First principle lattice energy calculations for enantiopure and racemic crystals of α-(trifluoromethyl)lactic acid: Is self-disproportionation of enantiomers controlled by thermodynamic stability of crystals?

Abstract

The lattice energies for the enantiopure and racemic crystals of α-(trifluoromethyl)lactic acid were calculated by a combination of the DFT calculations with the periodic boundary condition and the MP2 calculations of the interactions with neighboring molecules. The lattice energies calculated for the two crystals (−16.56 and −17.35 kcal/mol, respectively) show that the racemic crystals are thermodynamically more stable, although the racemic crystals sublime faster than the enantiopure crystals. The calculations suggest that the relative thermodynamic stability is not the cause of the faster sublimation rate of the racemic crystals compared with the enantiopure crystals. Although the crystals have hydrogen-bonding networks, the dispersion interactions contribute to the lattice energies significantly. The MP2 calculations for the evaluation of the dispersion interactions with the neighboring molecules are important for an accurate evaluation of the lattice energies. The relative thermodynamic stability of the two crystals is not determined solely by the hydrogen bonds. The interactions with other neighboring molecules also play important roles in determining the relative stability. We demonstrate that the geometry optimization is essential for an accurate evaluation of the lattice energy by the first principle calculation. The interaction energies calculated using the structure by X-ray diffraction often have large errors.