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Einstein-Debye model for density-functional prediction of vibrational free energies of molecular crystals
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DOI：10.1039/d6cp00089d.png)
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Abstract
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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, Fvib, 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 Fvib, with a computational cost that is up to 4.5 times lower. Considering the magnitudes of free-energy differences between polymorphs, |Delta Fvib|, 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 Delta Fvib 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.
Keywords:
Einstein-Debye approximation
vibrational free energy
molecular crystals
density-functional theory
crystal structure prediction
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