Influences of Basis Set and Electronic Exchange-Correlation on Low-Frequency Vibrations and Stability of Paracetamol Polymorphs

In molecular crystals, many solid state phase transitions can be attributed to the entropy of intermolecular vibrations at low frequencies, where the weak noncovalent interactions dominate, and simulations based on density functional theory (DFT) suffer from relatively large errors. In this work, the precision of two critical computational parameters are evaluated, namely the choice of local basis set and (DFT-based) Hamiltonian. Each is documented in detail for the vibrational properties and thermodynamic stability of two polymorphs of paracetamol, which are chosen due to the representative chemical interactions and the good availability of high-quality reference data. Comparisons are made with experimentally measured low-temperature geometries, Raman spectra, and temperature–pressure phase diagrams. These results highlight the substantial influences of basis set, revealing the importance of both the cardinality (i.e., ζ) and the diffuseness; the failure to account for either factor might lead to unexpected results. The features of low-frequency vibrations that most significantly affect the relative stability of molecular crystals are identified and shown to be captured when the triple-ζ def2-TZVP basis set is adopted; on the contrary, widely used double-ζ basis sets are shown to be inadequate. The improvement attributed to the inclusion of Fock exchange is revealed to be marginal, especially with triple-ζ basis sets. By systematically improving levels of precision, the current work disentangles competing sources of errors impeding accurate crystal structure predictions and polymorph energy rankings. This facilitates the predictability and reliability of DFT in thermodynamic modeling of molecular crystals.