanced local energy minimisation algorithm which addresses molecular flexibility directly.

A key conclusion of this earlier study was that the intra-molecular contribution to the crystal energy is very significant. Therefore, flexibility needs to be taken into account directly for investigating pressure-mediated transitions in greater detail, as molecular conformation is often altered during transformations and pressurisation.

In the study reported in this paper, a set of low-energy structures generated by the earlier study along with the experimentally resolved forms are pressurised in steps of 1GPa from 0 to 9 GPa. The DMAFlex algorithm is used to effect the minimization at each pressure level. It is shown that there is considerable re-ranking and increasing energy separation between independent forms as the pressure is raised. As a result, the number of independent, energy plausible structures is different at distinct pressures, demonstrating that a single search at one pressure is not sufficient to identify all energy plausible structures that may occur at higher pressures.

The Form II to Form V reversible transition on the application of pressure was studied in more detail, both by pressurizing Form II and by de-pressurizing Form V. Below a pressure of about 3.5GPa, we were not able to obtain Form V: any attempt at minimizing crystal enthalpy starting from this structural form resulted in a Form II crystal. This appears to be in agreement with the fact that Form V has not been observed experimentally at low pressures.

Above 3.5GPa, we were able to obtain both forms. The crystal enthalpy of Form V is computed to be slightly higher than that of Form II at all pressures, but the energy difference is small compared to the total energy and to the various approximations involved in the computational model. Therefore, at ambient temperature, entropic contributions to the free energy may be the factor determining the relative stability of the two forms and indeed the pressure at which the transition between them occurs.




[1] Fabbiani, F.P.A. et al; Cryst. Gr. Des. 7, 1115 (2007)

[2] Nowell, H. and Price, S.L.; Acta Cryst., B61, 558, (2005)

[3] Karamertzanis, P. G. and Price S. L.; J. Chem. Theory Comput., 2, 1184 (2006)