Correlation effects on the interelectronic distributions of localized electron pairs
It has been shown previously that a wealth of chemical insight may be drawn from studying the interelectronic distribution function for localized electron pairs within a molecular system (Hennessey et al. in Phys Chem Chem Phys 16(46):25548–25556, 2014); however, these accounts have been limited due to the relative inaccuracy of the underlying Hartree–Fock electronic structure model that has been employed. In the current work, we study how the interelectronic distribution function of single electron pairs, represented by localized molecular orbitals, changes between a Hartree–Fock and density functional electronic structure model. We find that localized electron pairs expand, relative to a Hartree–Fock model, in a small but significant way when modelled with density functional theory. More specifically, we generally find that compact electron pairs (i.e. those pairs having narrow distribution functions near small interelectronic distances) result in a smaller change due to correlation than electron pairs more broadly distributed. This counterintuitive effect is attributed to the fact that compact electron pairs are generally held close together by a relatively rigid confining potential (i.e. attraction from local nuclei and repulsion from neighbouring electrons). However, in cases where a series of species all have nearly identical nuclear structure in the vicinity of the LMO of interest, more compact electron pairs did in fact experience the greatest change in interelectronic separation and electron repulsion upon the incorporation of a correlated model. Also, if one allows the geometry of the molecular species to relax, bonds associated with LMOs having compact interelectronic distributions tend to elongate the most with a correlated model (relative to Hartree–Fock) and the resultant deformation of the interelectronic distribution functions then show the most significant changes due to correlation. The results presented herein demonstrate the utility of Kohn–Sham density functional theory for the description of localized chemical space within the scope of the localized pair model.