4 FIG. 4: (Color online) (a) Calculated IETS spectra of pentanedithiol for two different electrode separations that differ by 0.1 nm (top-red more stretched than bottom-blue). The dashed curves are rounded using a smoothing filter equivalent to that used in the processing of the experimental data. The corresponding black curves (vertical axis scale arbitrary) represent the density of vibrational modes for these two configurations. The different peaks are labeled according to the character of the mode (st=stretch, rc=rock, wg=wag, tw=twist, sc=scissor). (b),(c) Eigenchannel scattering states [21] corresponding to electrons originating in the left and right electrode, respectively. The visualizations represent isosurfaces of the real part of the wave functions (with sign). (d),(e) Illustration of an active (d) and a silent (e) mode from the spectrum for the less stretched configuration. lent agreement between experiment and theory, even the magnitude of the inelastic signals is quantitatively repro- duced. All the peaks appearing in the PDF in Fig. 2(c) can be identified with some group of peaks in Fig. 4(a): peak A corresponds to a C–C stretch with some contri- bution from CH$_{2}$ twist; B to C–S stretch with some CH$_{2}$ rock; C to CH$_{2}$ wag and twist; D to CH$_{2}$ scissor; E to Au–S–C stretch; F to Au–S stretch; and G to CH$_{2}$ rock and twist. The fact that the calculated peaks have the same intensities as the measured peaks [see Fig. 1(c)] al- lows us to draw an important conclusion: the electrons are indeed tunneling through a pentanedithiol molecule suspended between the electrodes. brational deformation potential, and final electron state. Therefore, propensity rules can be understood from sym- metry considerations. For the pentanedithiol junction an eigenchannel analysis shows that the IETS can be ratio- nalized by just considering inelastic scattering between the two scattering states belonging to the most trans- mitting eigenchannel. These states, shown in Fig. 4(b) and (c) for electrons originating in the left and right elec- trode, respectively, possess a σ -type symmetry and can therefore only couple via modes with longitudinal char- acter. For instance, we get a large signal from the C–C stretch mode (¯ hω = 127 meV) illustrated in Fig. 4(d), while scattering is suppressed for the essentially trans- verse mode (¯ hω = 106 meV) illustrated in Fig. 4(e). For comparison with the experimental curves the rounding introduced by the ac modulation used to mea- sured the differential conductance has also been included in the theory curves, shown with dashed lines in Fig. 4(a) and the top and bottom curves (thick black traces) in Fig. 1(c). As a result of this rounding the individual peaks cannot be resolved. Fig. 1(c) shows the excel- Comparison with the experiment also requires to take into consideration that the molecules are in different states of strain. We have calculated the spectra for sev- eral different elongations of the molecule to determine the strain dependence of the modes. In this way we can characterize the C–C (C–S) mode, i.e., peak A (B), by a shift of − 5 . 0 ( − 2 . 9) meV/ ˚ A, consistent with the ex- perimental results. This is a strong indication that the