Measuring competing outcomes of a single-molecule reaction reveals classical Arrhenius chemical kinetics

Table of Contents

Single-molecule manipulation with multiple reaction outcomes

Single toluene molecules adsorb onto the Si(111)−7 × 7 surface by attaching to an adjacent adatom-restatom pair on the surface in a ‘butterfly’ configuration¹⁸. They form two covalent chemical bonds with the silicon atoms (2, 5-di-σ bonding), which are strong enough for stable imaging with a scanning tunnelling microscope at room temperature¹⁹. Using passive imaging parameters (+1 V and 100 pA), the toluene molecules appear as dark features in Fig. 1a at the regular locations where we expect bright adatoms via tunnelling through the adatom empty-state orbitals. That route for tunnelling electrons is blocked since the 2, 5-di-σ bonding saturates the dangling bonds of the underlying silicon adatom-restatom pair (see Fig. 1c and blue and pink circles on the corresponding schematic in Fig. 1d). Figure 1b shows the undoped silicon surface where all remaining dark features are either the periodic corner hole locations of the Si(111)−7 × 7 unit cell (in pink) or adatom vacancies. The toluene-silicon bonds can be controllably cleaved by increasing the energy of the tunnelling electrons above an energy threshold (1.4 eV) defined by the electronic structure of the molecule^20,21 which is well below the carbon-methyl dissociation energy (4.4 eV)²². We find the toluene molecule can either switch to a (free) adjacent adatom site or move further (either complete desorption from the surface or longer range diffusion). Here, we refer to the latter as ‘desorption’. The outcome of such single-molecule reactions, desorption or switching, can be established by subsequent imaging of the same area. But herein lies the challenge—a chemical reaction takes tens of femtoseconds to occur; in scanning tunnelling microscope (STM) experiments, an electron arrives at the molecule every picosecond or so; and the time resolution of STM electronics is typically milliseconds. This stark disconnect between the timescale of chemical reactions and the time resolution of the experimental technique means that we can only infer the mechanism of single-molecule reactions from a measurement of the probability of manipulation rather than a time-resolved measurement. Moreover, contained within that reaction probability are other factors: the local density of electronic states of the sample, the electronic configuration of the STM tip at the time of the experiment, thermal and electric-field contributions. It is therefore difficult to deconvolve the measured reaction probability in order to determine the mechanisms behind multiple reaction outcomes that would allow reaction control.

**Fig. 1: Inelastic tunnelling electron-induced single-molecule manipulation.**

Figure 1c, d shows the three possible outcomes that we measure in our charge-injection experiments: (I) desorption, where the molecule has detached from both its original adatom and restatom, revealing a clean (bright) silicon adatom (II) switching, where the molecule has moved to an adjacent adatom site, seemingly retaining or reforming its original restatom bond^23,24, and (III) no reaction, where the manipulation site appears unaltered in the subsequent STM image. The number of unreacted molecules is included in our analysis of the probability of manipulation but is explicitly excluded from the branching ratio analysis. Instead, we specifically chose the two manipulation outcomes—desorption and switching—as both should have a common initialisation through a physisorbed state^25,26, with switching having the lowest activation energy barrier, and desorption (either complete detachment or diffusion to a non-adjacent adatom site) a higher barrier¹⁹. Thus the ratio of these two outcomes should be sensitive to any change in the common excited state dynamics. The scenarios where the molecule does not react or reattaches to its original adsorption site, following an excitation into the physisorbed state, do not change the overall behaviour of the measured outcome branching ratios but just the overall values. Therefore, they are deliberately excluded from our analysis of the reaction outcome branching ratio (see Supplementary Note 4 for a detailed reaction outcome probability tree).

We choose the branching ratio between the two outcomes as our measurement metric, rather than the raw probabilities. As long as we capture several individual manipulation events with the same tip state, any variation due to the tip state, e.g. the gap E-field, small variation in position, or any other factor, will effectively cancel out in the analysis of branching ratios. This is evident when we report the current dependence of manipulation. We do, of course, ensure as much as we can, that those factors are controlled and held constant—using computer control, image cross-correlations, etc.

The negative ion resonance-induced manipulation of the single toluene molecule in Fig. 1c is achieved by halting the STM tip on top of the toluene molecule and ‘injecting’ electrons with preset tunnelling current parameters (here, +1.6 V and 300 pA) in a similar fashion to ref. ²⁷. During the injection experiment, the height of the probe tip is recorded as shown in Fig. 1e: (i), the tip is halted atop the molecule, still at the passive imaging parameters. To protect the tip state while switching to the desired injection parameters, the feedback loop is disengaged and the tip is retracted 0.4 nm away from the surface; (ii) the feedback loop is re-engaged; (iii) the tip approaches the surface, this time at the height corresponding to the injection parameters; (iv) after 20 ms of electron injection, the molecule reacts: the bond with the underlying silicon adatom is cleaved and the tip retracts by a distance Δz_M to compensate for the higher local density of electronic states of the bright silicon adatom. At this point, in an ideal experiment the injection should stop – if any further electrons are injected, the molecule, which may still be in the vicinity of the tip, could continue to be excited and so could react again. Therefore, the subsequent STM image may not be a true picture of a single reaction outcome. To stop the electron injection after the manipulation has taken place, we set a threshold of tip height change of Δz > 30 pm (see Supplementary Note 1). Once such a change is detected by the control electronics, the experiment is stopped in step (v) by reducing the injection current to a minimum safe value of 5 pA. In step (vi) the feedback loop is disengaged and the STM tip is pulled back again to return to the passive imaging parameters. The time delays between steps (iv) and (v), and (v) and (vi) correspond to the minimum response time of the STM control electronics and are the limit of our present experimental capabilities.

At each injection energy, we induce and record over 100 single-molecule reactions. Assuming a first-order rate equation dN(t)/dt = − N(t)k_d − N(t)k_s for the fraction of manipulated molecules N after a time t, we can deduce an overall time-dependent probability of manipulating a single molecule given by $P(t)=1-\exp (-kt)$, where the measured overall rate k is the sum of the two outcomes: k_d for the rate of desorption and k_s for the rate of switching. Figure 2a shows this for injections at +1.4 V and +1.9 V at 750 pA. To extract the specific rate of manipulation associated with each reaction outcome, k_d and k_s, we measure each population as a function of time. Every time a molecule desorbs or switches, we record the reaction outcome and so we can look at the branching ratio in much the same fashion as a coin-flip experiment. We treat our experiments collectively as if we are following a set of N₀ molecules and measuring when they desorb or switch and thus we measure the time-dependent population of those two outcomes, N_d(t) and N_s(t). Combining those measurements with the number yet to react N(t) gives N₀ = N(t) + N_d(t) + N_s(t). Therefore the time-dependent population of switched molecules is dt_s(t)/dt = N(t)k_s, and similarly dN_d(t)/dt = N(t)k_d. Taking the ratio of these and integrating gives N_d(t) = (k_d/k_s)N_s(t) with the branching ratio defined as B = k_d/k_s. Therefore Fig. 2b which shows N_d(t) vs. N_s(t) has a gradient equal to the branching ratio of our single-molecule reaction. In this way, the branching ratio is extracted from a direct measurement of its time dependence, rather than by looking at only the final data point. An alternative method for extracting this time-dependent branching ratio involves fitting to each pathway separately. This method is discussed in Supplementary Note 2. Before turning to why the gradient (branching ratio) has a voltage dependence, we need to first probe the manipulation mechanism itself.

**Fig. 2: Measured molecular reaction outcomes.**

Tunnelling current and injection position dependence

Figure 3a shows the tunnelling current dependence of the desorption and switching rate for electrons injected at +1.6 V. Each data point comes from an analysis of data similar to Fig. 2a. The solid lines represent power law fits, where the rate, k ∝ Iⁿ, and where n is the number of electrons that drive a single-molecule reaction. For desorption n = (0.8 ± 0.1) and for switching n = (0.8 ± 0.1) which suggests that both outcomes are driven by a one-electron process. Such non-integer results are typical for these experiments due to the sensitivity the raw probabilities can have on the precise location of the tip relative to the target or the tip state. For example, the pioneering early STM reports of hydrogen desorption from Si(100) gave n = 15²⁸ or n = 10²⁹. However, a following report with noticeably larger current range, reported n = 0.3, 1.3, 0.3 depending on the exact experimental procedure, evidence of (on average) a one-electron process³⁰. Therefore, the absolute rates, k_d and k_s, will depend on the exact state of the STM tip, whereas the branching ratio of the rates will naturally lead to a normalization of these tip-state effects. Figure 3b shows a near-constant branching ratio over the probed tunnelling current range. This invariance with tunnelling current further shows that both outcomes are one-electron processes and that there is no tip-induced quenching of the excited state²⁷. For multi-electron processes, e.g. dynamics induced by multiple electronic transitions (DIMET), the branching ratio can exhibit orders of magnitude difference when the molecule is excited with different tip states or with different currents^10,17. The uncertainties of Fig. 3b are calculated through purely binomial statistics. A more accurate error estimate can be obtained through beta distribution analysis³¹, which accounts for the finite number of experimental measurements, and yields similar values to the simpler binomial statistics. For all data points, except at 200 pA, the uncertainties represent a fractional uncertainty of ≈20%. To reduce the uncertainty to ≈1%, we would need to perform 62, 500 individual molecular experiments. The data point at 200 pA, where only 8 molecules were manipulated, illustrates clearly the importance of inducing a large number of manipulation events for reliable statistics. To highlight the variation in the branching ratio, the percentage of manipulated molecules that desorb is indicated on the right hand axis in all figures.

**Fig. 3: Current and position dependence of single-molecule reaction rate and branching ratio.**

Figure 3c–e shows the position dependence of our single-molecule reaction. We inject electrons at +1.8 V and 750 pA into three distinct crystallographic locations of the Si(111)−7 × 7 surface as marked on the STM image and corresponding schematic diagram in Fig. 3c. Location (1) is the centre of the adatom forming a σ bond with the toluene molecule. Location (2) is the mid-point between the adatom and adjacent rest-atom, which we take to be the centre of the adsorbed toluene molecule. Location (3) is on top of the restatom forming the other σ bond with the toluene molecule. For each injection location, we again induce over 100 individual single-molecule reactions. Figure 3d, e shows the position dependence of the manipulation rates and their corresponding branching ratios. The desorption rate is about an order of magnitude lower for injections into (1), the adatom site, compared to the other two injection locations. A similar, yet less striking, trend is observed for the switching rate. By contrast, the branching ratio is largely independent of the injection location, with only a small drop in the measured branching ratio for injections into (1), the adatom site. To ensure that we are always injecting into the same position, and thereby remove this sensitivity to the injection site in the current and voltage sweeps, before each injection we take multiple passive images and use their cross-correlations to measure the lateral tip drift and to feedback a compensation drift value until the measured lateral tip drift speed is below 3 pm s⁻¹.

Energy dependence

A more pronounced trend is observed for the rate of manipulation and branching ratio as a function of energy of the injected electrons, shown in Figs. 4, 5. The measured combined rate of manipulation (i.e. both desorption and switching) is displayed in Fig. 4d on a linear scale, and 4e on a logarithmic scale. It demonstrates a near-exponential onset at +1.4 V and the measured manipulation rate spans across two decades. In ref. ³² we developed a model to quantitatively link the local density of states of the surface to the measured reaction probability per injected electron in molecular nanoprobe experiments. In molecular nanoprobe experiments, the STM tip first injects a charge into a surface state. Following an ultrafast relaxation within the surface state, the charge then propagates across the surface causing a molecular manipulation event at a location that is tens of nanometres remote from the original tip position^33,34. By considering the first step of this nonlocal manipulation effect to be the same as the first step of a scanning tunnelling spectroscopy (STS) measurement we showed that the increase in the rate of manipulation k as a function of energy of the injected charge is in fact due to the overall fraction of the tunnelling current s_i(V) captured by the specific surface electronic state. Therefore, the rate of manipulation k is proportional to the product of the calculated s_i(V) and a state-specific probability of manipulation per injected charge carrier β_i

$$k\propto \Sigma _i\beta _is_i(V).$$

(1)

**Fig. 4: Energy dependence of single-molecule reaction probability for injections into the adatom site.**

Here, we apply this model to the manipulation rate measured by injecting directly into an adsorbate toluene molecule. Figure 4a shows empty-state STS measurements taken over 25 clean silicon adatoms and 7 unreacted toluene molecules. Gaussian functions are fitted to each spectrum and the overall fits show good agreement with the measured data. In the molecular spectrum, we identify the state with a Gaussian fit centred at +1.7 V as the LUMO of toluene (highlighted in blue). It is the onset of this state that is responsible for the observed reaction onset threshold at +1.4 V (indicated by the vertical line). The two lower-lying states are derived from the silicon surface (see refs. ^26,35) and are also present in the adatom STS. Any attempt to measure states above +2.0 V results in the immediate manipulation of the molecule. Instead, for completeness, here we also present the measured STS of a clean silicon adatom, which contains the surface-derived and manipulation-active state, U₂³⁶, with a corresponding Gaussian fit centred at +2.3 V and highlighted in pink. Figure 4b presents a spectrum combining the clean adatom STS with the LUMO state from the toluene STS. Figure 4c shows the computed fraction of tunnelling current, s_i(V), captured by each state calculated from the Gaussian parameters in Fig. 4b as per the recipe from ref. ³². The total rate of manipulation is therefore simply given by the weighted sum in Eq. (1) and results in an excellent fit to the experimental data in Fig. 4d, e. At +1.4 V all of the current that contributes to manipulation is captured by the toluene LUMO state and manipulation is mediated through the molecule, with the manipulation probability per electron given by the only fitting parameter $\beta _{{\rmLUMO}}=1.2 \times 10^−10$. This is in agreement with previous reports of the energy threshold of electronic manipulation^20,21. As the bias voltage increases further, the U₂ state opens up and competes for the current. It starts to dominate the manipulation above ≈ + 2.0 V (vertical line) due to its higher manipulation probability per electron $\beta _{{\rmU}_2}=3\times 10^-9$ and results in the nonlocal manipulation process previously reported^33,37. Importantly, the fit to this model implies an ultrafast energy relaxation of the injected electron prior to manipulation. Below the +2.0 V threshold the manipulation is mediated directly through the LUMO of the molecule. Above this threshold, the electron relaxes down to the bottom of the U₂ state before molecular manipulation takes place.

The rates of manipulation for desorption and switching are presented separately in Fig. 5a. Both outcomes display a similar trend to the overall probability of manipulation from Fig. 4, with near-exponential increase in the manipulation rate with the energy of the injected electrons. By contrast, the branching ratio between the two measured outcomes increases monotonically up until a threshold of +2.0 V. This increase corresponds to a desorbed percentage change from ≈70% to over 85%. Above this bias voltage, the branching ratio is independent of the energy of the injected electrons. This invariance in the measured outcome branching ratio with electron energy is easily explained by considering the ultrafast relaxation step proposed above since all manipulation events take place after the electron has relaxed down to the bottom of the U₂ surface state. Therefore, similar to the state-specific probability of manipulation, there is also a state-specific outcome branching ratio set by the energy of the relaxed electron. (The data point at +2.1 V is discussed in more detail in Supplementary Note 3 and the variation is attributed to the quality of the data at this injection bias voltage.)