title: Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H2+, He2+, LiH+, and Ne2+.
abstract: The common density functionals for the exchange-correlation energy make serious self-interaction errors in the molecular dissociation limit when real or spurious noninteger electron numbers N are found on the dissociation products. An "M-electron self-interaction-free" functional for positive integer M is one that produces a realistic linear variation of total energy with N in the range of M-1<N<or=M, and so can avoid these errors. This desideratum is a natural generalization to all M of the more familiar one of one-electron self-interaction freedom. The intent of this paper is not to advocate for any functional, but to understand what is required for a functional to be M-electron self-interaction-free and thus correct even for highly stretched bonds. The original Perdew-Zunger self-interaction correction (SIC) and our scaled-down variant of it are exactly one- and nearly two-electron self-interaction-free, but only the former is nearly so for atoms with M>2. Thus all these SIC's produce an exact binding energy curve for H2+, and an accurate one for He2+, but only the unscaled Perdew-Zunger SIC produces an accurate one for Ne2+, where there are more than two electrons on each fragment Ne+0.5. We also discuss LiH+, which is relatively free from self-interaction errors. We suggest that the ability of the original and unscaled Perdew-Zunger SIC to be nearly M-electron self-interaction-free for atoms of all M stems in part from its formal resemblance to the Hartree-Fock theory, with which it shares a sum rule on the exchange-correlation hole of an open system.
authors.affiliation: Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118, USA.
authors.forename: Adrienn
authors.initials: A
authors.lastname: Ruzsinszky
authors.forename: John P
authors.initials: JP
authors.lastname: Perdew
authors.forename: Gábor I
authors.initials: GI
authors.lastname: Csonka
authors.forename: Oleg A
authors.initials: OA
authors.lastname: Vydrov
authors.forename: Gustavo E
authors.initials: GE
authors.lastname: Scuseria