Real-space representation of electron correlation in π-conjugated systems

π-electron conjugation and aromaticity are commonly associated with delocalization and especially high mobility of the π electrons. We investigate if also the electron correlation (pair density) exhibits signatures of the special electronic structure of conjugated systems. To that end the shape and extent of the pair density and derived quantities (exchange-correlation hole, Coulomb hole, and conditional density) are investigated for the prototype systems ethylene, hexatriene, and benzene. The answer is that the effects of π electron conjugation are hardly discernible in the real space representations of the electron correlation. We find the xc hole to be as localized (confined to atomic or diatomic regions) in conjugated systems as in small molecules. This result is relevant for density functional theory (DFT). The potential of the electron exchange-correlation hole is the largest part of vxc, the exchange-correlation Kohn-Sham potential. So the extent of the hole directly affects the orbital energies of both occupied and unoccupied Kohn-Sham orbitals and therefore has direct relevance for the excitation spectrum as calculated with time-dependent DFT calculations. The potential of the localized xc hole is comparatively more attractive than the actual hole left behind by an electron excited from a delocalized molecular orbital of a conjugated system.