Density functionals that are one- and two- are not always many-electron self-interaction-free, as shown for H_2~+, He_2~+, LiH+, and Ne_2~+

摘要

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 2.Thus all these SIC's produce an exact binding energy curve for H_2~+, and an accurate one for He_2~+, but only the unscaled Perdew-Zunger SIC produces an accurate one for Ne_2~+, 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 exchanges-correlation hole of an open system.