DFT-based study of electron transport through ferrocene compounds with different anchor groups in different adsorption configurations of an STM setup

In our theoretical study in which we combine a nonequilibrium Green's function approach with density functional theory (DFT) we investigate compounds containing a ferrocene moiety which is connected to (i) thiol anchor groups on both sides in a para-connection and (ii) a pyridyl anchor group on one side in a meta-connection and a thiol group on the other side in a para-connection, in both cases with acetylenic spacers in between the ferrocene and the anchors. We predict possible single-molecule junction geometries within a scanning tunneling microscopy (STM) setup, where we find that the conductance trend for the set of conformations is intriguing in the sense that the conductance does not decrease while the junction length increases, which we analyze and explain in terms of the Fermi level alignment. We also find a pattern for the current-voltage ($I-V$) curves within the linear-response regime for both molecules we study, where the conductance variation with the molecular configurations is surprisingly small.

Figure 1

(a) s-FDT with a phenylthiolate group on each side; (b) s-FPT with a pyridyl group on one side and thiolate on the other side. In both cases tetrabutylammonium (${\mathrm{NBu}}_4$) cations are assumed as counter ions.

Figure 2

Junction geometries for (a) s-FDT and (b) s-FPT with different rotation angles.

Figure 3

Adsorption geometries for type A adsorption (left panels) and type B adsorption (right panels) for the molecules (a)–(c) s-FDT and (d)–(f) s-FPT, where the distances $d_{\text{Au-S}}$ between the respective sulfur and gold sites resulting from on-top adsorption of both anchor groups are (a) 3.32 Å, (b) 3.17 Å, and (c) 3.18 Å for s-FDT and in all cases are identical for type A (left panels) and type B adsorption (right panels), while for the asymmetric s-FPT $d_{\text{Au-S}}/d_{\text{Au-N}}$ were found to be (d) 3.30/2.76 Å (left panel) and 3.11/3.14 Å (right panel), (e) 3.60/3.01 Å (left panel) and 3.70/3.13 Å (right panel), and (f) 3.55/2.74 Å (left panel) and 3.55/2.85 Å (right panel) by our optimization procedure as described in the text. The contacted gold positions on the surface for each adsorption geometry are marked in white, while the Au atoms on the second-nearest-neighbor shell line between these positions are marked in black for geometries of type A.

Figure 4

(a) Adsorption energies and (b) rotation energies of junctions of adsorption type A depending on the angle between the two anchor groups. All values are given in eV.

Figure 5

Dependence of conductance on the voltage from DFT calculations with SO corrections, where dots in each panel represent adsorption geometries of type A and squares represent those of type B for selected molecular configurations of (a) s-FDT with a rotation angle of $0^{\circ }$ (black), ${54}^{\circ }$ (green), ${89}^{\circ }$ (cyan), ${125}^{\circ }$ (blue), and ${180}^{\circ }$ (red) and (b) s-FPT with a rotation angle of $0^{\circ }$ (black), ${50}^{\circ }$ (blue), ${92}^{\circ }$ (cyan), ${117}^{\circ }$ (green), and ${180}^{\circ }$ (red).

Figure 6

Zero-bias conductance for a selected range of structures as calculated from $\mathcal{T}\left(E_F\right)$ with NEGF-DFT (a) and (c) without and (b) and (d) with SO corrections depending on (a) and (b) the rotation angle between anchor groups and (c) and (d) the junction length defined as the distance between the surface plane of the substrate and the contact Au atom on the tip.

Figure 7

Eigenenergies of the HOMO and LUMO from a subdiagonalization of the molecular part of the transport Hamiltonian for the junction setups of (a) s-FDT and (b) s-FPT in Fig. 6, respectively. The black circles in both panels represent the energy positions of the systems without SO correction, and the red circles represent the results with SO correction.

Figure 8

Junction length dependence of (a) the conductance without SO corrections, (b) the eigenenergy of the HOMO from a subdiagonalization of the molecular part of the transport Hamiltonian of the junction (solid line) and vacuum level alignment (dotted line), where, for the latter, shifted values taking into account the contribution from partial charging are also shown as crosses (Bader analysis) and triangles [integration over $\mathrm{\Delta }n\left(z\right)]$, (c) electronegativities of the free molecules dependent on the rotation angle, and (d) partial charges on the molecules in the junction from a Bader analysis (crosses) as well as from integration over $\mathrm{\Delta }n\left(z\right)$ in the molecular region (triangles) in units of electrons. For all panels symbols and lines are shown in black for s-FPT and in red for s-FDT.

Figure 9

Localization patterns for the HOMO from cluster calculations containing the free molecule and the two or three Au contact atoms defined by the respective junction geometries for (a) s-FDT and (b) s-FPT.

Figure 10

Electron density difference $\mathrm{\Delta }n\left(z\right)$ between the junction density and that of its two components (black lines), where the functions attributed to the molecular region are highlighted in green and the running integral over this molecular part is plotted in red for (a) s-FDT and (b) s-FPT.