Are Kohn-Sham Conductances Accurate?

We use Fermi-liquid relations to address the accuracy of conductances calculated from the single-particle states of exact Kohn-Sham (KS) density functional theory. We demonstrate a systematic failure of this procedure for the calculation of the conductance, and show how it originates from the lack of renormalization in the KS spectral function. In certain limits this failure can lead to a large overestimation of the true conductance. We also show, however, that the KS conductances can be accurate for single-channel molecular junctions and systems where direct Coulomb interactions are strongly dominant.

Figure 1

(a) KS and interacting conductances as a function of gate voltage, calculated for the Hubbard molecule. (b) HOMO and LUMO Luttinger integrals, their sum $L_H+L_L=0$, and $10L_H^2$ calculated for the same model. At the conductance valley, KS overestimates the conductance. At the conductance peak ${\mathcal{G}}_{\mathrm{KS}}$ is exact to first order in $L_H$.