(515f) Computational Prediction of Effects of Pressure on Organic Crystal Structure

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 ~10^o.

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.

References

[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)