Non-covalent interactions descriptor using experimental electron densities

Non covalent interactions (NCI) play a crucial role in biology (protein-drug recognition) and in the design of new materials (self-assembly). A novel electron density (ED) based descriptor of non-covalent interaction was proposed in 2010 by Johnson et al.[1]. It exploits a key quantity in DFT, the reduced density gradient s(r), and reveals NCI in terms of low s-value isosurfaces, defined in low-ED regions and on which the ED is mapped with a colour related to the sign of the local density curvature along the second largest variation direction and to the magnitude of the ED itself. Though directly obtainable from experimental EDs, up to now such descriptor has been applied only to theoretical EDs or to independent atom model (IAM) densities. In this work, we explore the application of this new descriptor to NCI in the bulk, using X-ray derived EDs. In particular, molecular crystals represent ideal supramolecular entities for studying non covalent interactions and the global effect that the crystal field has on them. Austdiol [2], benzene [3] and the two polymorphs of the anti-ulcer drug famotidine [4] were chosen as representative case studies. Atom-centred multipole expansions (XD2006 package [5]) were adopted in the refinement against the experimental structure factors and the grid files for implementing the NCI descriptor were obtained with an ad-hoc code. The NCI isosurfaces obtained from experiment have been also compared with those calculated using ab-initio fully-periodic wavefunctions and the IAM densities. Moreover, the picture provided by this new descriptor was compared with the one obtained using Quantum Theory of Atoms in Molecules, QTAIM [6]. We found that the NCI descriptor is able to distinguish the different types of non-covalent interactions, and also to rank their strength, especially for Hydrogen Bonds (HB). It can also mirror the presence of weak van der Waals interactions, usually difficult to be properly described, in particular using ED-based descriptors. Furthermore, this descriptor turned out to be able to recover the delocalized character of interactions like C-H···? also when QTAIM is not. IAM gives a correct description only for the very weak interactions whose NCI isosurfaces are well separated from the molecular skeleton(s) and for those interactions which are easily anticipated by packing geometry. The very good general agreement we found between theoretical and experimental isosurfaces leads us to conclude that the NCI descriptor can be also successfully applied to experimentally derived multipolar ED. It is therefore an emerging, powerful tool to investigate non-covalent interactions, and able also to give complementary information to the 'conventional' QTAIM approach.