Empirically augmented density functional theory for predicting lattice energies of aspirin, acetaminophen polymorphs, and ibuprofen homochiral and racemic crystals

Purpose. Lattice energies of drug crystals are closely associated with many important physicochemical properties including polymorphism of the crystals. Current quantum mechanical methods that can be applied to calculate the lattice energy of most drug crystals are not capable of fully considering the van der Waals interaction energy, a dominant component in the lattice energy. Herein, we report the results of using empirically augmented quantum mechanical methods for predicting the lattice energies of selected drug crystals. Methods. Long-range van der Waals energies were evaluated by atom-atom pairwise C-6 R-6 functions that were damped at short interatomic distance where interatomic interactions could be better evaluated by density functional theory (DFT). The atomic C-6 coefficients were taken from literature, and three damping functions were tested. For the quantum mechanical calculations, different basis sets were tested with aspirin as the model system. Basis set superposition error (BSSE) was considered. In addition to aspirin, acetaminophen Form I and Form II, and s(+)- and (+/-)-ibuprofen were calculated and the results were compared to experimental values. Experimentally determined single crystal structures were optimized prior to both empirical and DFT energy calculations. Results. Lattice energies calculated by the empirically augmented quantum mechanical methods are in very good agreement with experimental values, suggesting the approach is acceptable. The results also indicate that the long-range van der Waals or dispersion energy is a significant part of the lattice energy, which cannot be accurately estimated by the DFT methods alone. Conclusions. Due to the empirical nature for estimating the dispersion energy, choosing the right empirical parameters is crucial. The methods and parameters tested seem to be able to produce reliable values of lattice energies of the drug crystals.