Understanding thermodynamic properties at the molecular level: multiple temperature charge density study of ribitol and xylitol.

X-ray diffraction data of high quality measured to high resolution on crystals of the two pentitol epimers ribitol (centric) and xylitol (acentric) at 101, 141, and 181 K and data on the two compounds previously recorded at 122 K have formed the basis for multipole refinements with the VALRAY system. Our analysis showed that it is possible to obtain a reliable crystal electron density for an acentric compound (xylitol) from X-ray diffraction data and that the thermal motion can be deconvoluted from the static density in this temperature range. The Bader-type topological analysis of the static electron densities revealed virtually identical intramolecular interactions as well as very similar hydrogen bond interactions of ribitol and xylitol; the only minor differences are found in the weaker intermolecular interactions. The high-level periodic DFT calculations are in accordance with the thermodynamic measurements that show that the two pentitols have identical sublimation energies. A rigid body normal coordinate analysis was performed on the atomic displacement parameters obtained at the four different temperatures. The translational and librational mean square deviations derived through this analysis were used in a quantum statistical approach to derive frequencies of the corresponding harmonic oscillators. The analysis showed a consistent vibrational model for all temperatures. The frequencies were subsequently used to calculate crystal entropies assuming an Einstein-type behavior. These calculations show that the crystal entropy of ribitol is 8 J K(-1) mol(-1) higher than the crystal entropy of xylitol, confirming that it is a difference in the entropy of the two compounds that causes the difference in their free energy. Our results presented in this Article show the potential to use X-ray diffraction data to obtain physicochemical properties of crystals.