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

Area of Science:

• Crystallography
• Materials Science
• Computational Chemistry

Background:

• Determining thermodynamic properties of crystalline materials is crucial for understanding their behavior.
• X-ray diffraction (XRD) and theoretical computations offer complementary data for material characterization.
• Polymorphism in di-methyl 3,6-di-chloro,2,5-di-hydroxy-terephthalate presents an opportunity to study thermodynamic relationships.

Purpose of the Study:

• To investigate if combined X-ray diffraction data and theoretical computations can reliably determine thermodynamic properties.
• To analyze the thermodynamic relationship between the yellow and white polymorphs of di-methyl 3,6-di-chloro,2,5-di-hydroxy-terephthalate.
• To assess the influence of different computational approaches on the accuracy of thermodynamic property determination.

Main Methods:

• Collection of multi-temperature single-crystal X-ray diffraction data for yellow and white polymorphs.
• Periodic Density Functional Theory (DFT) calculations of vibrational frequencies and normal mode vectors.
• Application of two methods: normal coordinate analysis and normal mode refinement using XRD data.
• Comparison with literature data and *ab initio* DFT supercell calculations.

Main Results:

• Both yellow and white polymorphs are enantiotropically related.
• The yellow polymorph is stable at low temperatures, while the white polymorph is stable at higher temperatures.
• Different methods yielded varying phase transition temperatures.
• Anharmonicity was identified as a significant factor in the yellow polymorph.
• High-frequency vibrational modes significantly contribute to vibrational entropy and enthalpy.
• Larger anisotropic displacement parameters do not always correlate with higher vibrational entropy.

Conclusions:

• Combined X-ray diffraction and theoretical computations can provide valuable insights into thermodynamic properties.
• The study successfully characterized the enantiotropic relationship and temperature-dependent stability of the polymorphs.
• The importance of considering anharmonicity and high-frequency modes for accurate thermodynamic property determination was emphasized.