(557b) Modeling and Prediction of the Crystal Structure of Pharmaceutical Co-Crystals

Pharmaceutical
co-crystals, comprising an active pharmaceutical ingredient (API) and another
pharmaceutically acceptable molecule, can be used to address intellectual and
physical property issues in pharmaceutical development without changing the
chemical composition of the API. The search for suitable co-crystals is
hindered by the lack of computational tools to investigate whether the
formation of the heteromeric is thermodynamically favoured over the homomeric
crystals, and predict their structures.

This
paper presents a novel methodology for the prediction of co-crystal structures,
based only on the atomic connectivity of the component molecules and assumed
stiochiometry. The method uses global crystal energy minimisation, for both the
single- and two-component crystals. This allows a comparison of the relative
stability of the co-crystal with respect to the energies of the two
pure-component crystals, and can therefore predict when co-crystal formation is
thermodynamically favoured.

Crystal structure prediction of co-crystals is a challenging
problem because of the presence of two, often flexible, crystallographically
independent molecules in the asymmetric unit. Hence, a search that is
sufficiently broad to reliably locate all energetically competitive minima on
the crystal energy surface can typically be performed only with empirical,
computationally inexpensive models that may lack sufficient realism for
accurate prediction of relative energies. Therefore, the results of such a
search need to be refined using more accurate models for both the intra- and
inter-molecular contributions to the lattice energy.

In
this paper, we propose a 3-stage algorithm:

·        
Stage I: Global Search for
low-energy minima.

This is carried out using an approach¹
based on low-discrepancy sequences. The intramolecular energy is approximated 
using Hermite interpolants² on
a grid of isolated-molecule energies, and its gradients with respect to all
torsion angles that can be affected by intermolecular forces. The grid is
pre-calculated using a number of quantum mechanical energy minimisations. The
intermolecular interactions are modelled using a computationally inexpensive
isotropic model, comprising an empirical repulsion-dispersion potential^3;4
and a set of conformationally invariant atomic charges.

·        
Stage II: Re-ranking of
low-energy crystal structures based on improved electrostatic interactions.

The low-energy minima computed at Stage I are used as
initial points for local energy minimisations. In this case, intramolecular
energy and intermolecular repulsion-dispersion contributions are computed as at
Stage I, but the intermolecular electrostatic interactions are modelled⁵ by
a set of distributed multipole moments on each atom up to hexadecapole.⁶ The
variation of the charge density with conformation is restricted to the analytic
rotation of the atomic multipole moments with the local environment of each
atom.

·        
Stage III: Re-ranking of
low-energy crystal structures based on conformation-dependent electrostatic
interactions and accurate intramolecular energies.

The low-energy minima computed at Stage II are used as
initial points for local energy minimisations involving a nested 2-level
optimisation approach.⁷ The
outer level manipulates the molecular conformation (i.e. the flexible torsion
angles) while the inner one determines the optimal crystal structure for a
molecule of fixed conformation (as determined by the current outer iteration).
The intra-molecular energy and the atomic multipole moments are determined at
each outer iteration using ?on-the-fly? quantum mechanical calculations. Given
the cost of this calculation, Stage III is applied only to very few
(lowest-energy) crystal structures determined by Stage II.

The above algorithm is applied to the prediction of
the structure of the co-crystals of p-aminobenzoic acid with 2,2'-bipyridine.
The application of the algorithm to pure p-aminobenzoic acid resulted in its
low-temperature polymorph⁸
being ranked 1^st i.e. being identified as the one of lowest energy.
The experimentally known crystal structure⁹ of 
2,2'-bipyridine was ranked 2^nd. The known p-aminobenzoic acid/2,2'-bipyridine
crystal structure¹⁰ is
also ranked 1^st. Since its energy is almost equal to the sum of the
global minimum crystal energies of the component molecules, the predicted
thermodynamic driving force for forming the cocrystal is small. We discuss the
limitations of this methodology, including the possibility that p-aminobenzoic
- 2,2'-bipyridine co-crystal formation may be kinetically rather than
thermodynamically driven.

Keywords: co-crystals, crystal structure prediction,
polymorphism, global optimisation

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