Optical suppression of energy barriers in single molecule-metal binding

Transient bonds between molecules and metal surfaces underpin catalysis, bio/molecular sensing, molecular electronics, and electrochemistry. Techniques aiming to characterize these bonds often yield conflicting conclusions, while single-molecule probes are scarce. A promising prospect confines light inside metal nanogaps to elicit in operando vibrational signatures through surface-enhanced Raman scattering. Here, we show through analysis of more than a million spectra that light irradiation of only a few microwatts on molecules at gold facets is sufficient to overcome the metallic bonds between individual gold atoms and pull them out to form coordination complexes. Depending on the molecule, these light-extracted adatoms persist for minutes under ambient conditions. Tracking their power-dependent formation and decay suggests that tightly trapped light transiently reduces energy barriers at the metal surface. This opens intriguing prospects for photocatalysis and controllable low-energy quantum devices such as single-atom optical switches.

Supplementary Note S1. Dark-field scattering spectroscopy Dark-field spectroscopy was performed on a modified Olympus BX51 coupled to an Ocean Optics QE65000 spectrometer using a 50 µm optical fibre. An incoherent white light source was used as excitation source. Excitation and collection were through an Olympus LMPLFLN100XBD NA 0.8 objective. Automated scans were run to measure many hundreds of individual NPoMs across the sample, using a Python particle tracking code. (35) A standard diffuser was used as a reference to normalise the scattering spectra.
). In both nanocavity and picocavity, the charge state is 0 and the spin state is a singlet. In each picocavity, the Au adatom on top is Au (0) . The bottom thiol is attached to two Au atoms to ensure an even number of electrons (otherwise attaching to one Au atom changes the system to a doublet, introducing undesirable impacts making comparison impossible). Note in (F) and (I), picocavity intensities are divided by 5, to be comparable with the nanocavity intensities on the same scale.

Fig. S4. Further picocavity SERS spectra examples (red).
Variations and dynamics of picocavities due to different relative positions of Au adatom to nearby single molecule (see below Fig. S9), compared to the stable nanocavity SERS spectra (black).

Supplementary Note S2. Identification of picocavities and flares
The extraction of picocavities and flares is based on using a spectral dissimilarity metric of normalized Euclidean distance (ED), (36) while the segmentation uses a support vector machine (SVM) supervised machine learning model. The detailed steps are as follows: 1) Time dependent SERS spectra (Fig. S5A) are converted to dissimilarity series using their normalized ED distance between successive spectra , : (S1) As shown in Fig. S5B, the flares induce much higher ED distance variation than picocavities which thus allows their separation. The background of the time-dependent dissimilarity shows the intrinsic fluctuation of these time dependent SERS series, and is subtracted by an iterative polynomial method. The background-subtracted time-dependent dissimilarity of several clean SERS scans (without picocavities or flares) are selected for calculating the lower threshold for picocavities, threshold p = 2 x mean + 8 x (standard deviation). The lower flare threshold is obtained by comparing the ED values of flares (ED f ) and picocavities (ED p ) with the same spectral intensity, giving threshold f = threshold p x(ED f /ED p ). A second flare threshold is set at double the first flare threshold to confidently catch higher intensity flares.
2) Fluctuations above the first picocavity threshold (see Fig. S5B, orange dashed line) and below the first flare threshold (see Fig. S5B, green dashed line) are identified as picocavity events. Those higher than the second flare threshold (see Fig. S5B, red dashed line) are identified as flare events. For the mixed region (between first and second flare thresholds), the SERS spectra of each event are averaged, and the SERS background from the average spectrum is extracted and subtracted using an iterative polynomial method. After this the ED distances are recalculated to examine the contributions of sharp Raman peaks and smooth emission background. Depending on which contributes most to the dissimilarity variation, the event is assigned as a picocavity or flare. If both contribute, the event is considered as containing both picocavity and flare components. 3) The events (picocavities or flares) separated in step 2 are segmented individually, in order from high to low threshold. Each trapped event is then removed from the dissimilarity series to avoid affecting the further segmentation of other regions. For performing the segmentation, dissimilarities below the threshold are set to 0 and time dependent dissimilarities converted to an th discrete difference in time, as shown in Fig. S5C (this example segments events above the first picocavity threshold but below the first flare threshold). A semi-supervised approach using a support vector machine (SVM) model (with code in the open-source python library of pyAduioAnalysis (48)) is first trained with the discrete difference series, and then the SVM classifier is applied to output a probability series (giving confidence levels, see  where time−series is the total number of time-series, empty is the number of empty time-series (without seeing any picocavities or flares over the time-series duration ). is the probability of picocavity or flare formation, which is converted to formation rate.
Formation rates obtained by are used for Fig. 3C, and summarised in Table S1-2. Note that no empty timeseries are seen for BPT at 255 μW μm −2 meaning its flare formation rate ( ) cannot be generated this way. Additional data from BPT-Br is plotted in Fig. S6 confirming validity of the fit from the main text: with ( ) = 0 /( / + 1).

Fig. S6. Formation rate of four different molecules.
Additional BPT-Br data is extracted from 758,500 spectra recorded in 1,517 time-series. Table S1. Statistics of picocavities and flares across a range of laser power at room temperature, =300 K. time−series is the total number of time-series, is duration of each time-series, spectra is the total number of spectra. and are the number of picocavities and flares, respectively. ,empty and ,empty are the number of empty time-series (without seeing any event over ). and are the formation rate of picocavities and flares, respectively.

BPT
where the constant of proportionality is set to normalise the discrete probability distribution. We now perform maximum log-likelihood estimates of the measured set of lifetimes = { } by defining The most likely values for the parameters , , are those that maximise the log-likelihood of measuring the observed values. Uncertainty bounds are placed on these values using the standard result of altering the parameter until drops by We note that the number of fast flares seen for MBN and MPy are too small to give reliable fits to histogram decay rates. The single exponential probability density function is used to perform maximum log-likelihood estimates of each lifetime for slow decay rates.

Supplementary Note S5. Molecule-metal coordination bonds
We estimate the molecule-Au (0) adatom interaction energies for MPy, BPT, and MBN systems with a series of constrained DFT optimizations. In these calculations the molecules are attached to two gold atoms via their thiol groups, and a third gold atom (adatom) close to the N atom of MPy and MBN, and the C atom of BPT (see (S9) with 0 and 0 giving the position and depth of the minimum. These parameters are summarized in Table  S6A. In Fig. S11A, the fitted Morse potential curves are overlain to show that the same BPT<MBN<MPy order is observed for the interaction energies as for the induced charges in the presence of an external electric field (Fig. 5,S17). The calculations are repeated for molecule-Au (I) coordination bonds ( Table S6b, Fig. S11B). This is to show that even with very rare cases when Au (I) is formed on nanoparticles due to lattice strain, the binding energies follow the same BPT<MBN<MPy order as for molecule-Au (0) .         (15) provided by full time-dependent DFT of the optical field around a picocavity Au adatom appears to match well that from a metallic sphere (permittivity ) of the size of an atom (radius ) in the uniform field ℰ of the nanocavity gap (permittivity ). The field is concentrated at the tip of the atom (see below), in a field distribution which looks like that from a dipole positioned at the atom centre (Fig. S14).  The field at radial coordinates ( = + , ) of a dipole at the origin is given by Ensuring that there is no field parallel to the metal sphere surface (so . �=0), we get = 4 0 3 ℰ̂ For long wavelengths where the metal is very good this is correct. There is a modification to this for smaller | | (i.e. not perfect metals): where codes for the shape of the protrusion and is 1/3 for a sphere. (49) Fig. S15. Local field enhancement ℵ near metal of specific asperity (here for a sphere above surface).
In this model, the extra enhancement ℵ reaches 20 for an aspect ratio of the picocavity of 2:1 (i.e. with the Au atom perched on top of another atom, completely out of the facet), and is 3.6 for the hemisphere drawn in Fig. S14. It also depends on wavelength.
The field outside the metal sphere in ( , ) coordinates is then (50) Comparison to the TDDFT and classical solutions of the field around the picocavity matches this well.(15)
We note that the simple energy estimate here misses a contribution due to optical field expelled from the metal when the picocavity exists (as seen in TDDFT simulations). This can be understood from the much higher in-plane ∥ required to localise light around the single atom, which gives a much higher imaginary out-of-plane ⊥ , and thus short decay length into the metal set by the gap size . (28) The energy from this expulsion is estimated as This rough estimate suggests a larger energy for the picocavity field, by a factor up to /~10. A more detailed calculation at the single atom level is thus required but is currently beyond both classical theory and DFT, for instance to include contributions within the metal from terms in { }.(51)

Supplementary Note S8. Optical Forces
We now discuss the models that are most plausible for understanding how only 1-10 μW/µm 2 of incident CW light is capable of pulling a Au adatom out of the facet, which the experimental data shows. The rectification of the optical frequency fields produces a gradient force ∝ ∇ℰ 2 that acts on the atoms in the facet. (52) To understand the scale of forces required, we note that for the typical Au adatom barrier energy of 1eV (25,26,53) when moving a Au atom out by the 0.1 nm distance needed to create the intense picocavity hotspot would require that 0 ≃ Δ /Δ ≃ 1 /10 −10~2 nN is provided. We show below it is hard to directly develop this force using the intensities used in our experiments. We also note adatom surface diffusion barriers are of similar scale. (54) The model explored here in most detail is a field-plucking model in which the light locally polarizes the tip of the molecule to enhance the force between it and the Au atom (via rectified dc optical forces). One other model more carefully considered below and discarded is the hot atom model in which all the photon energy is given to one Au atom (instead of a hot electron) which can now escape over the barrier.

Field-plucking model
Considering that the total energy (Eq. S11) is produced by moving the adatom out by a distance (the radius of the atom), we get (as our Model 1) This is equivalent to the optical power density ( / ) exerted on an area 2 and enhanced by the optical intensity in the nanocavity, and for the values above comes to 1 pN per mW of tightly focussed incident light. This is thousands of times smaller than 0 for the intensities used in our experiments. It thus appears to be much too small to explain why we can pull out picocavities with intensities of 10 μW or less (for MPy), and 50 μW for BPT.
We consider possible enhancements to the optical force from: Induced local molecular dipole: produced by the picocavity optical dipole field which induces changes in the charge distribution of the nearby molecule. The nearby electric dipole induced by the light perturbs the molecular orbitals (both the charge that they contain, and also possibly their shape). Effects can arise both from the local field at the atoms, as well as the field gradient at the atoms (since varies on the scale of the atom from Note S6). Full DFT calculations allow us to estimate these perturbations. Initially we make an approximation that such changes can be localised as an induced point dipole at the core position (at distance ℓ) of the nearest atom to the Au (since the picocavity field decays so fast spatially), 2 = 0 ℰ(ℓ) + 0 ∇ℰ(ℓ) Ideally it would be possible to identify , from DFT, but separating them is challenging since the influence of the optical dipole nearby produces both , ∇ at the atomic site. Whilst is related to 0 , it measures the polarizability of the tip atom ( ) and not the whole molecule (which gives 0 in a uniform applied field).

Plasmonic dipole multiplication:
This local dipole (Fig. S13) then induces additional image dipoles in the nearby metal, and this creates a term which can become extremely large. A simple way to estimate this comes from assuming the final dipole elicited at the atomic site is produced from the sum of the quasistatic field initially created there as well as the additional induced field ℰ from image charges,(38) where is the distance of the dipole from the metal surface (as above). There will be changes in this from the curvature of the picocavity surface, and also from image charges in the other metal facet, but since this tip molecule atom is so close to the picocavity adatom, it can be a reasonable approximation. The dipole produced = ℰ = (ℰ + ℰ ) then yields when solving for ℰ the effective polarizability These image charges thus amplify the dipole produced at the atomic site, by a value that depends critically on its separation and polarizability. If we look at typical values of 0 for HCN (2.6 Å 3 ), benzene (10 Å 3 ), pyridine (9.5 Å 3 ), we see that = ( 0 ℵ/8) 1/3 ~1.1Å for ℵ=1 and ~2.9Å for ℵ=20. For < the dipole becomes infinite in this model. This 'polarization catastrophe' is normally suggested to induce a perturbation that becomes so large that it breaks the molecule, or by deforming it switches on a permanent dipole when it is so close to the metal. It is thus plausible that the resulting force which is also now amplified, instead of breaking the molecule, now breaks the Au binding to the facet in order to pull out a picocavity. Local polarizability of molecule tip: While the above derivation uses the full 0 in , this should be modified. Instead of applying a uniform field on the molecule to induce this dipole (as conventionally calculated), here we need the local polarizability just on the molecule tip atom closest to the adatom. Thus instead we take = ( ℵ/8) 1/3 using values from DFT. To estimate the induced dipole produced by a picocavity, we use DFT simulations of a Au adatom in different locations around the molecular tip (Fig. S17). We place a fixed dipole in these different positions (pointing towards the tip atom) and extract the induced charge shifts across the whole molecule. Table  S5 shows the stable positions of minimum energy found for the adatom-molecule system, using the coordinate system in Fig. S10. The induced charge on the tip (N or C) atom of the molecule is then extracted as a measure of the point dipole at this atom. The component of polarizability from a z-directed metal atom dipole is then the induced charge multiplied by cos 2 (for projection direction of field, and projection of vector polarizability). This is clearly seen to scale with the coordination strength of the bond (Fig. S18B) as well as the experimental critical intensity (Fig. S18C). We now estimate the amplified force in this model. We take the dipole-dipole energy between the picocavity adatom dipole, and the induced dipole on the nearest atom (N or C) located at ℓ = + , hence assuming a radially-directed field ℰ at the nearby atomic site Substituting and simplying as a function of = ℓ − , Very near the metal surface / <1, so we can define = 2 cos 2 . −3 {3 − 6 / } to obtain ~− 0 ℰ 2 3 The force that arises when gaining this energy by moving out the adatom by to be next to the molecule is then (similar as in Eq. S12) given by Compared to the previous estimate of the force (Eq. S12), we now have the additional final term which diverges as the atom core approaches to the surface adatom within ~~1-2 Å (Fig. S19). Note that (defined in Eq. S13) comes from the image dipole enhancement of the molecular tip dipole, and estimates the magnitude of this molecular tip dipole.
Including the local field (ignoring the ∇ℰ term), and provisionally taking = 0 , ~6 −3 0 = 48( / ) 3 with parameters for pyridine, giving the average forces shown in Fig. S19. This suggests that picocavities can arise from the polarization divergence due to image charges at the facet surface. It creates such large forces (nN) that the Au atom is pulled from the facet, which then modifies the polarization divergence as discussed below. We note that the optical pressures focussed on the single atom here approach a million bar. Another way to consider this divergent polarizability is the local effective refractive index, which in this formalism approaches loc =10 for the molecule 0.2 nm from the facet in a 1 nm gap containing initial refractive index of 1.5. However we also stress that a full calculation needs to account for the interpenetration of the electron clouds on Au and tip atom (C or N) which smears out the divergence (as in the Jones-Jennings-Jepsen model (55)), as well as not using point dipoles but delocalised electrons and treating fully the screening electrons in the metal in a quantum model. Another issue is that the image plane position can be further out from the metal nuclear core by Total Au atom potential: We now combine the intensity-dependent optical force term derived in Eq. S14 together with the original potential for moving a Au atom from inside the facet to its adatom position, to give Model 2. Inside the facet the Au-Au coordination number is 9, but this reduces to 2 as it pulls out of its pit position (black circle, Fig. S20A).
The potential energy as the Au atom is pulled out of the facet onto the surface follows Fig. S20B, showing the ~1 eV size of the barrier normally preventing any adatoms escaping onto a flat facet at room temperature. Note that step edges and defects do not change this unless they directly reduce the initial coordination number (so only for Au atoms at vertices and edges). Using DFT to model the energy of the Au-molecule energy as a function of separation (Fig. S20C) shows the coordination bond whose energy depth varies from 160 meV for BPT (shown here) to 1 eV for MPy. These can combined into a static potential before light is then applied to the system (Fig. S20D).
Our experiments (see main text) imply that (i) adatoms (giving picocavities) or adlayers (giving flares) are produced thermally over (ii) an energy barrier which for increasing light intensity is progressively reduced in height. This leads to a model for the probability of creating a picocavity or a flare = 0 exp�− ( )/ � where the forward barrier ( ) can then be extracted from the experimental data. We find that ( ) lies on a universal curve for different molecules (Fig. S21) if it is plotted as a function of ( ) where ∝ / is the local polarizability extracted from the DFT (see above) for the tip atom on the molecule. This universal curve is fit rather well by shown as the dashed curve, which as needed retains the initial ( = 0) = 0~1 eV barrier with the light off, but rapidly reduces with light intensity. For picocavities to become likely to excite thermally (at ( ) = ) then = 0 /~40 at room temperature.
Even at the highest light intensity it is clear that this barrier does not disappear, which matches what is seen in the experiments with still a residual thermal barrier even at the largest powers. While this fit function is only approximate, it gives the main features here, and in particular cannot be replicated by any laser-heating model. Considering optical forces alone, which would tilt the potential seen in Fig. S20D to gradually reduce the barrier, the problems are that (i) the optical forces alone are too weak to overcome the high initial barrier, and (ii) after the barrier becomes low enough for thermal excitation over it, at slightly higher intensities it would then disappear, giving instant picocavities which is not what is seen in experiment. Instead we suggest that what happens is that when the light is applied, the additional force brings the adatom slightly closer to the molecule. This slightly decreases the barrier, and allows the adatom to approach slightly more (Fig. S22B), enhancing tip polarizability and thus reducing the barrier, to bring the adatom yet closer, in a positive feedback. What stops this ultimately is the overlap of the electron clouds of Au adatom and molecule tip atom (by Pauli exclusion). We thus assume that there is a closest distance of approach which is possible, irrespective of power (modelled as a saturation, see Fig. S22A). The resulting barrier energy to adatoms escaping from within the Au surface then decreases as laser intensity increases (Fig. S22C), which yields a picocavity formation rate in good agreement with experiment. In the fits presented in the main text, we use the Eq. S15 to extract values of the critical intensity. In addition, the reduction of barrier when illumination is present would explain why the decay of picocavities tracks the optical power in exactly the same way as their creation rate (Fig. 3). No other model can explain this. If we instead use an optical force (Model 1) which simply scales with the field gradient ( ∝ ∇ℰ 2 ), and is set here artificially strong enough to overcome the Au binding 0 (Fig. S22D), then there is a sudden turn on of picocavities when the barrier is overcome (dashed line Fig. S22E), which is not what is observed. In addition, this model would also suggest that the reverse barrier once picocavities have been created is equally large, so picocavities would never be observed to decay (again contradicting experiment).

Supplementary Note S9. Summary of evidence
We collect here a summary of the different phenomena, and how they support the field-plucking model. A list of the experimental features observed is: E1) The picocavity generation rate increases with laser power above threshold, then saturates (instead of exponential growth). E2) Histogram of creation times for picocavity decays exponentially, implying a fixed probability of creation. E3) Different molecules have characteristic picocavity generation rates (per local intensity). A stronger metal-molecule coordination bond gives a lower laser threshold (easier to create), and lower decay rate (harder to destroy). E4) Picocavity decay rates depend on laser power exactly as creation rates. More than two-thirds of picocavities are less stable, decaying ten-fold faster. E5) Picocavities are produced independently (one does not cascade many, or turn off all). There is only very slight statistical evidence that if a picocavity is observed, it gives an increased likelihood to see a second one in the same scan. E6) Picocavity SERS lines fluctuate over ~1s (at rates 4cm -1 /s for BPTCN for 25μW).(21) E7) Picocavity creation rates are found to be much slower on (100) Au facets.(56) E8) Picocavities are much harder to create at low temperature above threshold, and much more stable to decay. E9) Picocavity SERS rise times are 60μs, decay times around 80μs. (57) The field-plucking model explains: E1) Light intensity needs to be high enough to reduce the barrier to thermal energy scales in order to start picocavity formation. But this barrier does not completely disappear due to limits on approach of electronic orbitals. E2) Thermal excitation over an optically-reduced barrier explains this. E3) Rate of optically-induced barrier reduction depends on local polarizability at the molecule tip. For alkanethiols the polarizability is very small, and few picocavities are observed (though their observation is challenging since their Raman cross sections are also small -flares which do not depend on the Raman cross section are however also minimal).
E4) With light off, the energy well for picocavities is also much higher than . The system needs optical reduction of the barrier to allow the adatom to return into the facet. Adatoms can thus be trapped on the suface. E5) Whichever molecule tip has the largest local polarizability will act first, depending on nearby ions, the exact registration with atoms on facet, and likely other factors sensing the local atomic environment. E6) Thermal diffusion inside the coordination-bond potential well allows Brownian motion of the adatom (exciting different thermal superpositions of vibrational sub-levels). Illuminating with light reduces this barrier, softens the adatom potential well, and increases diffusion rates.
E7) The initial barrier height is ~2 eV larger on Au(100) (23,56,58) and thus requires much larger laser powers for optical plucking. E8) At low temperature, a much larger laser power is needed to reduce the barrier height sufficiently to allow thermal excitation of picocavities. This would not be the case for any heating effect (since to get to T=10,000K it is not relevant whether starting at T=10K or T=300K). At T=10K, once formed, picocavities are stable for extremely long times if the light is off, as the full 1 eV barrier is restored.

Supplementary Note S10. Alternative models
We explore several other models to try to explain these observations. A) Hot-atom ejection, where the Au atom is given the entire plasmon energy to get over the barrier 0 . This is similar to the 'hot-electron model', in which the plasmon decays giving its energy to a single electron, and we now envisage this same energy is given to a single surface Au atom. If 0 > ℏ (Fig. S23B) then it is not clear how thermal energies would be sufficient to supply the remaining energy.
Atom tunnelling is found to be negligible since for an atom of wavevector , ~�2 0 � 1/2 /ℏ~145 so that a tunnelling probability ∝ exp(− ) is too small to play any role. If 0 < ℏ then it is hard to see why the molecule itself would make any difference in producing different picocavity generation rates. This model also does not fit the temperature dependence, nor gives any understanding of how picocavities could decay since a similar barrier has to be overcome ( 0 ), while it is not clear how the hot atom forces would attract it back now into the facet (there is no equivalent of hot hole emission for atoms).

B) Electronic Raman scattering (ERS) electronic ejection,
where the driven Raman process acting on electrons in the Fermi sea generates a kick against a single Au atom. A simple estimate for the momentum change between the two electronic states separated by the plasmon energy is = ℏΔ = �2 ( + ℏ ) − �2 . If this momentum change acts over typical scattering times of 10fs it would thus give forces of ~10pN/photon, again too small to have any effect here. C) Multiphoton absorption, where excitation of the Au atom in its vibrational well would be followed by subsequent excitation to get it over 0 . Recently we have shown that multi-photon absorption in molecules in these gaps is strongly enhanced.(59) It is difficult however to see why the molecule at the surface would influence the excitation of the Au atom to high energies, while sensible estimates of the number of plasmons absorbed per µW incident shows that at 5 µW there would be 30 ps between absorption events, long enough for all vibrational energy injected into a single Au atom to have decayed. There is also little evidence of a multiphoton power dependence in the signatures described.

D) Optomechanical forces,
where vibrational driving of the Au-Au bonds leads to a parametric instability that drives out a Au adatom. The natural oscillation frequency of this Au-Au facet bond assuming a parabolic potential so that = � / and with 0~1 2 2 gives an estimate for ℏ = 7 meV or 60 cm -1 .
There are few experiments which have attempted to look at Au-Au vibrational frequencies, mostly in heavy-metal dimer (60) or trimer molecules,(61) and they give reports from ℏ =10-100 cm -1 in various molecular complexes, with none seen so far for bulk Au. Thermal population of these low energy vibrations is insufficient to reach the 0 energy barrier.