1.06 1.08 1.1 1.12 0.1 0.105 0.11 0.115 0.12 0.125 0.13 displacement (nm) peak position (V) 0.08 0.09 0.1 0.11 0.12 0.13 peak position (V) c 3 0 1 2 3 0 0.5 1 1.5 G/G 0 × 10 $_{−}$3 conductance PDF × 10 3 a −4 −3 −2 −1 0 0 0.2 0.4 0.6 0.8 log( G/G 0 ) b conductance PDF −0.2 −0.15 −0.1 −0.05 0 0.05 0.1 0.15 0.2 20 40 60 80 100 A B C D E F G A B C D E F G c V bias (V) peak PDF ( 1/V) FIG. 3: Peak position as a function of the tip retraction in Fig. 1. Circles correspond to peak A around 125 mV (left y -axis) and triangles to peak B around 80 mV (right y -axis). Filled (open) symbols represent data obtained at positive (negative) voltage polarity. The continuous lines are a guide to the eye. FIG. 2: (Color online) (a) Probability density function (PDF) of the low-bias conductance for 540 spectra in 33 different molecular junctions acquired at low temperatures (4.2 K). The low-bias conductance of a given spectra is the ratio I/V at V = 25 mV obtained from the simultaneously measured I vs V curve. In the PDF we have used ϵ = 3 × 10 $^{$_{−}$5}$. (b) PDF for the low-bias conductance measured at room temperature in solution (green curve). (c) PDF of peaks (dips) in the IETS spectra at positive (negative) voltages. Voltages around zero have been excluded due to the presence of zero-bias anomalies. In the PDF we have used ϵ = 3 mV. molecular junction is subject to a varying stress: the junction is stretched up to the breaking point. The ef- fect of this stretching on the vibrational spectra is to shift the position of peaks of types A and B to lower voltages (a maximum of 5-10 mV), i.e., to lower frequencies, as shown in Fig. 3. It is not possible to follow the evolu- tion of the other modes as the corresponding peaks are less well-defined. The observed frequency redshift is sim- ilar to that observed for atomic gold chains [3], where the inelastic signal originates from a longitudinal mode that softens with stretching, reflecting the weakening of the interatomic bonds [20]. The conductance jump at a displacement of 1.095 nm in Fig. 1(a) results in a fre- quency jump in Fig. 3, demonstrating that its origin is in a strain relaxation of the junction, probably due to an atomic rearrangement in the electrodes [15]. takes place via tunneling. Note that these two PDFs cor- respond to two different situations and are not directly comparable: in Fig. 2(b), the PDF is obtained from all measured traces and includes all points of the trace while in Fig. 2(a) the PDF includes a single point per spectra. We have chosen to use probability density (PDF) instead of the conventional histograms, so that the probability of finding a value in a certain range can be obtained by in- tegration of the PDF in that range. To obtain the PDF, f ( x ) from a set of experimental data, x$_{i}$ we use the stan- dard definition, f ( x ) = (1 /N ) ∑$_{i}$ δ ( x − x$_{i}$ ), where N is the number of data, and we approximate the Dirac delta function to a Lorentzian function, δ ( x ) ≈ ϵ/π x $^{2}$+ ϵ $_{2}$, with an adequately small ϵ . In Fig. 2(c), we show the PDF of peaks (dips) in the IETS spectra appearing at positive (negative) voltages. All peaks above the noise level are used to construct the PDF without further selection. We have normalized the PDF to the number of spectra and consequently this function represents the probability of finding a peak in a given interval of the bias voltage. The symmetry of the features reflects the antisymmetry of the IETS spectra. Some peaks are present in all spectra. More precisely, the probability is unity for finding a peak in the interval (125 ± 10) mV (peak of type A), as well as for finding one in (85 ± 13 . 5) mV (peak of type B). These signals can be observed directly in the individual spectra, cf. Fig. 1. During the measurement of the IETS spectra the Fig. 4(a) shows the calculated vibrational spectrum for a pentanedithiol between two Au electrodes for two dif- ferent electrode separations. The spectra are quite sim- ilar to those calculated for octanedithiol junctions [24]. We observe that there are active and inactive modes due to approximate selection (propensity) rules [26]. The strength of the IETS signal can be related to a matrix element involving three factors: initial electron state, vi- In order to understand how the peak positions and amplitudes in the IETS spectra relate to the vari- ous vibrational modes of the molecular configuration and their dependence on stretching, we have performed first-principles transport calculations based on non- equilibrium Green’s functions techniques [22, 23]. Our simulations attempt to mimic the experimental situation with the molecule suspended between two metal elec- trodes, as shown in Fig. 4, assuming that the S atoms are bound to Au adatoms on Au(111) surfaces [25]. The cal- culated zero-bias conductance of the pentanedithiol junc- tions is of the order 0.005 G$_{0}$ per molecule, i.e., about a factor of 5 higher than the experimental value.