Effect of the self-interaction error for three-electron bonds:: On the development of new exchange-correlation functionals

The dissociation behavior as well as the equilibrium properties of radical cations with three-electron bonds, namely He-2(+.), N2H6+., O2H4+., F2H2+., and Ne-2(+.) are investigated using standard and self-interaction-corrected density functional theory (SIC-DFT) in connection with a variety of pure and hybrid exchange-correlation (XC) functionals. The impact of the self-interaction error (SIE) on the results of standard DFT is analyzed considering the individual orbital contributions to the SIE, the dependence of the SIE on the separation distance between the dissociation fragments, and its impact on the equilibrium properties of 2-6. A local analysis of the SIE in terms of exact and DFT exchange holes reveals that the SIE mimics not only non-dynamic but also an increasing amount of dynamic electron correlation effects as the number of valence electrons is enlarged. Standard DFT describes the dissociation of three-electron bonds qualitatively incorrectly. This can be traced back in the first instance to the SIE of the bonding beta electron, which mimics a spurious long-range correlation with a non-existing delocalized alpha electron in the same bond. A comparison of the covalent (symmetric) and ionic (symmetry-broken) state of radical cations 2-6 at large interaction distances provides further insight in the inconsistencies of the DFT description: (i) Not only the SIE but also the approximate description of the interelectronic exchange contributes to the incorrect description of the dissociation. (ii) Dissociating three-electron bonds show a specific form of long-range correlation effects, which is neither accounted for by standard DFT, SIC-DFT nor Hartree-Fock theory. Indeed, SIC-DFT provides a qualitatively better description of the dissociation of radical cations, however in general a poor performance when describing equilibrium properties. There is no need for SIC-DFT methods. Instead, there is need for XC functionals with exact exchange and long-range correlation effects (e.g. mimicked by the exchange SIE) absorbed in the correlation functional. Implications of our findings for the construction of new density functionals are discussed.