Einstein-Debye model for density-functional prediction of vibrational free energies of molecular crystals

Accurately predicting the relative free energies of polymorphic molecular crystals is an important aspect of crystal structure prediction (CSP), which has found considerable utility in solid-form pharmaceutical development to assess the risk of conversion to a more stable, late-appearing polymorph. In this work, we investigated the Einstein-Debye phonon approximation to evaluate the vibrational free energy, F_vib, in conjunction with dispersion-corrected density-functional theory. Three data sets were considered: (1) the "PV17" benchmark of seventeen polymorph pairs exhibiting little or no conformational flexibility; (2) four large, flexible compounds that appeared in previous CSP blind tests; and (3) a new "FP10" set of 10 highly flexible drug molecules that each have two or more known polymorphs. It was found that the Einstein-Debye approximation provides a good balance of accuracy and efficiency, giving mean absolute errors of ≤1.4 kJ mol^-1 relative to full supercell calculations of F_vib, with a computational cost that is up to 4.5 times lower. Considering the magnitudes of free-energy differences between polymorphs, |ΔF_vib|, a very broad distribution was observed, with average values in excess of 3 kJ mol^-1. In CSP studies of drug-like molecules, we recommend that ΔF_vib be considered for all candidate structures within at least ca. 6 kJ mol^-1 of the global electronic-energy minimum to provide a high probability of identifying the correct free-energy minimum.