Many-body correlations and coupling in benzene-dithiol junctions

Most theoretical studies of nanoscale transport in molecular junctions rely on the combination of the Landauer formalism with Kohn-Sham density functional theory (DFT) using standard local and semilocal functionals to approximate exchange and correlation effects. In many cases, the resulting conductance is overestimated with respect to experiments. Recent works have demonstrated that this discrepancy may be reduced when including many-body corrections on top of DFT. Here we study benzene-dithiol (BDT) gold junctions and analyze the effect of many-body perturbation theory (MBPT) on the calculation of the conductance with respect to different bonding geometries. We find that the many-body corrections to the conductance strongly depend on the metal-molecule coupling strength. In the BDT junction with the lowest coupling, many-body corrections reduce the overestimation on the conductance to a factor 2, improving the agreement with experiments. In contrast, in the strongest coupling cases, many-body corrections on the conductance are found to be sensibly smaller and standard DFT reveals a valid approach.

Figure 1

Side and front views for the different geometries of BDT attached to gold (111): (a) BDT-$h$, (b) BDT-$p$, and (c) BDT-$n$. For sake of clarity, all gold layers are not shown in the figures: only one (respectively 4) in the front (respectively side) views. The Au, C, S, and H atoms are represented by yellow (light grey), grey, green (dark grey), and white spheres, respectively.

Figure 2

Conductance $\mathcal{G}\left(E\right)$ in units of ${\mathcal{G}}_0$ as a function of the energy $E$ for BDT-$h$ (top panel), BDT-$p$ (middle) and BDT-$n$ (bottom panel). Black line: DFT; blue line: diag-$G_0{W}_0$; yellow line: diag-COHSEX; red line: full-COHSEX. The insets are zooms over the zero-bias conductance $\mathcal{G}(E=0)$ region. The zero of the energy is set to the Fermi energy $E_F$.

Figure 3

DFT vs diagonal $G_0{W}_0$ energies for BDT-$p$ (blue squares), BDT-$h$ (red circles), and BDT-$n$ (green diamonds). The zero of the energy is set to the Fermi energy $E_F$. In the insets we plot the GW corrections vs DFT energies at different scales.

Figure 4

Local density-of-states (LDOS) difference between full-COHSEX and diag-COHSEX calculated in an energy window of 0.8 eV around the Fermi level for BDT-$h$, BDT-$p$, and BDT-$n$. Four isovalues are represented: $+4\rho$ in orange, $+1\rho$ in dark red, $-1\rho$ in dark blue, and $-4\rho$ in light blue, with $5\times {10}^{-4}$ $e^{-}$/Å${}^3$ in BDT-$h$, and $6\times {10}^{-4}$ $e^{-}$/Å${}^3$ in BDT-$p$ and BDT-$n$. The Au, C, S, and H atoms are represented by yellow, grey, green, and white spheres, respectively.