Conductance of an Ensemble of Molecular Wires: A Statistical Analysis

We report on a first principles analysis of quantum transport through molecular wires made of 4,4’bipyridine and 6-alkanedithiol contacted by Au electrodes. We investigate how charge transport is altered due to small structure changes at the molecule-electrode contacts. These changes include distance between the molecule and the contact, extra metal atoms at the Au surface, binding sites, molecular orientation, and bias voltages. By investigating hundreds of wires we extract a statistical picture on transport properties of the two different molecules. We compare quantitatively with the corresponding experimental data.

Figure 1

Statistic analysis of transport properties for molecular wires with different binding sites and orientations. The distance between the two Au lead surfaces is fixed at 11.38 Å for bipyridine wires and 12.38 Å for alkanedithiol wires. Each N atom in bipyridine and each $S$ atom in alkanedithiol can bind to one of the nine sites marked in the middle inset of (c). (a) Histogram of transmission coefficient at Fermi energy, $T(0)$, for the ensemble of bipyridine wires. Inset: schematic showing an approximate geometry of the bipyridine wires. (b1)–(b4) histograms of the quantity $S(E_1,E_2)$ in different energy ranges for the bipyridine wires. (c) Histogram of $T(0)$ for the ensemble of alkanedithiol wires. Middle inset: the numbers indicate binding sites in the ensemble. Right inset: schematic showing an approximate geometry of the alkanedithiol wires. (d1)–(d4) Histograms of $S(E_1,E_2)$ for the ensemble of alkanedithiol wire.

Figure 2

Transmission coefficients $T=T(E)$ at zero bias versus electron energy for 4,4’bipyridine and 6-alkanedithiol wires with small differences in the contact region. Top row: wires without extra Au atoms extruding from contacts; middle row: with one extruding Au atom; bottom row: with one extruding atom at each surface. Different lines correspond to different contact distances $d$ measured from the nitrogen atom in the bipyridine or $S$ from the alkanedithiol to the Au surface or the extruding atom (same $d$ to both leads). Dashed line (red): $d=1.5\AA$; solid line (black): $d=2.0\AA$; dotted line (blue): $d=2.5\AA$. Fermi energy of the leads is shifted to $E=0$.

Figure 3

Current-voltage characteristics for Au-4,4’bipyridine-Au wires (left panel) and Au-alkanedithiol-Au wires (right panel) on different binding sites. The molecule is set perpendicular to the electrode surface, and rotated for multiples of $\frac{\pi }{4}$ along its axis. Different symbols correspond to rotations along the molecular axis for every $\frac{\pi }{4}$ (equivalent configurations are not included).