DFT-based transport calculations, Friedel's sum rule and the Kondo effect

Friedel's sum rule provides an explicit expression for a conductance functional, $\mathcal{G}[n]$, valid for the single impurity Anderson model at zero temperature. The functional is special because it does not depend on the interaction strength $U$. As a consequence, the Landauer conductance for the Kohn-Sham (KS) particles of density functional theory (DFT) coincides with the true conductance of the interacting system. The argument breaks down at temperatures above the Kondo scale, near integer filling, $n_{\text{d}\sigma}\approx 1/2$ for spins $\sigma{=}\uparrow\downarrow$. Here, the true conductance is strongly suppressed by the Coulomb blockade, while the KS-conductance still indicates resonant transport. Conclusions of our analysis are corroborated by DFT studies with numerically exact exchange-correlation functionals reconstructed from calculations employing the density matrix renormalization group.