Measuring the Force of Interaction between a Metallic Probe and a Single Molecule

Precision current measurements are recorded at 5 K during the approach and contact between a Pt-inked probe and the carbon-carbon double-bond region of an isolated 1,3-cyclohexadiene molecule chemisorbed on a Si(100) surface. Scanning tunneling spectroscopic data reveal systematic features in the current at specific probe-molecule separations. Aided by density functional theory calculations, we show that these features arise from interaction forces between the probe and molecule, which can be interpreted as the relaxation of the probe-molecule system prior to and during contact.

Figure 1

STM images of (a) $63.5\times 63.5\mathrm{nm}$ Pt(111) surface area with 0.1 nA and 0.45 V sample bias and (b) $13\times 12.6\mathrm{nm}$ $1,3\mathrm{\text{−}}\mathrm{CHD}/\mathrm{Si}(100)$ surface area with 0.1 nA and 0.7 V sample bias. (c) $I$, (d) $dI/dZ$, and (e) $d^{2}I/d{Z}^2$ are simultaneously recorded on the bare Pt(111); gray (inwards to surface) and black (outwards), and on the 1,3-CHD maximum red (inwards) and green (outwards). The bottom curves in (c)–(e) are from a separate 1,3-CHD experiment and are shifted with respect to the 1,3-CHD-ordinate scale to allow comparison. The spectra were taken with constant rate of $0.32\AA /\mathrm{s}$. The crosshatched area in (c)–(e) indicates the hysteresis-free range of probe-sample separations.

Figure 2

The dependence of the apparent tunneling barrier height ${\varphi }_A$ on the probe-sample separation $Z_{\mathrm{piezo}}$. The gray and red curves represent experimental results on bare Pt(111) surface, and on the 1,3-CHD molecule, respectively, derived from Eq. (2). The molecule data (red curves) are averages of the inward and outward traces in Fig. 1. The black and green curves are fits to these experimental data using Eq. (4), with (black) and without (green) a barrier interaction term in the potential. The crosshatched area indicates the hysteresis-free range in Figs. 1c, 1d, 1e. For comparison, the force gradient ($dF/dZ$) derived from the black curve is presented as a dotted blue curve. The $dF/dZ$ amplitude is rescaled and vertically shifted to emphasize the qualitative agreement with the red curve in (a).

Figure 3

Schematic model of the probe-sample system under investigation. The $\mathrm{C}\mathrm{C}$ moiety attachment to the surface is modeled by a spring that responds to the presence of the approaching probe. The parameters applied in the fitting procedure are illustrated in the figure. The different panels represent the model with no probe-molecule interaction (a), and with attractive (b) and repulsive (c) interaction.

Figure 4

The probe-$\mathrm{C}\mathrm{C}$ moiety interaction potential determined using the density functional theory (DFT) calculated vertical displacement of the $\mathrm{C}\mathrm{C}$ moiety (solid black line) and by fitting the experimental data in Figs. 1c, 1d, 1e, 2 using the Morse$+$barrier potential (solid red line). The dotted lines represent interaction potentials without barrier. The horizontal blue bars connected by lines represent the calculated energy and bond-length ranges for the $\pi$ and di-$\sigma$ bonded ethylene species on a Pt surface with various numbers of relaxed Pt atoms [20]. The inset shows the result after subtracting the dotted from the solid curves and represents the potential barriers found in the DFT calculations (black curve) and in the experiment (red curve).