Modelling temperature-dependent properties of polymorphic organic molecular crystals

Abstract

We present a large-scale study of the temperature-dependence of structures, free energy differences and properties of polymorphic molecular organic crystals. Lattice-vibrational Gibbs free energy differences between 475 pairs of polymorphs of organic molecular crystals have been calculated at 0 K and at their respective melting points, using a highly accurate anisotropic multipole-based force field and including thermal expansion through the use of a (negative) thermal pressure. Re-ranking of the relative thermodynamic stability of the polymorphs in each pair indicates the possibility of an enantiotropic phase transition between the crystal structures, which occurs in 21% of the studied systems. While vibrational contributions to free energies can have a significant effect on thermodynamic stability, the impact of thermal expansion on polymorph free energy differences is generally very small. We also calculate thermal expansion coefficients for the 864 crystal structures and investigate the temperature-dependence of mechanical properties, and pairwise differences in these properties between polymorphs.

Fig. 1. Calculated phonon density of states for the monoclinic phase I of paracetamol as a function of temperature. The thermal expansion causes a shift in the density of states towards lower frequencies.

Fig. 2. Calculated volumetric thermal expansion (dashed lines) compared to experimental reference data (solid lines) of: monoclinic m-nitrophenol (MNPHOL mc); 1,2-ethanediamine form Iα (ETDIAM Iα); β-sulfur (FURHUV β); glutaric acid form β (GLURAC) and paracetamol form I (HXACAN I).

Fig. 3. Quasiharmonic calculated free energy curves of polymorphs of paracetamol and m-nitrophenol. (a) Shows the calculated absolute free energy vs. temperature curves for polymorphs I, II and III of paracetamol, which are correctly found to be monotropic and in the experimentally observed stability order. (b) Shows the calculated difference in free energies between the monoclinic (mc) and orthorhombic (o) forms of m-nitrophenol. The known enantiotropic transition at 350 K is almost reproduced.

Fig. 4. Distributions of experimental (green) and predicted (blue) melting point temperatures for the 418 polymorph families.

Fig. 5. (a) Distribution of calculated volumetric thermal expansion coefficients in the set of 864 crystal structures. (b) Pairwise absolute differences in volumetric thermal expansion coefficients for 475 polymorph pairs.

Fig. 6. (a) Distribution of T = 0 K calculated bulk moduli for the entire set of crystal structures. (b) Pairwise absolute differences in bulk modulus between polymorphs at 0 K.

Fig. 7. (a) Distribution of T = 0 K calculated shear moduli for the entire set of crystal structures. (b) Pairwise absolute differences in shear modulus between polymorphs at 0 K.

Fig. 8. Distributions of the calculated percentage decrease between 0 K and the melting point in (a) the bulk moduli and (b) the shear moduli of all crystal structures in the set.

Fig. 9. (a) The absolute contribution to the calculated free energy due to thermal expansion for all structures in the polymorph set, calculated at the melting point (T _m) as the difference between the quasi-harmonic (thermally expanded) and harmonic free energy, A ^QHA(T _m) – A ^HA(T _m). (b) The pairwise differences in contribution due to thermal expansion to the relative thermodynamic stability of polymorphs at their respective melting temperatures, Δ(A ^QHA(T _m) – A ^HA(T _m)). Distributions are shown for molecular crystals with predicted (blue) and experimental (green) melting points.

Fig. 10. The correlation between the free energy difference in each polymorph pair at 0 K (including vibrational zero-point energy) and the free energy difference at the melting point temperature (T _m) in the quasi-harmonic approximation. The shaded green triangular region marks the 21% of polymorph pairs that were re-ranked by vibrational energy. Green and red data points denote polymorphs for which we have used experimentally measured and predicted melting points, respectively.

Fig. 11. The quasi-harmonic vibrational energy differences at the melting point (T _m) relative to the 0 K relative stability between pairs of polymorphs. The 0 K energies include vibrational zero-point energy. The background colours indicate pairs that have diverging (red) and converging (yellow and green) free energy curves, and which pairs are re-ranked (green). Green and red data points denote polymorphs for which we have used experimentally measured and predicted melting points, respectively.