Radial exchange density and electron delocalization in molecules

The six-dimensional exchange density Gamma(X)(r1,r2) is a measure of electron delocalization at the Hartree-Fock level. Fixation of r1 to a constant point results in a three-dimensional function, which displays electron delocalization that originates from r1 in position space. In this work, the dimensionality of Gamma(X)(r1,r2) is lowered from six to four by integration with regard to r2 over sphere surfaces of radius d, centered at r1 = r. The resulting radial exchange density Gamma(X)(d,r) is visualized for constant d values as a function of r. This approach indicates regions of position space which are origins of delocalization over a certain distance d. The shape of these regions very strongly depends on d. Structures similar to pi orbital densities are observed at large d values (4.5 au) in unsaturated carbon compounds, while smaller values (1.5 au) can result in structures, which resemble the Laplacian of the electron density. The abundance of different spatial structures inherent in the radial exchange density implies interesting capabilities for the orbital-independent interpretation of electronic structures in position space.