X-ray diffraction data as a source of the vibrational free-energy contribution in polymorphic systems

Abstract

As with most research, our work would not have been possible without standing on the shoulders of giants. In this case we have stood on the shoulders of Professor Jack Dunitz and the late Professor Håkon Hope. We would like to pay tribute to Professor Dunitz's many contributions to crystallography, including his work on the compounds studied here: the polymorphs of di­methyl 3,6-di­chloro-2,5-di­hydroxy­terephthalate. Professor Hope was a true pioneer in the use of low-temperature crystallography and without his help and guidance our helium-cooled 5 K experiments would not have been possible.

In this contribution we attempt to answer a general question: can X-ray diffraction data combined with theoretical computations be a source of information about the thermodynamic properties of a given system? Newly collected sets of high-quality multi-temperature single-crystal X-ray diffraction data and complementary periodic DFT calculations of vibrational frequencies and normal mode vectors at the Γ point on the yellow and white polymorphs of di­methyl 3,6-di­chloro-2,5-di­hydroxy­terephthalate are combined using two different approaches, aiming to obtain thermodynamic properties for the two compounds. The first approach uses low-frequency normal modes extracted from multi-temperature X-ray diffraction data (normal coordinate analysis), while the other uses DFT-calculated low-frequency normal mode in the refinement of the same data (normal mode refinement). Thermodynamic data from the literature [Yang et al. (1989), Acta Cryst. B45, 312–323] and new periodic ab initio DFT supercell calculations are used as a reference point. Both approaches tested in this work capture the most essential features of the systems: the polymorphs are enantiotropically related, with the yellow form being the thermodynamically stable system at low temperature, and the white form at higher temperatures. However, the inferred phase transition temperature varies between different approaches. Thanks to the application of unconventional methods of X-ray data refinement and analysis, it was additionally found that, in the case of the yellow polymorph, anharmonicity is an important issue. By discussing contributions from low- and high-frequency modes to the vibrational entropy and enthalpy, the importance of high-frequency modes is highlighted. The analysis shows that larger anisotropic displacement parameters are not always related to the polymorph with the higher vibrational entropy contribution.