The interactions of crystal faces in solution play a key role for the morphology of crystals and for the formation of crystal aggregates from liquid suspensions. The understanding and control of these phenomena is of crucial importance, especially for the development and formulation of new pharmaceutical compounds.

Experimentally the characterization of individual crystal faces with respect to their different interactions, i.e. dispersion, polarity, and hydrogen bond interactions, is very difficult. Only recently first quantitative results for the wetting angles of different solvents on different crystal faces of paracetamol have been measured based on sufficiently large single crystals. In this context computational modelling often is the only access to such properties, but the usual force-field based Monte-Carlo approaches for the calculation of the respective free energies are on the one hand extremely time consuming and often suffer from the insufficient accuracy of the underlying force-fields for the demanding chemical functionality often present in drug compounds.

In this paper we present an extension of the quantum chemically based COSMO-RS method to the calculation of free energies (and enthalpies ) of crystal faces in solution. COSMO-RS is a statistical thermodynamics of interacting molecular surfaces, based on the surface polarity information gained from DFT/COSMO calculations. COSMO-RS is widely validated in chemical engineering thermodynamics for the prediction of activity coefficients, solubilities and vapour pressures of demanding compounds in pure and mixed solvents. Here we present for the first time an extension which allows for the efficient calculation of the surface polarity (sigma-profile) of crystal faces. The sigma-profiles themselves already yield detailed information about the surface interactions of the various faces. Consecutive, very fast COSMO-RS calculations even more yield the free energies of the crystal faces per unit surface area in the different solvents, and hence allow for the prediction of surface tensions and wetting angels.

First results will be discussed and compared with the available experimental information for paracetamol. Further application ideas for the characterization of the agglomeration behaviour of crystallites will be presented.

[1] J.Y.Y. Heng and D.R. Williams, Langmuir 2006, 22, 6905-6909

[2] A. Klamt, "COSMO-RS: From Quantum Chemisty to Fluid Phase Thermodynamics and Drug Design", Elsevier, 2005