Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals

Semilocal density functional approximations for the exchange-correlation energy can improperly dissociate a neutral molecule XY (Y not =X) to fractionally charged fragments X(+q)...Y(-q) with an energy significantly lower than X0...Y0. For example, NaCl can dissociate to Na(+0.4)...Cl(-0.4). Generally, q is positive when the lowest-unoccupied orbital energy of atom Y0 lies below the highest-occupied orbital energy of atom X0. The first 24 open sp-shell atoms of the Periodic Table can form 276 distinct unlike pairs XY, and in the local spin density approximation 174 of these display fractional-charge dissociation. Finding these lowest-energy solutions with standard quantum chemistry codes, however, requires special care. Self-interaction-corrected (SIC) semilocal approximations are exact for one-electron systems and also reduce the spurious fractional charge q. The original SIC of Perdew and Zunger typically reduces q to 0. A scaled-down SIC with better equilibrium properties sometimes fails to reduce q all the way to 0. The desideratum of "many-electron self-interaction freedom" is introduced as a generalization of the one-electron concept.