Enthalpy of Sublimation in the Study of the Solid State of Organic Compounds. Application to Erythritol and Threitol A. J. Lopes Jesus, Luciana I. N. Tome ´ , M. Ermelinda Euse ´ bio,* and J. S. Redinha Department of Chemistry, UniVersity of Coimbra, 3004-535, Coimbra, Portugal ReceiVed: March 30, 2005; In Final Form: July 5, 2005 The enthalpies of sublimation of erythritol and L-threitol have been determined at 298.15 K by calorimetry. The values obtained for the two diastereomers differ from one another by 17 kJ mol -1 . An interpretation of these results is based on the decomposition of this thermodynamic property in a term coming from the intermolecular interactions of the molecules in the crystal (Δ int H°) and another one related with the conformational change of the molecules on going from the crystal lattice to the most stable forms in the gas phase (∆ conf H°). This last term was calculated from the values of the enthalpy of the molecules in the gas state and of the enthalpy of the isolated molecules with the crystal conformation. Both quantities were obtained by density functional theory (DFT) calculations at the B3LYP/6-311G++(d,p) level of theory. The results obtained in this study show that the most important contribution to the differences observed in the enthalpy of sublimation are the differences in the enthalpy of conformational change (13 kJ mol -1 ) rather than different intermolecular forces exhibited in the solid phase. This is explained by the lower enthalpy of threitol in the gas phase relative to erythritol, which is attributed to the higher strength of the intramolecular hydrogen bonds in the former. The comparison of the calculated infrared spectra obtained for the two compounds in the gas phase supports this interpretation. 1. Introduction The gas phase is commonly used as a reference state for thermodynamic properties on the grounds that at low pressure no account for the molecular interactions is needed. Hence, the tendency is to ascribe the differences of the molecular transfer process between a condensed state of matter and the gas state to molecular interactions in the former state. However, the structural differences in the gas state, even between similar compounds, are often big enough to affect the values determined experimentally for the transfer properties, sometimes exceeding those in the solid or liquid phase. This paper deals with the enthalpy of sublimation of erythritol and threitol, diastereomers of 1,2,3,4-butanetetrol, and uses this property in the study of the solid state of these compounds. To follow the sublimation process, we have to define three quantities: enthalpy of sublimation, ∆ sub H°, the variation of enthalpy associated with the transfer of the substance under consideration from the crystalline solid to gas phase; enthalpy of interaction, ∆ int H°, the change in enthalpy associated to a hypothetical process corresponding to one mole of infinitely separated molecules with the conformation of the crystal joining together to form a mole of crystalline form, and enthalpy of conformational change, ∆ conf H°, defined as the enthalpy in- volved in the change of 1 mol of substance from the conforma- tion in the crystal to the lowest Gibbs energy conformation in the gas state. Sublimation can be considered a process taking place in two steps: First, the molecules pass from the solid state to a hypothetical state consisting of isolated molecules retaining their conformation; second, the molecular conformation changes from the one in the solid state to the one characteristic of the gas state. Hence, the following relation holds for the enthalpy ∆ int H° can be determined if ∆ conf H° is calculated. In this work, the enthalpy of sublimation is determined by calorimetry. For obtaining the enthalpy of conformational change, one needs to know the enthalpy of the isolated molecules in the gas state as well as the enthalpy of the isolated molecules which retain the geometry exhibited in the crystal. Both quantities are derived by theoretical calculations at the DFT level. By combining the data obtained experimentally for ∆ sub H° with those obtained by theoretical calculations for the molecular conformation in the initial and final states, ∆ int H° is calculated from eq 1. This property is straightforwardly related with molecular interactions in the solid and can be identified with ∆ sub H° in cases for which ∆ conf H° is negligible. Another result from this research deserving to be pointed out is the contribution to the knowledge of the structure of compounds widely occurring in nature, that find numerous applications in food and pharmaceutical industries. 1,2 Indeed, erythritol is used as a sweetener in the vast market of “light” and “reduced caloric” products. As it meets most of the criteria of an ideal excipient for pharmaceutical formulations, it has become a promising ingredient in the pharmaceutical industry. Moreover, the knowledge of the structures of erythritol and threitol is a valuable contribution to understanding the structures of this important class of higher molecular weight polyols. 2. Materials and Experimental Methods The compounds under study were the best grade com- mercially available. The purity of erythritol, specified by the supplier Fluka, is higher than 99 mol %. The original substance was dried under vacuum at 353 K for 2 days before using. * To whom correspondence should be addressed. ∆ int H° )-∆ sub H° + ∆ conf H° (1) 18055 J. Phys. Chem. B 2005, 109, 18055-18060 10.1021/jp051621n CCC: $30.25 © 2005 American Chemical Society Published on Web 09/02/2005 Downloaded by PORTUGAL CONSORTIA MASTER on July 13, 2009 Published on September 2, 2005 on http://pubs.acs.org | doi: 10.1021/jp051621n