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

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.