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One-electron self-interaction and an incorrect asymptotic behavior of theKohn-Sham exchange-correlation potential are among the most prominentlimitations of many present-day density functionals. However, a one-electronself-interaction-free energy does not necessarily lead to the correctlong-range potential. This is here shown explicitly for local hybridfunctionals. Furthermore, carefully studying the ratio of the von Weizs\"ackerkinetic energy density to the (positive) Kohn-Sham kinetic energy density,$\tau_\mathrm{W}/\tau$, reveals that this ratio, which frequently serves as aniso-orbital indicator and is used to eliminate one-electron self-interactioneffects in meta-generalized-gradient approximations and local hybridfunctionals, can fail to approach its expected value in the vicinity of orbitalnodal planes. This perspective article suggests that the nature andconsequences of one-electron self-interaction and some of the strategies forits correction need to be reconsidered.

One-electron self-interaction and the asymptotics of the Kohn-Sham potential: an impaired relation