Forces and conductances in a single-molecule bipyridine junction

Inspired by recent measurements of forces and conductances of bipyridine nanojunctions, we have performed density functional theory calculations of structure and electron transport in a bipyridine molecule attached between gold electrodes for seven different contact geometries. The calculations show that both the bonding force and the conductance are sensitive to the surface structure, and that both properties are in good agreement with experiment for contact geometries characterized by intermediate coordination of the metal atoms corresponding to a stepped surface. The conductance is mediated by the lowest unoccupied molecular orbital, which can be illustrated by a quantitative comparison with a one-level model. Implications for the interpretation of the experimentally determined force and conductance distributions are discussed.

Figure 1

(Color online) A bipyridine molecule suspended between Au electrodes. The insets illustrate the variation of the surface contact geometry, where clockwise from top right to bottom left a single ad layer with one to seven Au ad atoms (white spheres), where $N_c$ varies from three to nine (see text), on top of a flat Au (111) surface are shown. Smaller dark spheres define the nitrogen positions.

Figure 2

(Color online) Top: Binding energies for a single N-Au bond as a function of $N_c$. The inset shows the HOMO. The solid (dashed) line marks calculations using the PW91 (Ref. 10) (RPBE (Ref. 11)) XC functional. The position of the $d$ band center with respect to the Fermi level is shown as a dotted line. Bottom: Rapture force as a function of $N_c$. The horizontal dotted line indicates the experimental value and the gray shaded area marks the region defined by the experimental error bars.

Figure 3

(Color online) Top: Conductance in dependence on $N_c$ for torsion angles $\alpha =0°$ (black line) and 25° (gray line) in units of the conductance quantum $G_0=2e^2∕h$. The dashed line refers to a simple model explained in the text. The horizontal dotted line shows the experimental value. Bottom: Transmission functions for all nanojunctions $(\alpha =0°)$. The peaks are due to the LUMO, shown in the inset, which rises continuously in energy as $N_c$ increases.