A fuzzy-atom analysis of electron delocalization on hydrogen bonds

The extent of electron delocalization is quantified for set of cyclic complexes exhibiting two or more hydrogen bonds (HBs). In particular, the delocalization index (DI) between the atoms directly involved in the HB, and the ING (a normalized n-center delocalization index) have been evaluated using several fuzzy-atom schemes, namely Becke, Becke-ρ, Hirshfeld, and Hirshfeld-Iterative. The results have been compared with the widely used Quantum Theory of Atoms in Molecules (QTAIM) atomic definition. The DI values are found to correlate very well with geometrical or topological descriptors widely used in the literature to characterize HB systems. Among all fuzzy-atom methods, the ones that can better accommodate the different partial ionic character of the bonds perform particularly well. The best performing fuzzy-atom scheme for both pairwise and n-center electron delocalization is found to be the Becke-ρ method, for which similar results to QTAIM model are obtained with a much reduced computational cost. These results open up a wide range of applications of such electron delocalization descriptors based on fuzzy-atoms for noncovalent interactions in more complex and larger systems.