Letter

# Reorganization energy upon charging a single molecule on an insulator measured by atomic force microscopy

• Nature Nanotechnologyvolume 13pages376380 (2018)
• doi:10.1038/s41565-018-0087-1
Accepted:
Published:

## Abstract

Intermolecular single-electron transfer on electrically insulating films is a key process in molecular electronics1,2,3,4 and an important example of a redox reaction5,6. Electron-transfer rates in molecular systems depend on a few fundamental parameters, such as interadsorbate distance, temperature and, in particular, the Marcus reorganization energy7. This crucial parameter is the energy gain that results from the distortion of the equilibrium nuclear geometry in the molecule and its environment on charging8,9. The substrate, especially ionic films10, can have an important influence on the reorganization energy11,12. Reorganization energies are measured in electrochemistry13 as well as with optical14,15 and photoemission spectroscopies16,17, but not at the single-molecule limit and nor on insulating surfaces. Atomic force microscopy (AFM), with single-charge sensitivity18,19,20,21,22, atomic-scale spatial resolution20 and operable on insulating films, overcomes these challenges. Here, we investigate redox reactions of single naphthalocyanine (NPc) molecules on multilayered NaCl films. Employing the atomic force microscope as an ultralow current meter allows us to measure the differential conductance related to transitions between two charge states in both directions. Thereby, the reorganization energy of NPc on NaCl is determined as (0.8 ± 0.2) eV, and density functional theory (DFT) calculations provide the atomistic picture of the nuclear relaxations on charging. Our approach presents a route to perform tunnelling spectroscopy of single adsorbates on insulating substrates and provides insight into single-electron intermolecular transport.

## Main

The chemical structure of NPc and the constant frequency shift Δf image of NPc on NaCl are shown in Fig. 1a. NPc is adsorbed on a 14 monolayer (ML) NaCl film supported by a Cu(111) substrate (Supplementary Fig. 1) at 5 K. Owing to the NaCl film thickness, electron tunnelling through the film is quenched and the only possible electron-transfer pathway is between the tip and NPc, as sketched in Fig. 1b.

We measure the hole reorganization energy Ereorg of a single molecule adsorbed on an insulating film based on a statistical analysis of single-electron transfer measurements between a metallic tip and NPc. Figure 1c depicts the AFM detection of a single-electron transfer cycle that involves the outer-sphere13 redox reaction of NPc ($NPc 0 → NPc + → NPc 0$). An electron is detached from the highest-occupied molecular orbital (HOMO) by sweeping the sample voltage, starting from 0 V, at approximately −2.3 V. This corresponds to an oxidation of NPc0 ($NPc 0 → NPc +$, denoted as ox0). The electron transfer from the molecule to the tip is identified as a step in the frequency shift versus sample voltage ($Δf ( V )$) spectrum20. The horizontal shift of the extrapolated Kelvin probe parabolas (dashed lines) indicates that the molecule becomes positively charged. Subsequently, sweeping from negative voltages back to zero leads to the electron reattachment to NPc+ from the tip, which corresponds to a reduction of NPc+ ($NPc + → NPc 0$, denoted as red+). Interestingly, red+ occurs at a less-negative voltage than ox0, which results in a hysteretic behaviour of the oxidation and reduction cycles.

The observed difference in the oxidation and reduction voltages is an effect of the reorganization energy, which can be understood from the corresponding single-electron transfer processes. These processes are the vertical (Franck–Condon) transitions ox0 (red+) that occur at a fixed equilibrium geometry geo0 (geo+) of NPc0 (NPc+), as schematically displayed in Fig. 1d. The net energy change for the oxidation and reduction (the sum of the ox0 and red+ energy changes) equals Ereorg. Ereorg is associated with the relaxations of the nuclear positions, that is, the relaxation energies λ+ and λ0, also called the heterogeneous reorganization energies23.

Therefore, Ereorg is given by the energy difference between the red+ and ox0 energy levels. Both levels can be probed by single-electron tunnelling at appropriate voltages. By starting with NPc0 (NPc+) and varying the sample voltage, the Fermi level of the metal tip aligns with the ox0 (red+) energy level and an electron tunnels to (from) the tip, as schematically represented in the electron energy diagram in Fig. 1e. In a free-energy picture, the applied bias voltages will shift one specific charge-state curve vertically with respect to the other. For the voltages associated with the ox0 (red+) energy level, the minimum in free energy of the NPc0 (NPc+) configuration intersects with the free-energy curve of NPc+ (NPc0) and an electron is transferred to (from) the tip from (to) the molecule. Experimentally determining $E reorg$, then, requires measuring the voltages associated with the red+ and ox0 energy levels. However, many repetitions of the charge-transfer cycle reveal that the red+ and ox0 voltages vary between measurements (indicated by gray shading in Fig. 1c) and therefore requires statistical analysis. These fluctuations occur because each transition reflects only one single tunnelling event, being stochastic in nature. In addition, the ox0 (red+) levels are significantly broadened due to the strong coupling between an electron and the optical phonons in the ionic film and the zero-point fluctuations of their phonon coordinates at the low temperature of the experiment10,24,25.

If both the ox0 and red+ processes could be observed in a steady-state situation, then the corresponding current would already represent an average of the statistical tunnelling process, as, for example, in the electron-detachment measurement of molecules on a bilayer NaCl with scanning tunnelling spectroscopy25. In this case, the current is proportional to the corresponding transition rate. Here, however, we could not rely on such intrinsic self-averaging, but instead detected individual tunnelling events. The transition rate can then be obtained from the average rate over many individual events. This new statistical approach to measure the rate of a specific charge-state transition is summarized in Fig. 2 for transitions between NPc0 and NPc+. First, the molecule was set to the desired charge state NPc0 (NPc+) by applying a voltage significantly above the red+ (below the ox0) voltage (Fig. 1e) and by approaching the tip closely to the molecule at a distance $z set$ to provide a high tunnelling rate. The electron transfer was then probed at appropriate values of voltage $V probe$ and tip height $z probe$. The latter was adjusted such that the charge transfer was detectable within the time resolution of 0.l s of our set-up. $z probe$ and zset are defined in Methods. The charge state was probed for a fixed probe time T of approximately 9 s and changes in the charge state were identified as steps in $Δf ( t )$. Such a single ‘set–probe’ measurement is shown for the red+ transition in Fig. 2a. The statistical variation of the tunnelling process was accounted for by recording 80 probe traces in total at a fixed $V probe$ (as shown in Fig. 2b) obtained in 4 different sets of measurements. After each set of measurements, the Δf feedback was enabled before another set was measured. The blue and green areas in the histograms shown in Fig. 2c,d correspond to the averaged residence times in the NPc0 and NPc+ state during the probe time T. The fraction r of the total probe time in which the molecule remains in the set charge state, at a certain $V probe$, is given by:

$r= A set A set + A final = 1 - e - Γ T Γ T$
(1)

Here, $A set$ and $A final$ are the areas that represent the averaged residence times during the probe time T of the initially set and final charge states, respectively. These areas are obtained from the Δf histograms of all the probe traces and exemplified in Fig. 2c in green and blue, respectively. The tunnelling rate Γ is the inverse of τ, the lifetime of the set charge state at probing conditions (Supplementary Information provides the derivation details). The evolution of r as a function of $V probe$ for the red+ transition is shown in Fig. 2d. Starting from $r=1$ at $V probe$ = $-1.8V$, which indicates $τ≫T$, r decreases until it reaches a saturation value $r sat ≈0.3$ at a greater $V probe$.

Next, we derived the single-electron differential tunnelling rate to determine the ox0 and red+ voltages. For every $V probe$, the rate Γ can be derived from the experimentally determined $r ( V probe )$ (equation (1)). Γ can be interpreted as a single-electron tunnelling current when multiplied by the elementary charge e. Consequently, the measured Gaussian-shaped differential conductance in the case of bilayer NaCl insulating films10 translates into a Gaussian shape of the corresponding dΓ/dVprobe in this experiment. Therefore, Γ(Vprobe) is well fitted by an error function. The derivative of this fitting function is analogous to a differential conductance, the maximum of which determines the ox0 and red+ voltages. In this analysis we assumed that the energy barrier is approximately constant for the voltage window of $V probe$. The additional broadening due to the tip oscillation amplitude of 6 Å is negligible (Supplementary Information gives the details).

The results for the two different charge-state transitions, ox0 and red+, are displayed in Fig. 3 (the fitted Δf levels are shown in Supplementary Fig. 2). Figure 3a,b shows the evolution of $r ( V probe )$ and rsat for the respective charge-state transitions. In Fig. 3b, a second zprobe demonstrates that rsat can be tuned by zprobe. The tunnelling rate Γ and single-electron tunnel current I for each transition are shown in Fig. 3c,d and are well described by an error function (indicated by a black line). The ox0 and red+ voltages (dashed red lines in Fig. 3c,d) are (−2.44 ± 0.04) V and (−1.48 ± 0.05) V, respectively. The errors stem mainly from the uncertainty of r in determining the saturation region rsat (error analysis is demonstrated in Supplementary Figs. 3–5). The second zprobe measurement in Fig. 3b displayed a similar red+ voltage level.

To obtain the ox0 and red+ energy levels from the corresponding voltages, the partial voltage drop across the NaCl dielectric film needs to be estimated. A calculation using a finite-element model of the tip and the insulator provides a voltage drop of ~17% across the insulating film (Supplementary Fig. 6)26. Accordingly, this correction yields ox0 and red+ energy levels of (−2.04 ± 0.15) eV and (−1.23 ± 0.10) eV, respectively. The absolute difference between these two energies is Ereorg, quantified as (0.81 ± 0.18) eV for NPc on NaCl. The uncertainty in the reorganization energy value is comparable to the errors obtained from photoelectron spectroscopy on molecular films27.

The full-width at half-maximum (FWHM) of the ox0 and red+ voltage levels were found to be distinctly different, being (0.6 ± 0.1) V and (0.25 ± 0.13) V, respectively. For an explanation of the difference in line widths, the potential energy landscape of NPc0 and NPc+ on NaCl along with the tip induced polarization of the film need to be addressed. This complex task deserves further investigation. The peak position of the ox0 level can be compared to scanning tunnelling spectroscopy measurements of NPc on bilayer NaCl (ref. 28). The peak position for the bilayer (−1.7 V) is shifted upward, the difference is discussed below. The peak width (~0.2 V) for the bilayer is smaller than the width reported here.

The measured values for the ox0 and red+ energy levels and the reorganization energy were corroborated by simulations based on DFT of the film and the adsorbed molecule using a perfect conductor model of the metal support and a force field between the metal and the surface (Methods gives details). These energies were computed for NaCl thicknesses between 2 and 5 ML. Using finite-size scaling based on the asymptotic behaviour of these energies with the inverse number of NaCl MLs, Ni, the extrapolated values at 14 ML are −2.08 eV and −1.29 eV for the ox0 and red+ energy levels, respectively, and 0.79 eV for the hole reorganization energy (Supplementary Fig. 7). These calculations are in good agreement with the corresponding experimental energies obtained above. However, the excellent agreement for the ox0 and red+ energy levels might be fortuitous because these energies involve a change of the charge state and, therefore, they are sensitive to the self-interaction error of the employed exchange-correlation functional in DFT. The measured upward shift of ~0.3 eV of the ox0 energy level for NPc on the bilayer NaCl compared to the 14 ML results is also in good agreement with the calculated value of 0.23 eV. This upward shift is predominantly caused by the image interaction with the metal surface (Supplementary Fig. 7). At 14 ML, the calculated reorganization energy is dominated by the ionic polarization in the film. An extrapolation to Ni = ∞ increases the reorganization energy of NPc on 14 ML by only 0.06 eV. The intramolecular contribution to the hole reorganization energy is less than 3%. A single-image charge-interaction model was used to estimate the influence of the metallic tip in the reorganization energy measurements. This estimate results in a small reduction of Ereorg of about 0.02 eV (Supplementary Fig. 9).

The calculated charge density difference between $NPc geo + +$ and $NPc geo + 0$ on NaCl(5 ML) is shown in Fig. 4a as a two-dimensional (2D) contour plot of this density integrated outwards from the molecular plane to the vacuum region. This hole charge density is more or less delocalized over the molecule and is very similar to the corresponding density of NPc in the gas phase (Supplementary Fig. 8). This charge delocalization is consistent with the homogeneous ionic relaxation pattern of the 5 ML film on charging, which is shown in Fig. 4b. The major ionic response to the hole charge occurs in the NaCl surface layer, with the Na ions underneath the NPc macrocycle having the greatest displacements (~7.5 pm), which reflects a higher hole charge density in the macrocycle compared to the phenyl groups. The atoms in the subsurface layers show a similar displacement pattern, but with significantly smaller displacements than for the surface layer. The similar magnitudes of these displacements in the subsurface layers are due to the long-range electric field from the delocalized hole-charge density. Despite this charge delocalization, the relative large reorganization energy can be reconciled by the results of a simple dielectric model (Supplementary Information gives the details). Somewhat surprisingly, the molecule is displaced slightly upward (~2.0 pm) upon charging.

In conclusion, we measured the hole reorganization energy caused by the charging of a single NPc molecule adsorbed on top of an insulating NaCl film. Our method revolves around detecting single-electron transfer processes, based on the single-charge sensitivity of AFM that allows us to measure transition rates that corresponds to currents in the zeptoampere range. We corroborated and analyzed our results by DFT calculations, in which the metal support of the multilayer film is treated implicitly. The experimental method can be extended to other insulating films (ionic and non-ionic) as well as other adsorbates, different charge state transitions and by being performed at elevated temperatures; moreover, it could also be applied to different AFM set-ups, provided conductive tips can be used. Quantification of the specific influence of the local environment on the reorganization energy of molecules and atoms on insulators can be readily achieved. The ability to measure reorganization energies at the atomic scale is indispensable to quantify and predict single-electron transfer processes between molecules on insulating films and, in turn, tune and manipulate their energy transfer rates29.

## Methods

### Scanning tunnelling microscopy and AFM measurements

Experiments were carried out with a combined scanning tunnelling/atomic force microscope that utilizes a qPlus tuning fork sensor30, which was operated in the frequency-modulation mode31 oscillating at 30.1 kHz. An oscillation amplitude of $A=6$ Å was chosen to optimize the signal-to-noise ratio in detecting single charges. The microscope was operated under ultrahigh vacuum ($p≈1 0 - 11$ mbar) and low temperature ($T≈5$ K) conditions. The tip was made of PtIr and was indented and characterized on the Cu(111) surface to yield and ensure a purely metallic tip, respectively. Voltages were applied to the sample. Positive height offsets used in zprobe refer to an increase in the tip–molecule distance. For the measurements in this Letter, zset was defined as the tip height of the imaging setpoint above the molecule ($-1.7Hz$ at 1 V). The zprobe was 10.2 Å from the imaging setpoint for probing the red+ transition, which corresponds to an effective tip–surface separation of about 22 Å (Supplementary Information gives the details). An increased zprobe of 11.2 Å was used to probe the ox0 transition to ensure similar tunnelling rates to those measured for the red+ transition at different Vprobe.

### Sample preparation

The substrate consisted of a 14 ML thick NaCl film grown on Cu(111) (Supplementary Information and ref. 32 give the details). This insulating layer prevents tunnelling between NPc and the Cu(111). Evaporation of a small quantity of NPc molecules on top of the surface resulted in an estimated coverage of ~60 molecules per 1,000 × 1,000 Å2 with molecules mostly being isolated from each other. Therefore, the charge transfer between molecules was inhibited33. As noted in a previous publication28, no tautomerization of the molecule can be identified while detaching an electron from the HOMO of NPc.

### DFT calculations

The ox0 and red+ energy levels and the hole reorganization energy of a single NPc molecule adsorbed on a NaCl film supported by a Cu(111) substrate were computed using a new method implemented in VASP34 that allows charged systems outside a metal surface to be handled in a supercell geometry35,36. In this method, the NaCl film and the adsorbed molecule were treated using DFT, whereas the support of the metals was described by a perfect conductor model and the residual interactions between the film and the metal were modelled by a simple force field. In this method the metal tip is not included.

In the calculations, the projector augmented wave method37 was used to describe the electron–ion interaction with a plane-wave cutoff energy of 400 eV. The electronic exchange and correlation effects were treated using the optB86b version of the van der Waals density functional38,39,40,41. The NaCl film was modelled by a slab with a [001] termination of bulk NaCl and 8 × 8 repetitions of the primitive surface unit cell, which corresponds to 64 Na and 64 Cl atoms in each layer. The film forms an incommensurate structure on the Cu(111) surface and, as suggested by experiments for a bilayer42, surface lattice constants of 3.895 Å, 3.91 Å, 3.93 Å and 3.94 Å were used in the calculations for the free-standing films with thicknesses between 2 and 5 ML. The same force field as that for Cu(100) was used, whereas the work-function difference of 0.26 eV between NaCl films on Cu(100) and Cu(111), which only affects the transition energies, was accounted for by increasing the effective work function by the same amount. The cation was obtained by constraining the film and the molecule to have a net charge of +1e. The lateral electrostatic interactions between the periodic images were compensated by using a dipole–dipole correction scheme43. All the atoms in the molecule and the NaCl film were allowed to relax during the structural relaxations until the forces were less than 0.02 eV Å–1. The Na site was found to be the most stable site of the adsorbed NPc molecule and the long axis of the molecule was oriented along the $[ 1 1 ̄ 0 ]$ directions. The calculated adsorption energy of NPc on the NaCl trilayer is 5.04 eV, which corresponds to about 60 meV per atom, in accordance with the scaling of the physisorption interaction with molecular size44. The ox0 and red+ energy levels are given by the vertical transition energies:

$ε ox 0 =E NPc geo 0 0 -E NPc geo 0 +$
(2)
$ε red + =E NPc geo + 0 -E NPc geo + +$
(3)

where the subscripts ‘$geo 0$’ and ‘$geo +$’ refer to the equilibrium geometries of the neutral and positively charged systems, respectively. In the calculation of the energy of NPc+, the electron is detached to the Fermi level of the tip. The calculated reorganization energy λ is then simply given by:

$λ= ε red + - ε ox 0$
(4)

### Data availability

The data that support the results within this paper and other findings of this study are available from the corresponding author on reasonable request.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Change history

• ### Update 19 April 2018

In the version of this Letter originally published, a technical error led to the following spurious text being included "Whis it it that this E_reorg term is differently highlighted than the E_reorg term in the first line of this paragraph? They are the same term."; this text has now been removed from all versions of the Letter.

## References

1. 1.

Joachim, C., Gimzewski, J. K. & Aviram, A. Electronics using hybrid-molecular and mono-molecular devices. Nature 408, 541–548 (2000).

2. 2.

Ratner, M. A brief history of molecular electronics. Nat. Nanotech. 8, 378–381 (2013).

3. 3.

Tao, N. J. Electron transport in molecular junctions. Nat. Nanotech. 1, 173–181 (2006).

4. 4.

Haiss, W. et al. Precision control of single-molecule electrical junctions. Nat. Mater. 5, 995–1002 (2006).

5. 5.

Moser, C. C., Keske, J. M., Warncke, K., Farid, R. S. & Dutton, P. L. Nature of biological electron transfer. Nature 355, 796–802 (1992).

6. 6.

Adams, D. M. et al. Charge transfer on the nanoscale: current status. J. Phys. Chem. B 107, 6668–6697 (2003).

7. 7.

Marcus, R. A. Electron transfer reactions in chemistry. Theory and Experiment. Rev. Mod. Phys. 65, 599–610 (1993).

8. 8.

Vaissier, V., Barnes, P., Kirkpatrick, J. & Nelson, J. Influence of polar medium on the reorganization energy of charge transfer between dyes in a dye sensitized film. Phys. Chem. Chem. Phys. 15, 4804–4814 (2013).

9. 9.

Brunschwig, B. S., Ehrenson, S. & Sutin, N. Solvent reorganization in optical and thermal electron-transfer processes. J. Phys. Chem. 90, 3657–3668 (1986).

10. 10.

Repp, J., Meyer, G., Paavilainen, S., Olsson, F. E. & Persson, M. Scanning tunneling spectroscopy of Cl vacancies in NaCl films: strong electron–phonon coupling in double-barrier tunneling junctions. Phys. Rev. Lett. 95, 225503 (2005).

11. 11.

Manke, F., Frost, J. M., Vaissier, V., Nelson, J. & Barnes, P. R. F. Influence of a nearby substrate on the reorganization energy of hole exchange between dye molecules. Phys. Chem. Chem. Phys. 17, 7345–7354 (2015).

12. 12.

Moth-Poulsen, K. & Bjørnholm, T. Molecular electronics with single molecules in solid-state devices. Nat. Nanotech. 4, 551–556 (2009).

13. 13.

Eckermann, A. L., Feld, D. J., Shaw, J. A. & Meade, T. J. Electrochemistry of redox-active self-assembled monolayers. Coord. Chem. Rev. 254, 1769–1802 (2010).

14. 14.

Blackbourn, R. L. & Hupp, J. T. Probing the molecular basis of solvent reorganization in electron-transfer reactions. J. Phys. Chem. 92, 2817–2820 (1988).

15. 15.

Bredas, J. L. & Street, G. B. Polarons, bipolarons, and solitons in conducting polymers. Acc. Chem. Res. 18, 309–315 (1985).

16. 16.

Gruhn, N. E. et al. The vibrational reorganization energy in pentacene: molecular influences on charge transport. J. Am. Chem. Soc. 124, 7918–7919 (2002).

17. 17.

Duhm, S. et al. Charge reorganization energy and small polaron binding energy of rubrene thin films by ultraviolet photoelectron spectroscopy. Adv. Mater. 24, 901–905 (2012).

18. 18.

Stomp, R. et al. Detection of single-electron charging in an individual InAs quantum dot by noncontact atomic-force microscopy. Phys. Rev. Lett. 94, 056802 (2005).

19. 19.

Bussmann, E. & Williams, C. C. Single-electron tunneling force spectroscopy of an individual electronic state in a nonconducting surface. Appl. Phys. Lett. 88, 263108 (2006).

20. 20.

Gross, L. et al. Measuring the charge state of an adatom with noncontact atomic force microscopy. Science 324, 1428–1431 (2009).

21. 21.

Roy-Gobeil, A., Miyahara, Y. & Grutter, P. Revealing energy level structure of individual quantum dots by tunneling rate measured by single-electron sensitive electrostatic force spectroscopy. Nano Lett. 15, 2324–2328 (2015).

22. 22.

Miyahara, Y., Roy-Gobeil, A. & Grutter, P. Quantum state readout of individual quantum dots by electrostatic force detection. Nanotechnology 28, 064001 (2017).

23. 23.

Bevan, K. H. Electron transfer from the perspective of electron transmission: biased non-adiabatic intermolecular reactions in the single-particle picture. J. Chem. Phys. 146, 134106 (2017).

24. 24.

Jortner, J. Temperature dependent activation energy for electron transfer between biological molecules. J. Chem. Phys. 64, 4860–4867 (1976).

25. 25.

Repp, J., Meyer, G., Stojković, S. M., Gourdon, A. & Joachim, C. Molecules on insulating films: scanning-tunneling microscopy imaging of individual molecular orbitals. Phys. Rev. Lett. 94, 026803 (2005).

26. 26.

Feenstra, R. M. Electrostatic potential for a hyperbolic probe tip near a semiconductor. J. Vac. Sci. Technol. B 21, 2080 (2003).

27. 27.

Kera, S. & Ueno, N. Photoelectron spectroscopy on the charge reorganization energy and small polaron binding energy of molecular film. J. Electron. Spectrosc. Relat. Phenom. 204, 2–11 (2015).

28. 28.

Liljeroth, P., Repp, J. & Meyer, G. Current-induced hydrogen tautomerization and conductance switching of naphthalocyanine molecules. Science 317, 1203–1206 (2007).

29. 29.

Imada, H. et al. Real-space investigation of energy transfer in heterogeneous molecular dimers. Nature 538, 364–367 (2016).

30. 30.

Giessibl, F. J. High-speed force sensor for force microscopy and profilometry utilizing a quartz tuning fork. Appl. Phys. Lett. 73, 3956 (1998).

31. 31.

Albrecht, T. R., Grutter, P., Horne, D. & Rugar, D. Frequency modulation detection using high-Q cantilevers for enhanced force microscope sensitivity. J. Appl. Phys. 69, 668 (1991).

32. 32.

Steurer, W., Gross, L. & Meyer, G. Local thickness determination of thin insulator films via localized states. Appl. Phys. Lett. 104, 231606 (2014).

33. 33.

Steurer, W., Fatayer, S., Gross, L. & Meyer, G. Probe-based measurement of lateral single-electron transfer between individual molecules. Nat. Commun. 6, 8353 (2015).

34. 34.

Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999).

35. 35.

Scivetti, I. & Persson, M. The electrostatic interaction of an external charged system with a metal surface: a simplified density functional theory approach. J. Phys. Condens. Matter 25, 355006 (2013).

36. 36.

Scivetti, I. & Persson, M. A simplified density functional theory method for investigating charged adsorbates on an ultrathin, insulating film supported by a metal substrate. J. Phys. Condens. Matter 26, 135003 (2014).

37. 37.

Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

38. 38.

Klimeš, J., Bowler, D. R. & Michaelides, A. Van der Waals density functionals applied to solids. Phys. Rev. B 83, 195131 (2011).

39. 39.

Dion, M., Rydberg, H., Schröder, E., Langreth, D. C. & Lundqvist, B. I. Van der Waals density functional for general geometries. Phys. Rev. Lett. 92, 246401 (2004).

40. 40.

Thonhauser, T. et al. Van der Waals density functional: self-consistent potential and the nature of the van der Waals bond. Phys. Rev. B 76, 125112 (2007).

41. 41.

Román-Pérez, G. & Soler, J. M. Efficient implementation of a van der Waals density functional: application to double-wall carbon nanotubes. Phys. Rev. Lett. 103, 096102 (2009).

42. 42.

Repp, J. et al. Charge-state-dependent diffusion of individual gold adatoms on ionic thin NaCl films. Phys. Rev. Lett. 117, 146102 (2016).

43. 43.

Scivetti, I. & Persson, M. Frontier molecular orbitals of a single molecule adsorbed on thin insulating films supported by a metal substrate: electron and hole attachment energies. J. Phys. Condens. Matter 29, 355002 (2017).

44. 44.

Björk, J. et al. Adsorption of aromatic and anti-aromatic systems on graphene through ππ stacking. J. Phys. Chem. Lett. 1, 3407–3412 (2010).

## Acknowledgements

We thank R. Allenspach for comments. Financial support by the European Research Council (advanced grant ‘CEMAS’, agreement no. 291194, and consolidator grant ‘AMSEL’, agreement no. 682144), EU projects ‘PAMS’ (contract no. 610446) and Initial Training Network ‘ACRITAS’ (contract no. 317348). The Leverhulme Trust (F/00 025/AQ) and the allocations of computer resources at Chadwick, The University of Liverpool, are gratefully acknowledged. I.S. acknowledges CCP5 funding and associated CoSeC support at STFC via EPSRC grant no. EP/M022617/1 and SLA for funding.

## Author information

### Author notes

• Bruno Schuler

Present address: Molecular Foundry, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

• Ivan Scivetti

Present address: Daresbury Laboratory, Sc. Tech., Warrington, UK

### Affiliations

1. #### IBM Research – Zurich, Rüschlikon, Switzerland

• , Bruno Schuler
• , Wolfram Steurer
• , Leo Gross
•  & Gerhard Meyer
2. #### Surface Science Research Centre, Department of Chemistry, University of Liverpool, Liverpool, UK

• Ivan Scivetti
3. #### Institute of Experimental and Applied Physics, University of Regensburg, Regensburg, Germany

• Jascha Repp

### Contributions

S.F, W.S., J.R., L.G. and G.M. designed the experiments. S.F., B.S., L.G. and G.M. performed the experiments. S.F. carried out the finite-element simulations. M.P. and I.S. were responsible for the DFT calculations. All the authors discussed the results and wrote the manuscript.

### Competing interests

The authors declare no competing interests.