## 3 Results and Discussion
As a consequence of the _cis_-TMC geometry adopted during the single-molecule contact, the phenyl ring comes closer and laterally faces the Au electrode [9], promoting a \(\pi\)-stacking interaction, in additional to the thiol bond [56; 57; 58], with interaction energies in the order of 20 kcal/mol [59]. The relative orientation of phenyl moiety with respect to the Au electrode and its close distance to the electrode surface is known to play an important role for stability and transport properties in single-molecule junctions [57]. Thus, the methyl-S-Au bond accompanied by phenyl-Au interactions provide the larger stability of the _cis_-TMC single-molecule junction relative to the _trans_ isomer [60]. Such cooperative stabilisation effect can be expected to lead to longer junction lifetimes and non-reversibility of the in situ _trans_-to-_cis_ isomerisation, in line with our observations. Despite the larger molecule | electrode coupling for _cis_-TMC, the overall conductance of the _cis_-TMC junction is dominated by the _gauche_ defect that breaks the \(\pi\)-orbital electron pathway through the molecule [32], yielding a lower conductance. To corroborate the hypothesis of in situ EEF-induced _trans_-to-_cis_ isomerisation in the single-TMC junction, we performed density functional theory (DFT) calculations to model the effect that an oriented EEF has on the _trans_-TMC molecule in the junction. Low-energy excited states are often the key to describe photoinduced isomerisation processes [61; 62; 63]. We then analysed how an electric field affects these energy levels via applied voltage bias. For the S\({}_{1}\) (first excited state), a dramatic change in the oscillator strength (spectroscopic transition probability) is observed for both the _cis_-TMC and _trans_-TMC conformers. Figure 4 shows (black line) that the S\({}_{0}\)\(\rightarrow\) S\({}_{1}\) transition is strongly forbidden in the absence of an electric field and is associated with delocalized orbitals extending along the molecule (see natural transition orbitals for the _trans_-TMC conformer in Figure 5). The addition of an EEF (blue and red curves in Figure 4) increases the oscillator strength dramatically for both _cis_-TMC and _trans_-TMC conformers (0\({}^{\circ}\) and 180\({}^{\circ}\) respectively along the X-axis rotation coordinate depicted in Figure 4) due to conjugation along the molecular chain, leading to large polarizability. In the case of _trans_-TMC, the enhancement of the oscillator strength is less dramatic than in the _cis_-TMC conformer (a factor of 12 instead of 600, Figure 4) because the transition to the S\({}_{1}\) state at zero field for _trans_-TMC is weak but not as forbidden as for _cis_-TMC. These differences are related to the reduction of symmetry associated with double bond rotation (see C\({}_{9}\)-C  
Figure 3: (a) Representative HC (green) and LC (orange) blinks of the trans-TMC junction formation in a typical static BJ experiment. 2D conductance maps built out of hundreds of trans-TMC blinking traces at V\({}_{\text{bias}}\) = (b) 7 mV, (c) 65 mV, and (d) 130 mV at a fixed gap distance. Counts are normalized to a maximum of 100.  
in Figure 1a), as illustrated in Figure A4. In _cis_-TMC case, natural transition orbitals [64], localized at each side of the double bond, indicate that the transition to S\({}_{1}\) will lead to the charge displacement along the charge transport direction, contributing to the current. Calculated energy profiles of the TMC _trans_-to-_cis_ isomerisation in the absence of an EEF for molecules in the ground state S\({}_{0}\), show expectedly large energy rotation barriers of ca. 48 (30) kcal/mol (Appendix A, Figure A3). These barriers are consistent with previous estimates of C=C double-bond rotation activation energies [65]. EEF, however, promotes the mixing of the \(S_{1}\), \(S_{2}\) and \(S_{3}\) states, in line with the observed enhancement of the oscillator strength (the overlap matrix is given in the Table A1 of the Supplementary Information).