(189av) Challenging Statistical Mechanics Approximations in Organic Crystal Thermodynamics

The physical and chemical properties of solid materials is largely influenced by the unique packing of the material, which becomes problematic when multiple solid forms, or polymorphs, exist. The particular packing of small organic molecules is of interest in fields such as as pharmaceutical formulation, organic electronics processing and explosives preservation. In recent decades, the focus has been on providing fast and efficient methods to predict favorable structures at any temperature of interest. When determining potential structures with computational methods the entropic and temperature effects cannot be neglected. Much of the work in crystal structure predictions are focused on predicting the static lattice energy landscape, which largely neglects the energy contributions due to crystal vibrations and thermal expansion.

The most accurate method to model organic material is through molecular dynamic simulations (MD), which account for all vibrational and thermal energy of the crystal lattice. With MD, our approach has developed a methods to compute the free energy difference between two crystal structures at a state point of interest, which can then be used with sample simulations at other state points to determine the free energy landscape at all temperature and pressures of interest. Alternatively, lattice dynamic (LD) approaches provide a less computationally demanding approach to determine the free energy of solid materials. We have also developed an approach to more efficiently to perform LD approaches, which now provides an easy approach to also perform anisotropic expansion.

These approaches have varying levels of accuracy and speed. The harmonic approximation (HA) uses only the lattice minimum harmonic vibrations to quickly compute the free energy. The drawback is that the HA does not account for thermal expansion and since all organic crystals expand with temperature most people use the quasi-harmonic approximation (QHA). Our new method for the QHA computes the gradient of thermal expansion of the crystal for either isotropic or anisotropic expansion to determine how the crystal geometry is altered as the temperature increases. Unfortunately, all three of these LD approaches fail to capture anharmonic vibrations, which effect the crystal energy at higher temperatures. To capture the full ensemble of crystal vibrations we compute the free energy differences between two crystals by moving each crystals along a reversible thermodynamic path to an ideal gas state at a single temperature point. Using sampled points at varying temperatures, we can compute the free energy differences between crystal polymorphs at all temperatures of interest.