Electric conductance of a mechanically strained molecular junction from first principles: Crucial role of structural relaxation and conformation sampling

Density functional theory (DFT) based molecular dynamics simulations have been performed of a 1,4-benzenedithiol molecule attached to two gold electrodes. To model the mechanical manipulation in typical break junction and atomic force microscopy experiments, the distance between two electrodes was incrementally increased up to the rupture point. For each pulling distance, the electric conductance was calculated using the DFT nonequilibrium Green's-function approach for a statistically relevant sample of configurations extracted from the simulation. With increasing mechanical strain, the formation of monoatomic gold wires is observed. The conductance decreases by three orders of magnitude as the initial twofold coordination of the thiol sulfur to the gold is reduced to a single S–Au bond at each electrode and the order in the electrodes is destroyed. Independent of the pulling distance, the conductance was found to fluctuate by at least two orders of magnitude depending on the instantaneous junction geometry.

Figure 1

Initial simulation setup with the BDT molecule attached to two Au(111) surfaces. The dashed lines represent the CPMD unit-cell size in the $z$ direction. The additional Au layers were added for the conductance calculations in which the scattering region included the BDT molecule and three Au layers on each side. Periodic images of Au atoms in the $xy$ plane are shown without bonds.

Figure 2

Snapshots from the simulation at different pulling stages of the Au–BDT–Au junction corresponding to the $z$ lengths of the unit cell 26.0 Å (a), 27.5 Å (b), 28.0 Å (c), 30.0 Å (d), 35.0 Å (e), and 36.0 Å (f).

Figure 3

First panel: Average total energy (black solid line/circles) and quadratic regression (dashed red line). Second panel: Mean conductance with error bars corresponding to standard deviation (black line/squares) and most probable conductance value with error bars corresponding to the histogram bin size (red line/circles). Third panel: Mean-square displacement in the $z$ direction, $d_z$, per Au layer (red line/squares, first layer; blue line/circles, second layer; green line/triangles, third layer). Inset: Magnified view of the regions where the steps in conductance occur. Last panel: Mean-square displacement in the $xy$ plane, $d_{xy}$, per Au layer (same color scheme as above.). All quantities are plotted as a function of the unit-cell size in the $z$ direction.

Figure 4

Conductance histogram of the Au–BDT–Au junction with fixed Au (red line/circles), fixed BDT (blue line/squares), and full dynamic (black line/triangles). The bin size in the inset was reduced to $0.005G_0$, while $0.1G_0$ was used for the main graph.

Figure 5

Au–S potential energy as a function of interatomic distance calculated with PBE and CCSD(T), respectively, using the SDD basis set.

Figure 6

Transmission benchmark test for a single geometry at 35.0 Å with $1\times 1$ (dashed green), $3\times 3$ (dotted red), $5\times 5$ (solid blue), and $10\times 10$ $k$ points (dotted-dashed black).

Figure 7

Conductance benchmark test for ten geometries taken from the CPMD trajectory at 30.0 Å ordered chronologically: $1\times 1$ (dashed green) and $5\times 5$ $k$ points (solid blue).