Anharmonic and Quantum Fluctuations in Molecular Crystals: A First-Principles Study of the Stability of Paracetamol

Molecular crystals often exist in multiple competing polymorphs, showing significantly different physicochemical properties. Computational crystal structure prediction is key to interpret and guide the search for the most stable or useful form, a real challenge due to the combinatorial search space, and the complex interplay of subtle effects that work together to determine the relative stability of different structures. Here we take a comprehensive approach based on different flavors of thermodynamic integration in order to estimate all contributions to the free energies of these systems with density-functional theory, including the oft-neglected anharmonic contributions and nuclear quantum effects. We take the two main stable forms of paracetamol as a paradigmatic example. We find that anharmonic contributions, different descriptions of van der Waals interactions, and nuclear quantum effects all matter to quantitatively determine the stability of different phases. Our analysis highlights the many challenges inherent in the development of a quantitative and predictive framework to model molecular crystals. However, it also indicates which of the components of the free energy can benefit from a cancellation of errors that can redeem the predictive power of approximate models, and suggests simple steps that could be taken to improve the reliability of ab initio crystal structure prediction.