Non-covalent Interactions descriptor using experimental electron density

Non covalent interactions (NCI) play a crucial role in biology (protein-drug recognition) and in the design of new materials (selfassembly). 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∝|∇ρ|/ ρ4/3, and reveals NCI in terms of low s-value isosurfaces, defi ned 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 fi eld has on them. Austdiol [2], benzene [3] and the two polymorphs of the antiulcer drug famotidine [4] were chosen as representative case studies. Atom-centred multipole expansions (XD2006 package [5]) were adopted in the refi nement against the experimental structure factors and the grid fi les 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 periodic wavefunctions and the IAM densities. On the basis of the experience gained on the investigated systems, it turns out that when applied to experimental EDs the NCI descriptor gives essentially similar information to that found for theoretical EDs. For instance, as shown in the fi gure below for benzene crystal, we fi nd that interactions having a presumably delocalized nature, such as π-π stackings or C-H⋅⋅⋅π contacts, are indeed seen as extended surfaces, at variance with the localized and discontinuous picture unavoidably provided by the bond path analysis. Moreover, we confi rm that mapping the ED on the s isosurface highlights the strength of the various interactions, while the sign of the curvature helps to distinguish true stabilizing interactions from simple steric repulsions. The visible difference between the NCI isosurfaces portrait found in benzene crystal on passing from the multipolar to the IAM density corroborates the stabilizing and not simply steric nature of the π-π stacking and CH⋅⋅⋅ π interactions. [1] E.R. Johnson et al., JACS 2010, 132, 6498-6506. [2] L. Lo Presti et al. J. Chem Phys. B 2006, 110, 6405-6414 [3] H.-B. Bürgi et al. Chem. Eur. J. 2002, 8, 3512-3521 [4] J. Overgaard et al. Acta Cryst. 2004, A60, 480-487 [5] http:// xd.chem.buffalo.edu/