Can One Define the Conductance of Amino Acids?

We studied the electron-transport properties of ten different amino acids and one dimer (di-methionine) using the mechanically controlled break-junction (MCBJ) technique. For methionine and cysteine, additional measurements were performed with the scanning tunneling microscope break-junction (STM-BJ) technique. By means of a statistical clustering technique, we identified several conductance groups for each of the molecules considered. Ab initio calculations revealed that the observed broad conductance distribution stems from the possibility of various binding geometries which can be formed during stretching combined with a multitude of possible conformational changes. The results suggest that it would be helpful to explore different experimental techniques such as recognition tunneling and conditions to help identify the nature of amino-acid-based junctions even further, for example, with the goal to establish a firm platform for their unambiguous recognition by tunneling break-junction experiments.


Clustering method and the 1D and 2D histograms of all classes for methionine and cysteine
The goal of the clustering analysis is to sort the breaking traces into groups which share the same plateaus. The K-means clustering algorithm is an unsupervised and reference-free learning tool which is able to analyse a high dimensional space. 1 To compare the breaking traces, we created a binned image of each and compared the height profiles. Each of the bins is referred to as a feature. Additionally, 1D histograms were created by adding up all bins at a fixed conductance. This information was added as extra features to the features of the corresponding binned image. As inputs, K-means needs the feature vector for every trace and the number of clusters into which it should group the traces. The optimal groups found by Kmeans are referred to as classes.
Every class can then be analysed individually. First, the 1D and 2D histogram of the traces inside the class were generated. From the 1D histogram it was determined whether the class has plateaus. If yes, their position Gi and standard deviation (Gi) were obtained by fitting the peak in the 1D histogram with a Gaussian. At these positions, all traces within the class were analyzed to find the average length and slope of the plateau.
To find the plateau length, the data points inside the conductance regime [Gi -(Gi), Gi + (Gi)] were detected in every trace. The plateau length was taken to be the distance between the first and last one of these points. The length was averaged over all traces and the standard deviation was computed. Including some points outside the plateau, does not change the obtained plateau length considerably, because the conductance drops fast at the plateau ends.
To obtain its slope, the plateau was fitted with a linear dependence for every trace. The plateau slopes are not normally distributed and have outliers far off the average slope. Therefore, the median of the slopes was computed. For the error, the two slopes were determined for which 20% of the values are below and 80% were above, respectively. The difference to the average slope was computed and the two differences averaged. Additionally, the tunnelling slope was fitted for every curve between conductance values of 10 -5 and 10 -6 G0 for comparison.      Figure S7: Comparison of the average plateau positions from clustering 6,000 methionine traces into 4, 5, 6 and 10 classes, respectively. Plateaus were only considered, if they were shorter than the molecule and less steep than the tunnelling slope.

Stability of the clustering method
A very important input parameter of the clustering method is the number of groups that the clustering has to yield. Figure S7 shows how the number of detected plateaus changes depending on the chosen number of clusters. If the data is divided into more classes, more plateaus at different positions will be found. Partly, new plateaus appear, like the ones at a conductance below 10 -5 G0 for 10 classes. Furthermore, existing clusters tend to split up into two. It can be true, that they actually correspond to two plateaus (corresponding to distinctively different junction configurations) that are lying close together, but it can also happen, that one plateau gets split up into two, while representing a very similar junction configuration. Conclusions can therefore only be drawn about whether plateaus exist in a certain conductance regime, not about how many plateaus there are exactly. Five classes were chosen as an intermediate number to visualize the conductance behaviour across the different molecules.

Preparation of the data
Before analysing the data, all traces were aligned such that the breaking starts at a displacement value of zero. Traces in which the conductance didn't drop to the noise level, meaning that the junction didn't break completely, were removed. Then, the noise level was subtracted. The displacement-axis was calibrated using the tunnelling slopes of the pure gold. Since the measurements are performed in air, work function values around (1.0 ± 0.2) eV were used in the fitting. 2,3 This corresponds to a tunnelling slope of approximately -4.4 nm -1 on the decadic logarithmic scale to which we calibrated all measurements. Gpeak / G0 / / (1.3 ± 0.5) · 10 -3 (7 ± 2) · 10 -5 (2.8 ± 0.6) · 10 -5
Besides the Au-cysteine-Au junctions considered in Figure 6 of the main text, we considered two more cases. Figure S8 displays the trapping of a gold atom between two neighboring molecules; this was suggested to be a plausible effect in break-junction measurements in the presence of thiolated molecules 4,5 and was claimed to give rise to conductance values much lower than for a standard Au-molecule-Au juntion. In the case of the cysteine-based junction considered here, the HOMO-related peak unfortunately lies quite close to the Fermi energy, corresponding actually to quite a high transmission at the Fermi level. However, given the already-mentioned inaccuracy of the HOMO-LUMO gap, this peak is most likely to lie at lower energy. Consequently, in view of the much lower transmission produced by this geometry in the energy region immediately above the Fermi level, one can foresee that the real gap would actually result in a much lower conductance. We now turn to discuss Figure S8b, where we have instead considered the formation of a dimer, the possible formation of which was suggested in Ref. 6 . This configuration clearly gives rise to a very low conductance (much lower than any of the other geometries considered for cysteine). The transmission curve also shows an interference feature close to the Fermi level; this in turn stems from the two highest occupied orbitals of the dimer (which are degenerate).

The role of the H ion of the COOH group
In the next figure (Fig. S9), we show a comparison between the transmission curves obtained for cysteine and methionine with and without the H atom of the COOH group. These two cases will be henceforth referred to as COOH and COO-. To this aim, we chose geometry "g" and "e" of Figure 6 of the main text for cysteine and methionine, respectively. All the structures were optimized as described in the "Method" section of the manuscript. For both molecules, in the transmission curve of the COOH geometries the LUMO appears closer to the Fermi energy as compared to the COO-case. For methionine, we also note that the interference feature disappears as a result of a change in the metal-molecule coupling. It is also worth mentioning that attempts to perform such a comparison for cysteine in geometry "j" (which is more similar to the structure "e" of methionine than "g" is) failed. This is because the presence of the additional H atom made the cysteine-gold bond at the O terminal weaker, causing the COOH-Au bond to break. Only by reducing the Au-Au distance considerably was the optimization possible, which led to the final geometry being the same as structure "g", i.e., with the formation of a NH2-Au bond. Figure S9: Transmission as a function of energy for cysteine in geometry "g" (left) and methionine in geometry "e"(right) of Figure 6 of the main with (red) and without (black) the H atom of the carboxyl group.

The effect of water
In order to understand how the presence of the water molecules surrounding the junctions would affect the electrical conductance, we analyzed a simple case in which a water molecule is placed in proximity of the NH2 group of a cysteine-and a methionine-based junction. The corresponding geometries are shown in the figure below (Fig. S10), together with the transmission curves for the structures with and without the presence of the water molecule. In both cases, the water causes the molecular resonance which is closer to the Fermi level to narrow down and to shift to lower energies, causing in turn a decrease in conductance. In order to reproduce the real experimental scenario, one should actually include a much higher number of water molecules. 10. Gas-phase energy levels In the following table we report the energy values (eV) for the Kohn-Sham HOMO and LUMO. 11. Di-methionine: additional geometries In Fig. S11, we show the transmission curve for di-methionine for the "1 x O-Au bond" and "2 x O-Au bond" structures as well as a for a geometry in which it is connected to gold via a S atom on both sides. The latter case yields the lowest conductance as expected, given the longer length of this junction as compared to the other two geometries. The "1 x O-Au bond" case shows an interference feature, which stems from the presence of two competing conductance paths. 12. Spatial distribution of the frontier orbitals Figure S12 shows the spatial distribution of the highest occupied orbitals for all amino acids studied in this work when connected to a gold atom on both sides as in the 1xO-Au geometries.
Figure S12: HOMO and LUMO for gas-phase molecules connected to one Au atom on each side. The Au atom is connected to the same anchor group as in the "1xO-Au bond" geometries and was here included in order to reproduce the same hybridization the molecular orbitals undergo when the amino acid is connected to gold clusters. The orbital corresponding to the main resonance close to the Fermi level is the HOMO-1 for all, except for cysteine and aspartic acid, for which is the HOMO.