Spatially resolved characterization of electron localization and delocalization in molecules: Extending the Kohn‐Resta approach

Abstract

In this work, the electron organization of many‐electron systems is considered in a context of the linear response theory extending the Kohn‐Resta view on electron localization phenomenon. The variances of the local electronic position and momentum operators are linked via the fluctuation‐dissipation theorem to the optical conductivity tensor, that is, to observable spectroscopic properties. It is demonstrated that the electron position variance density quantifies a degree of electron delocalization in each point of position space and distinguishes between metallic and insulating character of electronic states. The momentum variance density estimates a degree of electron localization and is immediately related to electronic kinetic energy density in the Ghosh‐Berkowitz‐Parr form giving a physical interpretation to the later. We show that electron localization and delocalization phenomena in atoms and molecules can be probed by external electric field. This approach provides new electronic descriptors distinguishing and quantifying chemical bonds of different types.

The explicit role of electron exchange in the hydrogen bonded molecular complexes

“…The non‐local density‐based descriptors 30–36 carry information about the mutual influence of electrons in spatially remote regions and detect subtle effects in chemical bonding. The source function (SF) 30,31 reveals the role of atoms, defined in terms of QTAIM, 37 in formation of H‐bonds 30 .…”

A Quantum‐Mechanical Map for Bonding and Properties in Solids

“…All three z ‐axis quantities in Figure b–d are so‐called response properties: they do not relate to conventional bond characteristics (such as the localization and delocalization of electrons), but rather to the unconventional way in which the bonds respond to external stimuli. In this light, it is interesting to mention recent studies on the electron organization of many‐electron systems in the context of linear response theory . They highlight the profound connection between variances in local electronic position and the momentum operators and the optical conductivity tensor—that is, between electron (de)localization in real and momentum space on the one hand, and the experimentally observable spectroscopic and conductivity properties on the other hand.…”

Revealing electronic features governing hydrolysis of cephalosporins in the active site of the L1 metallo-β-lactamase

“…Second, we explicitly reveal the electronic features in the active sites of the complexes. We apply the QTAIM 5,61 and other advanced bonding descriptors: source function, 11,62 Fermi hole, 15,63 electron delocalization indices, 16 delocalization tensor, 64 condensed linear response kernel 23 to analyze the QM part of each system, i.e. its active site.…”

“…Nevertheless, due to the semi-local nature of the ellipticity index, its proles fail to manifest effects of extensive electron delocalization in chemical bond picture. Therefore, to study electron delocalization in the N-C 4 -C 3 fragment in more detail and to reveal the inuence of the conjugated bonds in R 2 on the C 4 -C 3 bond in the NCF complexes, we applied the electron delocalization tensor D (see the ESI, † eqn (7)-(9)), 64 which is a quantitative measure of uncertainty in electrons' positions and reects various physical effects: from quantum uncertainty in position of each particle to mutual correlations in electron motion. The major eigenvalue of delocalization tensor density D(r), l 1 (r), expresses delocalization magnitude along the direction of maximum electron delocalization in a system.…”