Zero-bias molecular electronics: Exchange-correlation corrections to Landauer's formula

We show that standard first principles calculations of transport through single molecules miss exchange-correlation corrections to the Landauer formula—the conductance is calculated at the Hartree level. Furthermore, the lack of derivative discontinuity in approximations can cause large errors for molecules weakly coupled to the electrodes. From the Kubo response theory, both the Landauer formula and these corrections in the limit of zero bias are derived and calculations are presented.

Figure 1

Double barrier resonant tunneling cartoon of a molecule between two metallic leads; the LUMO has been shifted and broadened relative to the isolated molecule.

Figure 2

Conductance peak from resonance: the dashed line is the self-consistent approximate functional result, the dotted line is the approximate result as $\gamma \to 0$, and the solid line is the exact result. Here ${ϵ}_L=0$, $\mathrm{\Delta }ϵ=1$, and ${\gamma }_0=0.1$.

Figure 3

Transmission of benzene-dithiolate in the presence of a gate. The gate is realized by a square sheet of homogenously distributed dummy charges (total sum is denoted by $Q_G$) located a distance of $3.8\mathrm{\AA }$ above the carbon ring.