(136d) Can Lattice Dynamics with Anisotropic and Isotropic Thermal Expansion Accurately Estimate Thermodynamic Properties of Crystals Pharmaceutics Compared to Molecular Dynamics?

We compare three lattice dynamics methods to determine to what extent they can capture the free energy differences of organic polymorphs in comparison to full molecular dynamics (MD). Efficient methods to determine favorable crystalline structures of small organic molecules is pharmaceutically relevant in the drug development process. For different polymorphs the physical and chemical properties can vary significantly, which can lead to legal and production issues. Experimental approaches to capture all polymorphs are costly and time consuming. Alternatively, current computational methods are able to exhaustively search for the lattice minimum structures, but fail to emphasize the importance of entropic effects. While MD provides accuracy limited by the potential to capture thermal motion, the computational cost of the (quasi-)harmonic approximation (lattice dynamics) is far more feasible to use in a full scale crystal structure prediction.

We have implemented three lattice dynamic methods to determine what level of thermal expansion is required to compute the thermodynamic properties of small organic polymorphs in varying size and torsional degrees of freedom. The fastest method is the harmonic approximation (HA), which neglects thermal expansion but includes the entropy of harmonic vibrations, giving at least a crude estimate for polymorphic free energy differences. We also examine the quasiharmonic approximations, including both isotropic and anisotropic expansion, using new methodology to make the anisotropic expansion computationally feasible. Finally, we compare the relative free energies versus temperature curves generated with MD to compare all lattice dynamic models to.

For small and rigid molecules (1,4-Diiodobenzene and resorcinol), where the entropic difference between polymorphs is constant, we found that isotropic QHA was sufficient in determining polymorph free energy differences within error of MD out to 300K. However, for more flexible molecules (chlorpropamide and tolbutamide) anisotropic-QHA is required to correct for failures with an isotropic model. We hypothesize that failures between our anisotropic thermal expansion model and MD is due to anharmonic motions, especially in the case of disordered crystals.