Lattice Energy Partitions in Crystals of Flexible Molecules and the 40% Limit
Amrita Chattopadhyay, Adam Hill, S. E. Wright, Gregory J. O. Beran, Aurora J. Cruz‐Cabeza
Abstract
High Resolution Image Download MS PowerPoint Slide Flexible molecules change their conformations to optimize intermolecular interactions in the solid-state ─a process that comes at an intramolecular energy cost. The interplay between these opposing forces leads to beautifully balanced and elegant crystal structures. Yet, the relationship between intramolecular energy penalties and intermolecular stabilization has not been fully explored, largely because it requires models capable of accurately capturing components with distinct physical origins. In this work, we employ state-of-the-art hybrid DFT models to probe these interactions and quantify their energetic contributions to crystal lattice energies. After benchmarking 18 computational methods, we identify PBE-MBD/B2PLYPD as the method best reproducing experimental polymorph stabilities with mean absolute deviations of just 2.3 kJ·mol –1 across 17 polymorphic pairs. Using this model, we compute and analyze lattice energy partitions for 125 crystal structures spanning a diverse set of flexible compounds. Our analysis reveals a striking empirical trend─the “40% limit”─which shows that up to 40% of the intermolecular stabilization energy can compensate for intramolecular energy penalties associated with conformational variations. Furthermore, the probability of a higher-energy conformation being observed in the solid-state decreases as a function of the intra-to-intermolecular energy ratio and becomes negligible at the 40% mark. These findings are significant: they define the energetic limits of conformational flexibility in the solid-state and the intra-to-intermolecular energy ratios provide a quantitative tool to predict structures. They can be used to guide the conformational phase space sampling for crystal structure prediction, to rank hypothetical structures according to their crystallizability, or to anticipate difficulties of nucleation and crystal growth in crystal forms of flexible compounds.