Tuning Single-Molecule Conductance by Controlled Electric Field-Induced trans-to-cis Isomerisation

External electric fields (EEFs) have proven to be very efficient in catalysing chemical reactions, even those inaccessible via wet-chemical synthesis. At the single-molecule level, oriented EEFs have been successfully used to promote in situ single-molecule reactions in the absence of chemical catalysts. Here, we elucidate the effect of an EEFs on the structure and conductance of a molecular junction. Employing scanning tunnelling microscopy break junction (STM-BJ) experiments, we form and electrically characterize single-molecule junctions of two tetramethyl carotene isomers. Two discrete conductance signatures show up more prominently at low and high applied voltages which are univocally ascribed to the trans and cis isomers of the carotenoid, respectively. The difference in conductance between both cis-/transisomers is in concordance with previous predictions considering π-quantum interference due to the presence of a single gauche defect in the trans isomer. Electronic structure calculations suggest that the electric field polarizes the molecule and mixes the excited states. The mixed states have a (spectroscopically) allowed transition and, therefore, can both promote the cis-isomerization of the molecule and participate in electron transport. Our work opens new routes for the in situ control of isomerisation reactions in single-molecule contacts.


Introduction
The development of novel, more efficient ways to control molecular reactions has been a restless quest for synthetic chemists. Many different triggers, such as light, heat or external electric fields (EEF) are being used to promote chemical reactions [1,2]. EEF have been shown to be able to stabilize conventionally non-favourable electronic structures [3] and thus to enable new transition states [4,5] in a theoretically predictable manner. These field-induced chemical reactivity experiments, which are well reported in single-molecule devices [3,5], represent an exciting alternative to traditional bulk chemical catalyst approaches since EEF provide a cost-, material-efficient methodology to precisely control molecular reactions in a cleaner, more sustainable way.
In the molecular electronics (ME) field, one of the most appealing single-molecule reactions is the isomerisation reaction [6][7][8][9], because small changes in the molecular structure give rise to a significant change in the conductance of the molecular wire [8,9]. The molecular configuration constitutes a defining parameter for the intrinsic conducting properties of a molecule. Moreover, measuring single-molecule conductance can be used to follow structural changes in a molecular contact [10][11][12][13], opening the way to real time detection of electrical currents associated with in situ stimuli-induced molecular structural changes [5,14,15]. Charge transport across molecular systems as a function of molecule configuration has been widely studied theoretically [16][17][18] and experimentally [8,9,11,[19][20][21][22], including cis-/transisomerization. Different isomers exhibit characteristic conductance values that can be attributed to various effects, such as the potential energy barrier variation due to structural change [8,17,19], the different contact geometry [8,9,16,21], or the different energies of the frontier molecular orbitals with respect to the electrode Fermi levels for each isomer [17,18,22]. Behind unravelling the particular phenomenology for each system, the detection of electrical currents across molecules in metal|molecule|metal junctions [13,23,24] have been essential to electrically characterize structural changes of individual molecular systems [25].
Here, we report on single-molecule scanning tunnelling microscopy break junction (STM-BJ) conductance experiments of all-E-carotene with terminal 1,5-dimethyl-3-methylthiophenyl groups (trans-TMC, Figure 1a) and 9-Z-carotene with terminal 3methylthiophenyl groups (cis-TMC, Figure 1b) carotenoid derivatives. Both, trans-TMC and cis-TMC-syn molecules are chemically stable at room temperature [22,26]. Carotenoids contain a delocalized π-conjugated polyene backbone chain with planar configuration maximizing π-orbital overlap resulting in an efficient electron pathway [27][28][29]. They serve in several natural photosynthetic systems as energy/electron transfer mediator [30,31]. Our main findings indicate: (1) applying an STM bias voltage to the high-conductance (HC) trans-TMC-based molecular junction promotes the in-situ switching to a low-conductance (LC) cis-TMC-based molecular junction whose chemical compound cannot be synthesized wet chemically due to steric constraints. (2) The ratio of LC/HC signatures scales with the V bias (i.e., EEF) magnitudes. At low biases, the weaker EEF do not promote the isomerisation and thus trans-TMC is the only detectable isomer. In contrast, at medium and high biases, the EEF strength is enough to promote the isomerisation and the cis-TMC becomes electrically detectable. (3) According to our density functional theory (DFT) calculations the isomerisation is facilitated via an EEF-induced excited state in the trans-TMC. (4) The difference in junction's lifetime between cis-TMC and trans-TMC isomers is attributed to a relatively high stability and more constrained configuration of the former in the molecular junction. (5) The low conductance for the cis isomer is ascribed to the presence of a single point gauche defect in the carotenoid alkene backbone which breaks the π-orbital pathway thus lowering conductance [32].  (2) current plateau at Istep due to the formation of a molecular junction during tip retraction, (3) zero current (junction breakdown) stage when the tip is pulled away from the surface and the molecule detaches from one electrode. (d) Schematic of the blinking approach: (1) fixed inter-electrode distance, d, at a pre-defined tunnelling current, It. (2) current blink at, Im due to the spontaneous formation of a molecular junction (with a finite lifetime τ), (3) current drop to It upon spontaneous molecular junction breakdown.

Experiments
The conductance measurements were carried out with a mechanically and electronically isolated "PicoSPM II" microscope head controlled by Picoscan-2500 electronics (Agilent) using a homemade PTFE STM cell. Current signals from the STM were captured using a NI-DAQmx/BNC-2110 (National Instruments analogic-digital converter PC-interface acquisition system), analysed with LabVIEW software and plotted employing Python through Matplotlib [33]. All glassware and homemade PTFE cells were cleaned with freshly prepared piranha solution (volume ratio of 3:1 H2SO4:H2O2) before the experiments and subsequently rinsed with 18 MΩ cm −1 Milli-Q water (Millipore ® , Burlingtone, MA, USA). A Au(111) single crystal (10 mm × 1 mm, MaTeck) of 5N purity and an orientation accuracy of < 0.1˚ was employed as a substrate. Before each experiment, the Au(111) crystal was electro-polished to eliminate possible residual contamination, rinsed with Milli-Q water, annealed in a H2 flame for 10 minutes and then cooled down in Ar atmosphere. The crystal was then placed in the STM cell that was filled with 80 μL of pure mesitylene (purity 99 %, ACROS Organic, Thermo Fisher Scientific). One drop of a 0.5 μM mesitylene solution containing the target carotenoid molecule was added to the STM cell before starting the single-molecule conductance experiments. The employed molecules in this work, trans-TMC and cis-TMC-syn, were synthetized according to a procedure described by Kim et al. [22] (for synthetic details see Appendix A.4).

Simulations
All calculations were performed using the ORCA 4.2.1 software package [34]. DFT and time dependent DFT TD-DFT [35] calculations with the BP86 density functional [36,37], theDef2-TZVP basis set [38,39] and the D3 corrections [40,41]. State overlaps were calculated by the WF Overlap program [42] where excited states were constructed from (c) Schematic of the dynamic BJ approach: (1) current saturation; tip and substrate in contact, (2) current plateau at I step due to the formation of a molecular junction during tip retraction, (3) zero current (junction breakdown) stage when the tip is pulled away from the surface and the molecule detaches from one electrode. (d) Schematic of the blinking approach: (1) fixed inter-electrode distance, d, at a pre-defined tunnelling current, I t . (2) current blink at, I m due to the spontaneous formation of a molecular junction (with a finite lifetime τ), (3) current drop to I t upon spontaneous molecular junction breakdown.

Experiments
The conductance measurements were carried out with a mechanically and electronically isolated "PicoSPM II" microscope head controlled by Picoscan-2500 electronics (Agilent) using a homemade PTFE STM cell. Current signals from the STM were captured using a NI-DAQmx/BNC-2110 (National Instruments analogic-digital converter PC-interface acquisition system), analysed with LabVIEW software and plotted employing Python through Matplotlib [33]. All glassware and homemade PTFE cells were cleaned with freshly prepared piranha solution (volume ratio of 3:1 H 2 SO 4 :H 2 O 2 ) before the experiments and subsequently rinsed with 18 MΩ cm −1 Milli-Q water (Millipore ® , Burlingtone, MA, USA). A Au(111) single crystal (10 mm × 1 mm, MaTeck) of 5N purity and an orientation accuracy of <0.1°was employed as a substrate. Before each experiment, the Au(111) crystal was electro-polished to eliminate possible residual contamination, rinsed with Milli-Q water, annealed in a H 2 flame for 10 minutes and then cooled down in Ar atmosphere. The crystal was then placed in the STM cell that was filled with 80 µL of pure mesitylene (purity 99 %, ACROS Organic, Thermo Fisher Scientific). One drop of a 0.5 µM mesitylene solution containing the target carotenoid molecule was added to the STM cell before starting the single-molecule conductance experiments. The employed molecules in this work, trans-TMC and cis-TMC-syn, were synthetized according to a procedure described by Kim et al. [22] (for synthetic details see Appendix A.4).

Simulations
All calculations were performed using the ORCA 4.2.1 software package [34]. DFT and time dependent DFT TD-DFT [35] calculations with the BP86 density functional [36,37], theDef2-TZVP basis set [38,39] and the D3 corrections [40,41]. State overlaps were calculated by the WF Overlap program [42] where excited states were constructed from all TD-DFT orbital excitations with a weight larger than 1 × 10 −6 . This tight setting led to many determinants to account for the 10 first excited singlets, ranging from 4015 to 5333, depending on the calculation. Comparison between the overlap matrix before and after orthonormalisation demonstrates the adequacy of the determinant basis to account for the excited state wave functions as evidenced by the small relative angles between both matrices (0.023 and 0.004 for the cis-TMC and trans-TMC, respectively).

Results and Discussion
We have employed dynamic and static STM-BJ methods to characterize single-molecule TMC isomers conductance and to study the effect of the EEF generated by the STM bias voltage, on the conductance of the TMC single-molecule junction. Briefly, in the dynamic BJ approach (Figure 1c), the STM tip electrode is repeatedly moved into and out of contact with the substrate electrode at a constant piezo voltage ramp at 0.5 V/s with the STM piezo servo-feedback loop off. The junction conductivity is captured via the current versus time (or displacement) traces in the retraction stage. During the contact process (stage 1 in Figure 1c,), the two metal electrodes (STM tip and substrate) are in contact, which the corresponding current saturation due to high conductive nature of the metal/metal contact, and individual carotenoid molecules in solution spontaneously attach to them through the -SMe terminal groups that have a high affinity for Au [26]. When the tip is retracted from the substrate, the metallic contact breaks and makes it possible for a TMC molecule to bridge the nanoscale gap (stage 2 in Figure 1c). In such cases, the current trace exhibits characteristic step-like features or plateaus corresponding to the quantum conductance of the molecular junction. Upon further retraction of the tip, the molecule detaches from one electrode (stage 3 in Figure 1c). The collapse of the molecular junction (open gap) is accompanied by a sharp drop in current. In a typical dynamic BJ experiment, we collect thousands of current traces, and an automated selection process designed in LabVIEW selects the decays that show plateaus (formation of a molecular junction and accumulates them into 1D semi-logarithmic conductance histograms [26]. The same selection criteria to build all histograms are applied throughout all experimental series. The yield of decay curves showing plateaus that meet the selection criteria is typically around 25% of the total number of collected curves [43]. The data selection process results in 1D conductance histograms that show peaks above the tunnelling background baseline, providing an averaged single-molecule conductance value, G. G is defined as G = I step /V bias , where I step is the current plateau and V bias is the voltage applied between the two Au electrodes. In the static approach ( Figure 1d) [5], a fixed inter-electrode distance (electrode-electrode separation) is established between the STM tip and the substrate by setting a defined tunnelling current, I t , to flow between them. When the gap has stabilized and shows a constant I t versus time signal, the I t feedback is turned off and the actual tunnelling current monitored (stage 1 in Figure 1d). A sudden current increase to I m appears when a target molecule is spontaneously caught in the gap and transiently forms a molecular junction, lowering the resistance between the electrodes (stage 2 in Figure 1d) [44]. This sudden increase in current is commonly referred to as a blink. A current blink is characterized by its conductance value and by its lifetime. The (spontaneous) collapse of the junction (i.e., molecule detaches from one electrode) is evidenced by a sudden drop of the I m to I t [5,45,46] (stage 3 in Figure 1d). The number of individual blinks per fraction of time defines the accumulation yield and hundreds of them are plotted as 1D and 2D conductance histograms with a common x-axis time origin. All blinks are accumulated for evaluation without any selection using an automated process designed in LabVIEW. This process provides the averaged single-molecule conductance as a peak in the 1D histograms and prominent coloured regions of higher counts in the 2D blinking conductance-map histograms. The current corresponding to a trapped molecule (I blink ) is defined as I blink = I m − I t . Conductance values G are extracted from I blink divided by the V bias .
The 1D semi-logarithmic conductance histogram retrieved from single-molecule dynamic BJ experiments in the trans-TMC molecules exhibits two broad, overlapping conductance features ( Figure 2); 1.68 × 10 −4 G o (low conductance regime, LC) and 3.21 × 10 −4 G o (high conductance regime, HC), where G o = 2e 2 /h = 77.47 µS, the h Planck constant, the e elementary charge. The HC value is roughly twice of the LC value which might suggest the formation of multiple trans-TMC molecular junctions. However, several experimental observations rule out previous scenario: first, all the collected current traces show no correlation, displaying either HC or LC plateaus (Figure 2b), as opposed to current traces of junctions formed by multiple molecules that are characterized by the appearance of sequential plateau features due to consecutive molecular disconnections [47]. Second, junctions formed by multiple molecules also have a characteristic formation yield that decreases with the number of trapped molecules, i.e., the frequency of molecular junction formation decreases from the low conductive (few molecules) to the high conductive junctions (many molecules) [47,48]. The latter is the behaviour opposite to that observed in Figure 2a where the HC yield (27.7%) is significantly higher than the LC yield (17.4%). As such, we rule out that the HC values are related to a multiple molecule junction scenario and that the detection of the two current signatures must be a consequence of distinct single-molecule properties as discussed below. The 1D semi-logarithmic conductance histogram retrieved from single-molecule dynamic BJ experiments in the trans-TMC molecules exhibits two broad, overlapping conductance features ( Figure 2);1.68 × 10 −4 Go (low conductance regime, LC) and 3.21 × 10 −4 Go (high conductance regime, HC), where Go = 2e 2 /h = 77.47 μS, the h Planck constant, the e elementary charge. The HC value is roughly twice of the LC value which might suggest the formation of multiple trans-TMC molecular junctions. However, several experimental observations rule out previous scenario: first, all the collected current traces show no correlation, displaying either HC or LC plateaus (Figure 2b), as opposed to current traces of junctions formed by multiple molecules that are characterized by the appearance of sequential plateau features due to consecutive molecular disconnections [47]. Second, junctions formed by multiple molecules also have a characteristic formation yield that decreases with the number of trapped molecules, i.e., the frequency of molecular junction formation decreases from the low conductive (few molecules) to the high conductive junctions (many molecules) [47,48]. The latter is the behaviour opposite to that observed in Figure 2a where the HC yield (27.7%) is significantly higher than the LC yield (17.4%). As such, we rule out that the HC values are related to a multiple molecule junction scenario and that the detection of the two current signatures must be a consequence of distinct single-molecule properties as discussed below. The nanoscale inter-electrode distance of a molecular junction allows strong electric fields in the gap in the order of 10 8 to 10 9 V/m [5]. Such strong fields have been reported to promote single-molecule reactions of trapped molecules in an STM junction [3]. Given the cis-/trans-isomerization in carotenoids, we explore the possible electric field effect on the isomerization reaction in these systems. [25,[49][50][51][52][53]. The dynamic BJ approach can have detrimental effects when studying molecular configuration dynamics in a molecular junction due to the mechanical stress induced by the STM tip during retraction, which pulls on the molecule and can induce structural modifications [25,[49][50][51]. Instead, the static BJ approach (Figure 1b) avoids the aforementioned drawbacks by employing a fixed interelectrode distances also ensuring a constant gap EEF strength. The static BJ approach allows for a precise oriented EEF along the main junction axis. To this aim, we define three  The nanoscale inter-electrode distance of a molecular junction allows strong electric fields in the gap in the order of 10 8 to 10 9 V/m [5]. Such strong fields have been reported to promote single-molecule reactions of trapped molecules in an STM junction [3]. Given the cis-/trans-isomerization in carotenoids, we explore the possible electric field effect on the isomerization reaction in these systems [25,[49][50][51][52][53]. The dynamic BJ approach can have detrimental effects when studying molecular configuration dynamics in a molecular junction due to the mechanical stress induced by the STM tip during retraction, which pulls on the molecule and can induce structural modifications [25,[49][50][51]. Instead, the static BJ approach (Figure 1b) avoids the aforementioned drawbacks by employing a fixed interelectrode distances also ensuring a constant gap EEF strength. The static BJ approach allows for a precise oriented EEF along the main junction axis. To this aim, we define three EEF of increasing magnitudes (low, intermediate  (Figure 3c,d). These results are in agreement with the dynamic BJ results and provide further evidence that the observed conductance features originate from two distinct molecular features in the junction. The blink lifetime is the highest for the low-bias regime, reaching 0.73 s, decreasing to 0.44 s for HC and 0.58 s scores for LC at intermediate V bias and the shortest blink lifetimes, of 0.32 s for HC and of 0.42 s for LC, at high V bias . The decrease in blink lifetime with increasing V bias can be explained by a decrease in junction stability due to local heating effects and electromigration-induced mobility of metal atoms under higher EEFs. [54]. Note that at all the applied bias voltages, HC blinks display a 1.3 times longer lifetime as compared to LC blinks, which denotes an intrinsically higher junction stability in the case of HC junctions. The relative populations of the HC and LC junctions display a clear dependence on the applied EEFs. At low bias, all detected blinks correspond to the HC regime while at intermediate and high biases, the HC yield decreases significantly but LC features increase. At V bias = 65 mV, the LC/HC yield ratio is nearly one to one, 48 /52, respectively. At V bias = 130 mV, the LC/HC yield ratio increases to more than three, with the LC yield reaching 77 % of the total captured blinks. The observed behaviour in the blinking BJ approach is in accordance with the dynamic BJ results. In dynamic BJ experiments the varying gap distances produce overall higher EEFs even at the lower V bias due to the transiently lower electrode-electrode gap distances (starting at direct electrodeelectrode contact in the break-junction cycle, Figure 1c), which are sufficiently strong to induce the in situ trans-to-cis isomerisation and resulting in observed larger LC (cis-TMC) yields than in the blinking experiments. The observations for both BJ approaches suggest a conversion of HC to LC regimes in the presence of a sufficiently large V bias , i.e., a sufficiently strong applied EEF.
To test the HC to LC switching hypothesis, we perform voltage-pulse experiments where a high bias voltage pulse of 300 mV is applied for 10 ms during the lifetime of a HC blink to induce the switching to LC (Appendix A, Figure A1). After the voltage pulse, the junction switches from HC to LC and stays at the characteristic LC value at the returning low V bias of 30 mV prior to junction breakdown. Analogous voltage-jump experiments performed during LC blinks, show no conversion from LC to HC values. Both sets of experiments attest an irreversible process for the HC-to-LC conversion.
What is the nature of the two distinct V bias -dependent conductance features for trans-TMC in Figure 3? The static BJ results rule out a mechanical origin of the observed conductance switching initially observed in the dynamic BJ experiments, and point toward the bias voltage as the driving force for the observed bimodal conductance behaviour. Guided by previous literature that showed isomerisation reactions of individual molecules tuned by voltage differences [52,55], we hypothesize that applying a V bias to the TMC junction induces a trans-to-cis isomerisation of the molecule in the junction [52]. We have synthesized a homologous cis carotenoid (cis-TMC-syn) with a nearly identical structure ( Figure 1b) and use it as a control test. The cis-TMC-syn control junctions show identical yield, conductance and blinking lifetime as the LC regime observed for the trans-TMC junctions (see Appendix A.4 for details). These control findings strongly support our hypothesis that the trans-TMC undergoes an in situ isomerisation induced by the applied EEF along the junction.
The observed irreversibility of the isomerisation can be explained by preferential molecule|electrode coupling of the cis-TMC compared to trans-TMC [9]. We speculate that the cis-TMC structure offers an increased coupling between the distal phenyl ring and the Au electrode through van-der-Waals (π-) interactions [56,57]. 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 π-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 π-orbital electron pathway through the molecule [32], yielding a lower conductance. What is the nature of the two distinct Vbias-dependent conductance features for trans-TMC in Figure 3? The static BJ results rule out a mechanical origin of the observed conductance switching initially observed in the dynamic BJ experiments, and point toward the bias voltage as the driving force for the observed bimodal conductance behaviour. Guided by previous literature that showed isomerisation reactions of individual molecules tuned by voltage differences [52,55], we hypothesize that applying a Vbias to the TMC junction induces a trans-to-cis isomerisation of the molecule in the junction [52]. We have synthesized a homologous cis carotenoid (cis-TMC-syn) with a nearly identical structure ( Figure 1b) and use it as a control test. The cis-TMC-syn control junctions show identical yield, conductance and blinking lifetime as the LC regime observed for the trans-TMC junctions (see Appendix A.4. for details). These control findings strongly support our hypothesis that the trans-TMC undergoes an in situ isomerisation induced by the applied EEF along the junction.
The observed irreversibility of the isomerisation can be explained by preferential molecule|electrode coupling of the cis-TMC compared to trans-TMC [9]. We speculate that the cis-TMC structure offers an increased coupling between the distal phenyl ring and the Au electrode through van-der-Waals (π-) interactions [56,57]. 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 π-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 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 → 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 • and 180 • 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 10 Appl. Sci. 2021, 11, 3317 8 of 18 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). For trans-TMC molecules, the oscillator strengths of the S 0 → S 1 transition at fields on the order of 4.3 × 10 −2 V/nm increases to 0.2. Therefore, a voltage difference in the order of a few hundreds of mV for an inter-electrode distance (nanogap) adapted to the molecular size, should be sufficiently strong to induce a mixing between the S 1 and S 2 states, suggesting that the S 1 state participates in the current-induced excited-state dynamics and promotes the isomerisation. In our case, DFT calculations indicate that a voltage bias is likely to enhance the contribution of the S 1 state to the electron dynamics, promoting the isomerisation process. The applied bias voltage does not need to overcome the double-bond rotation barrier to promote conformational switching. Travelling electrons will activate isomerisation pathways by populating the π* orbitals connected with photo switching processes, as evidenced by the dramatic EEF-induced mixing of the key S 1 state.
ppl. Sci. 2021, 11, x FOR PEER REVIEW Figure 4. Oscillator strength for the S0 → S1 transition. Black, blue, and red colours co external electric fields (EEF) = 0, +2.3 × 10 −4 a.u. and −2.3 × 10 −4 a.u., respectively. Not difference in the enhancement of the oscillator between trans-TMC and cis-TMC con factor of 12 and 600, respectively).  Oscillator strength for the S0 → S1 transition. Black, blue, and red colours correspond to external electric fields (EEF) = 0, +2.3 × 10 −4 a.u. and −2.3 × 10 −4 a.u., respectively. Note the strength difference in the enhancement of the oscillator between trans-TMC and cis-TMC conformers (a factor of 12 and 600, respectively). To summarize, we can rationalize all observed experimental results with the assignment of HC and LC values to trans-TMC and cis-TMC isomers, respectively: Conductance. The cis isomer has a lower conductance value than the trans isomer. As previously reported [22], the breaking of the π-conjugation due to isomerisation lowers the transport efficiency along the polyene backbone [32].
Lifetime. The difference in lifetime between the HC blinks and the LC blinks reflects the different stability of each isomer in the molecular junction. The higher lifetimes of the LC blinks and the irreversibility of the trans-to-cis isomerisation can be attributed to a relatively higher stability of the cis-TMC isomer in the junction due to a more constrained To summarize, we can rationalize all observed experimental results with the assignment of HC and LC values to trans-TMC and cis-TMC isomers, respectively: Conductance. The cis isomer has a lower conductance value than the trans isomer. As previously reported [22], the breaking of the π-conjugation due to isomerisation lowers the transport efficiency along the polyene backbone [32].
Lifetime. The difference in lifetime between the HC blinks and the LC blinks reflects the different stability of each isomer in the molecular junction. The higher lifetimes of the LC blinks and the irreversibility of the trans-to-cis isomerisation can be attributed to a relatively higher stability of the cis-TMC isomer in the junction due to a more constrained configuration involving the terminal phenyl rings in the molecular anchoring to the electrodes.
Population vs. V bias . The ratio of LC/HC blinks increases with increasing V bias . DFT calculations suggest that the S 1 state remains spectroscopically dark at low fields, and therefore cannot promote electron transport. Thus, only high conductance associated with the trans-TMC isomer is observed. At high biases, the EEF induces an excited state mixing and hence promotes the trans-cis isomerisation, leading to an increasing number of (less conductive) cis conformers.

Conclusions
In the present study, an in situ electric field-dependent isomerisation in a singlemolecule junction is demonstrated. Our experimental platform allows modulating the EEF by modifying the bias voltage magnitude to well-defined nano-gaps between two metal leads, while detecting single-molecule current events. By characterizing both a trans-TMC and a synthetically homologous cis-TMC version, we have univocally assigned molecular conductance features to each isomer. Trans-TMC is then ascribed to the molecular junction displaying average conductance values of ca. 3 × 10 −4 Go, and the in situ generated cis-TMC is ascribed to molecular junctions average conductance values of ca. 1.6 × 10 −4 Go. We show that controlled voltage pulses can be used to in situ isomerize the trapped polyene molecular backbone in the nanoscale molecular junction. Our combined experimental results and DFT calculations ascertain that a controlled isomerisation irreversibly occurs in the trans-TMC-based single-molecule junctions when converted into a more structurally stable cis-TMC-based junction. The isomerisation rate dependence on the EEF strength is supported by the increasing yield of junction formation of the cis-TMC form as a function of the EEF magnitude. Under high bias regimes (i.e., strong EEF), the cis-TMC LC feature dominates the conductance histogram. We conclude that the isomerisation from the trans-to the cis-TMC is promoted in a controlled way under a specific EEF strength in the singlemolecule junctions. These findings have a special relevance in the field of electrocatalysis, since obtaining the cis-TMC isomer is unfeasible using traditional bulk synthetic routes due to steric constrains.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
All the data and additional information supporting the findings of this study are available from the corresponding authors upon reasonable request.

Conflicts of Interest:
The authors declare no conflict of interest.

Appendix A Appendix A.1. In Situ Irreversible High-Conductance (HC) to Low-Conductance (LC) Conversion
To induce HC-to-LC conversion in situ and to study its reversibility [6,52], a highvoltage pulse of 300 mV is applied for 10 ms during the lifetime of a detected HC blink, with the aim to switch the molecular junction to the LC regime ( Figure A1a,b). Immediately after the pulse, at V bias = 30 mV, the detected current decreases to the characteristic LC value ( Figure A1c), attesting the V bias -induced conversion of an individual trapped trans-TMC molecule. Eventually, the junction collapses spontaneously and the current suddenly drops to the I t value. Equivalent experiments performed during LC blinks show constant I m profiles independent of the bias pulse, without conversion from LC to HC values (see Figure A1d). Both sets of experiments point to an irreversible HC-to-LC conversion under the experimental conditions. LC value (Figure A1c), attesting the Vbias-induced conversion of an individual trapped trans-TMC molecule. Eventually, the junction collapses spontaneously and the current suddenly drops to the It value. Equivalent experiments performed during LC blinks show constant Im profiles independent of the bias pulse, without conversion from LC to HC values (see Figure A1d). Both sets of experiments point to an irreversible HC-to-LC conversion under the experimental conditions.

A.2. Energy Profile for trans-to-cis Rotation in the Absence of an Electric Field
Geometry optimisations for the cis-TMC and trans-TMC configurations reveal that both isomers present a similar energy, with a difference of 0.82 kcal/mol favouring the cis-TMC isomer. Of course, this energy difference is below the typical error of DFT methods, so we can consider both isomers to be of basically the same energy. Starting from the optimized cis-TMC isomer, the dihedral angle connecting both structures was rotated in 15° intervals ( Figure A2). The ground state energy profile was insensitive to the addition of an electric field of ±2.2 × 10 −4 atomic units (a.u.), i.e. 1.1 × 10 8 V/nm, and curves are indistinguishable from the ground state in Figure A3a.

Appendix A.2. Energy Profile for trans-to-cis Rotation in the Absence of an Electric Field
Geometry optimisations for the cis-TMC and trans-TMC configurations reveal that both isomers present a similar energy, with a difference of 0.82 kcal/mol favouring the cis-TMC isomer. Of course, this energy difference is below the typical error of DFT methods, so we can consider both isomers to be of basically the same energy. Starting from the optimized cis-TMC isomer, the dihedral angle connecting both structures was rotated in 15 • intervals ( Figure A2). The ground state energy profile was insensitive to the addition of an electric field of ±2.2 × 10 −4 atomic units (a.u.), i.e., 1.1 × 10 8 V/nm, and curves are indistinguishable from the ground state in Figure A3a.          As a control experiment for the trans-to-cis isomerisation process, we employ a homologous cis-TMC isomer control molecule, the cis-TMC-syn (see Figure 1b). The control molecule possesses an almost identical structure to cis-TMC and thus represents a suitable molecular reference to assign the LC feature in (Figure 3) to the cis-isomer. The missing methyl substituents on the phenyl rings on the carotenoid control compared to TMC are not expected to affect significantly the characteristic conductance value of the conjugated carotenoid wire, since CH 3 -and H-terminal groups exhibit comparable electron-donating character [26].
Unlike for trans-TMC that shows two discrete LC and HC regimes in the dynamic approach, the dynamic BJ cis-TMC-syn experiments exhibit a single (low) conductance value ( Figure A5a). cis-TMC-syn yield of 20.3 % and the conductance value of 1.77 × 10 −3 G o are nearly identical to the analogous concepts for trans-TMC junctions: a yield of 17.4 % and a LC value of 1.68 × 10 −3 G o. as Figure 2a shows. Figure A5c-e displays the 2D conductance maps of the cis-TMC-syn at the different applied EEF. Unlike for trans-TMC, cis-TMC-syn junctions show a unique and constant current signature at all three applied V bias regimes. The molecular conductance value extracted from the blinking approach of 1.60 × 10 −3 G o is in good agreement with the conductance value obtained from the dynamic approach. The extracted conductance values from the 2D blinking histograms of cis-TMC-syn junctions are statistically identical to those of the LC regimes measured in the trans-TMC at the same V bias ( Figure A6a, blue and orange plots).
Another remarkable similitude between cis-TMC-syn and LC trans-TMC junctions is the observed blinking lifetime that are correlated under equivalent bias regimes (see Figure A6b, blue and orange, respectively). For both measured species, the blinking lifetime is ca. a factor 1.3 larger than that of the HC trans-TMC junctions. Another remarkable similitude between cis-TMC-syn and LC trans-TMC junctions is the observed blinking lifetime that are correlated under equivalent bias regimes (see Figure A6b, blue and orange, respectively). For both measured species, the blinking lifetime is ca. a factor 1.3 larger than that of the HC trans-TMC junctions.  Another remarkable similitude between cis-TMC-syn and LC trans-TMC junctions is the observed blinking lifetime that are correlated under equivalent bias regimes (see Figure A6b, blue and orange, respectively). For both measured species, the blinking lifetime is ca. a factor 1.3 larger than that of the HC trans-TMC junctions.