Topological analysis of the electron delocalization range.

The electron delocalization range function EDR( r→;d) (Janesko et al., J. Chem. Phys. 2014, 141, 144104) quantifies the extent to which an electron at point r→ in a calculated wavefunction delocalizes over distance d. This work shows how topological analysis distills chemically useful information out of the EDR. Local maxima (attractors) in the EDR occur in regions such as atomic cores, covalent bonds, and lone pairs where the wavefunction is dominated by a single orbital lobe. The EDR characterizes each attractor in terms of a delocalization length D and a normalization N≤1, which are qualitatively consistent with the size of the orbital lobe and the number of lobes in the orbital. Attractors identify the progressively more delocalized atomic shells in heavy atoms, the interplay of delocalization and strong (nondynamical) correlation in stretched and dissociating covalent bonds, the locations of valence and weakly bound electrons in anionic water clusters, and the chemistry of different reactive sites on metal clusters. Application to ammonia dissociation over silicon illustrates how this density-matrix-based analysis can give insight into realistic systems. © 2016 Wiley Periodicals, Inc.