Mapping the electrostatic force field of single molecules from high-resolution scanning probe images

Abstract

How electronic charge is distributed over a molecule determines to a large extent its chemical properties. Here, we demonstrate how the electrostatic force field, originating from the inhomogeneous charge distribution in a molecule, can be measured with submolecular resolution. We exploit the fact that distortions typically observed in high-resolution atomic force microscopy images are for a significant part caused by the electrostatic force acting between charges of the tip and the molecule of interest. By finding a geometrical transformation between two high-resolution AFM images acquired with two different tips, the electrostatic force field or potential over individual molecules and self-assemblies thereof can be reconstructed with submolecular resolution.

ARTICLE

Received 5 Nov 2015 | Accepted 8 Apr 2016 | Published 27 May 2016

Prokop Hapala1, Martinvec1, Oleksandr Stetsovych1, Nadine J. van der Heijden2, Martin Ondrek1, Joost van der Lit2, Pingo Mutombo1, Ingmar Swart2 & Pavel Jelnek1

How electronic charge is distributed over a molecule determines to a large extent its chemical properties. Here, we demonstrate how the electrostatic force eld, originating from the inhomogeneous charge distribution in a molecule, can be measured with submolecular resolution. We exploit the fact that distortions typically observed in high-resolution atomic force microscopy images are for a signicant part caused by the electrostatic force acting between charges of the tip and the molecule of interest. By nding a geometrical transformation between two high-resolution AFM images acquired with two different tips, the electrostatic force eld or potential over individual molecules and self-assemblies thereof can be reconstructed with submolecular resolution.

DOI: 10.1038/ncomms11560 OPEN

Mapping the electrostatic force eldof single molecules from high-resolution scanning probe images

1 Department of Thin Films and Nanostructures, Institute of Physics, Academy of Sciences of the Czech Republic, v.v.i., Cukrovarnick 10, 162 00 Prague, Czech Republic. 2 Department of Chemistry, Condensed Matter and Interfaces, Debye Institute for Nanomaterials Science, Utrecht University, PO Box 80 000, 3508 TA Utrecht, The Netherlands. Correspondence and requests for materials should be addressed to P.J. (email: mailto:[email protected]

Web End [email protected] ) or to I.S. (email: mailto:[email protected]

Web End [email protected] ).

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Scanning probe techniques routinely provide detailed information on the electronic and geometric structure of molecules. For example, the frontier molecular orbitals1, the

chemical structure of molecules24 and bond orders5 can be imaged. The possibility to image molecules6 and atomic clusters7 with nearly atomic resolution, also at elevated temperatures811 provided a great stimulus for surface science1217.

From the perspective of chemistry, the capability to measure the charge distribution of a molecule is extremely useful as this property determines the chemical reactivity of a molecule, as well as many other molecular properties18. However, imaging the charge distribution within a single molecule remains a challenge. Thus far, kelvin probe force microscopy (KPFM)19 is the only technique able to measure a quantity that is related to the charge distribution of an individual molecule20: the local contact potential difference21. The acquisition and unambiguous interpretation of KPFM data on the atomic22,23 and submolecular level is a nontrivial task20,24. One of the primary difculties is that there is no clear denition to which physical quantity (electrostatic potential, eld or surface dipole and so on) the detected signal should be compared (see, for example, discussion in ref. 25). Furthermore, at the typical tip-sample distances required to obtain submolecular resolution in atomic force microscopy (AFM) images, the measured KPFM signal is governed by the complex interplay of local electrostatic elds of tip and sample, their mutual polarization26, mechanical distortions and the conductance due to overlap of molecular orbitals27. In this regime, the usual interpretation of KPFM data is longer valid28.

Very recently, two alternative techniques, the Scanning Quantum Dot Microscopy29 and the kelvin probe force spectroscopy28, were introduced. Both methods partially solve the deciencies of the KPFM method discussed above. Namely, Scanning Quantum Dot Microscopy is able to provide a quantitative analysis of the electrostatic potential, but only in the far distance regime, limiting the spatial resolution. The kelvin probe force spectroscopy method provides high spatial resolution but suffers from the same drawback of ambiguous denition of the observable as KPFM (ref. 28).

As the charge distribution is to be imaged with high-resolution resolution, the use of chemically passivated tips is essential3032. Several different types of forces and processes have been identied to be important for the contrast in AFM images acquired with such tips. These include the Pauli, van der Waals and electrostatic forces, as well as the exibility of the functionalized tip2,5,3339. The latter is especially important to understand the distortions in the appearance of molecules in submolecular resolution images34,36,4045.

Here we will show that the electrostatic forces acting between probe and an inspected molecule can signicantly affect the submolecular contrast. Furthermore, we will show that distortions of the high-resolution images induced by the electrostatic force can be used to map the electrostatic potential of the molecule with submolecular resolution.

ResultsGeneral considerations. To illustrate the central idea behind the method proposed here, we consider imaging a neutral molecule with an inhomogeneous charge distribution with a tip terminated by a positively charged exible probe particle. The probe particle is attracted to regions of excess electron density, whereas it is repelled from regions that have a positive charge. Consequently, positively/negatively charged areas will appear smaller/larger than they really are with such a tip, as illustrated in Fig. 1. The opposite tendency is true for negatively charged tips. Hence, the distortions in submolecular resolution AFM images acquired with charged

tips carry information on the charge distribution within the molecule. Here, we demonstrate how these image distortions can be used to determine the spatial distribution of the electrostatic eld above molecules with submolecular resolution. The technique is applied to reconstruct the local electrostatic eld of both individual molecules and self-assembled monolayers.

First, let us briey discuss the origin and character of the apparent bonds or sharp edges in high-resolution AFM/STM images. At close tip-sample distances, the repulsive Pauli interaction induces a signicant lateral deection of the probe particle. There is a discontinuity in the deection above saddle points of the energy landscape (Fig. 2a,b). The saddle points (sharp edges) are typically present over atoms or bonds at a tip-sample distance where the Pauli repulsion fully compensates the attractive forces. Consequently, the trajectory of the probe particle is split into branches, giving rise to sharp edges35,38,43. Hence, the apparent bonds correspond to saddle points of the potential

Vs(x,y)

a

+0.15 eV

0.15 eV

+0.15 eV

0.15 eV

+0.1 eV

b

f

x = Fel/K

x = Fel/K

x x+TIP

XTIP

XPP

x x0TIP

c

ZPP

Vs(X,Z)

+0.1 eV

0.1 eV

0.1 eV

dx = Fel/k

dx = Fel/k

Figure 1 | Schematic view of the impact of the electrostatic forces on the high-resolution AFM images. (a) Blue and pink lines represent the positions of sharp edges observed in high-resolution AFM images acquired using positively charged and neutral tips, respectively. Corresponding x,y cut-plane of the Hartree potential VS(x, y) above the molecule is displayed in the background. (b) Variation of the frequency shift Df as function of the tip positions xTIP for the neutral x0TIP and positively charged xTIP probe particle. (c) The lateral relaxation Dx of the probe particle with (blue) and without (pink) an effective charge on the tip is different above a molecule due to the presence of the electrostatic force. The electrostatic force originates from the interaction between the electrostatic potential of the molecule (VS) on the surface and the effective charge on the probe particle at its given position xPP.

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a

b

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2

dx<0

6

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4

dx<0

Xtip ()

Xtip ()

0.0

Position ()

16.0

0.4

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0.0 0.0 12.6 12.0 0.0 7.0

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Figure 2 | Height dependence of the position of the sharp edges in AFM images. (a) Simulated deections of the probe particle as a function of tip position. Grey lines represent the additional deection of the probe particle with respect to its optimal conguration in far distance. The deection of the probe particle to the left and right is indicated by blue and red, respectively. (b) Same as a but now in the presence of an additional constant lateral force (see Supplementary Fig. 2 and Supplementary Note 2 for more details). (c) Constant-height AFM image of PTCDA on Ag(111). Dashed lines with numbers 1,2,3 denote positions of different vertical cut planes. (df) Evolution of Df with height along the lines shown in c. The black dotted lines guide the eye to see relevant edges. The horizontal dashed line indicates the approximate z-distance of contrast inversion.

energy surface experienced by the probe particle at a certain tip-sample distance.

Figure 2a shows the simulated deections of the probe particle on tip approach over a one-dimensional chain of atoms separated by 2.9 (corresponding to the width of a typical benzene ring). The lateral deection of the probe particle to the left and right is depicted in blue and red, respectively. Note that the trajectories of the probe particle are split into two branches. The deection depends non-linearly on the tip height. However, the position of the sharp discontinuous boundary between bending left and right, that is, between blue and red regions, does not depend on the tip-sample distance. This is in agreement with our experimental observation that at close tip-sample distances the apparent position of various sharp edges in AFM images of a perylene-3,4,9,10-tetracarboxylic dianhydride (PTCDA) molecules on Ag(111) does not change with distance (Fig. 2cf). This nding can be rationalized by the fact that the position of sharp edges is determined by the distance where the bifurcation of the probe particle trajectory on tip approach happens. Consequently, while the lateral distortions of the probe particle may be large beyond this point, the lateral apparent position of the sharp edge remains constant.

The total lateral force Ftot is the sum of van der Waals (FvdW),

Pauli (FPauli) and optionally electrostatic (Fel) forces. The presence of the lateral force (Ftot) induces a lateral deection (dx) of the exible probe particle with respect to the tip position (xtip), see Fig. 2b. As long as dx is small, it is linearly proportional to Ftot acting on the probe particle, according to Hookes law: dx Ftot/K (refs 34,39), where K is the lateral bending stiffness of

the bond between the probe particle and the tip. Variation of the lateral electrostatic force Fel causes a shift of the characteristic feature at a different lateral tip position (indicated by x tip) with respect to the position with the absence of the electrostatic lateral force x0tip as shown in Fig. 1. Consequently, the positions of the

apparent bonds (xtip) in high-resolution AFM images do not correspond to their actual positions on the surface.

From the above, it is clear that the apparent shift of the characteristic features (Dx) in AFM/STM images, therefore, carries information about the lateral forces Ftot with atomic

resolution. The apparent shift is linearly related to the deection of the probe particle from the tip base: Dx gdx g(xtip xPP),

see Fig. 1. Here, xPP denotes the actual position of the probe particle and gE2. A detailed quantitative analysis including the denition of the g coefcient can be found in Supplementary Note 1. In the following discussion, we will express everything in an experimentally observable Dx instead of in dx. In this notation, Dx is linearly proportional to the lateral force: Dx Ftot/k, where

k K/g is an effective lateral stiffness.

In our analysis of the electrostatic eld, we will use the differences in the apparent positions of sharp contours recorded with two different tips. Specically, we extract and compare the apparent positions of the same contour feature (for example, a particular atom vertex or bond edge) from two high-resolution AFM images obtained with different tips or scanning conditions (labelled tip A and tip B) at approximately the same tip-sample distances. The apparent position of features acquired with the different tips are indicated by xtip,A and xtip,B, respectively. In the following, we are interested in the relative difference of the apparent positions dx x

tip,A

xtip,B. Because we measure the same object on the surface, the real position of any atom or bond that corresponds to a particular contour feature is the same for both images. Therefore, dx can be expressed as the difference between the image distortions in the two images of the same object:

dx xtip;A xtip;B 1

DxA DxB 2

FA=kA FB=kB: 3 Here, FA and FB are the total lateral force acting on the probe particle in case A and B, respectively. As shown in the Supplementary Note 1, only the van der Waals and electrostatic

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force components of the total force contribute to the apparent lateral distortions Dx. The reason why FPauli can be ignored is connected

with the rather abrupt onset of the Pauli repulsion, as we explain in Supplementary Fig. 1 using our hard-sphere model. The distortion then depends linearly on the lateral van der Waals and electrostatic forces (Supplementary Note 2 and Supplementary Fig. 2). In the following, we therefore use the following expression for the differences in the lateral distortions:

dx

FvdW;A Fel;AkA

FvdW;B Fel;BkB : 4

In this general form, there is unfortunately no clear way how to attribute partial relative distortions to each force component, for example, to determine the lateral electrostatic force eld Fel

component only from the high-resolution images. However, under certain assumptions and/or with the help of numerical simulations this problem can be circumvented.

We will now discuss an approach to extract the lateral electrostatic force eld component from equation (4). A detailed discussion is given in Supplementary Note 3. In general, the effective stiffness (k) and charge (Q) of the tips, as well as the van der Waals contributions are different for each tip. The charge of the probe particle depends on the conguration and chemical nature of the metal apex46, as well as how the Xe/CO is coordinated. Hence, even tips terminated with the same species can have a different charge. First, we will consider the simplest case: two high-resolution images are acquired with (nearly) identical tips, for example, Xe-terminated metallic tips, differing only in their effective charge. In principle, they can have different dipoles instead of effective charges, but this would not change the conclusion drawn later (Supplementary Note 4 and Supplementary Fig. 3). In this case, the following approximations hold: (i) the effective lateral stiffness k of both tips is identical or very similar (that is, kAEkB k); (ii) the lateral

components of the van der Waals forces for tip A and B are also almost identical at a given tip-sample distance. Since both tips are used to image the same object, the surface electrostatic eld (ES)

must be the same in both images. Under these approximations, equation (4) simplies to:

dx

Fel;A Fel;B

k

estimated from numerical simulations, as discussed later. We note here that the effect of the van der Waals contribution is indispensable only at the periphery of the molecule. Although it may be difcult to extract absolute values in this scenario, the overall shape of the electrostatic eld is preserved.

To test our approach to measure the electrostatic eld with submolecular resolution, we performed two different sets of experiments. First, we studied a densely packed self-assembled layer of PTCDA on Ag(111) with two differently charged but otherwise similar Xe-terminated tips. Second, we studied individual 1,5,9-trioxo-13-azatriangulene (TOAT) molecules on Cu(111) with a neutral CO terminated tip and a positively charged Xe tip.

Molecular layers of PTCDA on Ag(111). In the case of densely packed self-assembled molecular layers, the van der Waals force component varies slowly. In addition, the effective stiffness k for different tips typically has similar values (see later). Therefore, the term dxvdW in equation (6) can be neglected and the surface electrostatic eld is given by dES kAdx/QA.

Figure 3a,b show two constant-height AFM images of a self-assembled monolayer of PTCDA on Ag(111) acquired with a neutral and positively charged Xe tips at the same tip-sample distance (for more details see Methods section). Note that the apparent size of the anhydride groups, indicated by the green circles, is different in the two images. We attribute these differences to a repulsive electrostatic interaction between the positively charged Xe tip and the positively charged anhydride groups49. This assignment is supported by a very good agreement between experimental and simulated AFM images of PTCDA/ Ag(111) with different effective charges on the Xe tip (Fig. 3c,d). The determined values for kA, kB, QA and QB are: 0.16 Nm 1,0.20 Nm 1, 0.0 e and 0.3e, respectively, as shown in

Supplementary Fig. 4.

The abundant presence of sharp features in the AFM images allows us to use an automatic computer algorithm to determine the differences in the image distortions, that is, dx. First, two

AFM images are brought into register. Subsequently, the distortion eld is found by comparing the corresponding sharp features between the two images. The algorithm is based on matching small regions of the two images. The image is divided into small tiles, in our case regularly distributed circular areas with a diameter of the characteristic image feature (for example, CC bonds, carbon hexagons and so on). These circular areas are each matched to the other image by moving them laterally, searching for maximum correlation. The resulting shift vectors represent a good approximation of the distortion between the two images, and serve as input for the electrostatic potential determination. The green grids plotted in Fig. 3e,f visualize the determined deformation.

As argued above, the as-obtained deformation eld (grey arrows in Fig. 3g) is linearly proportional to the lateral electrostatic eld above the molecular layer, with proportionality constant kA/QA. The electrostatic potential obtained from the experimental images is shown in Fig. 3g and is in very good agreement with the electrostatic potential as calculated from density functional theory (DFT; Fig. 3h). The absolute magnitude 0.04 to 0.04 eV of the

electrostatic eld as determined experimentally is approximately three times smaller than estimated from DFT calculations. This discrepancy can be attributed to several effects, such as uncertainties in the absolute tip-sample distance where the electrostatic potential is measured; in the values of the effective charge Q and lateral stiffness k; in the nite oscillation amplitude and so on. We will address the limits of the method and their possible solutions later (see Discussion).

QA QB

k ES;

5

where QA, QB are the effective charges of tips A and B, respectively. This equation shows that we can obtain quantitative information about ES directly from the difference in the image distortions. The only parameters that are needed are the effective lateral stiffness k and the difference between the effective charges QA and QB. These can be estimated for each tip from a direct comparison between experimental and simulated high-resolution AFM/STM images35,47 (for more details see Supplementary Method: correlating the experimental and theoretical data sets to obtain the probe characteristics K and Q and Supplementary Fig. 4). Alternatively, k can be obtained directly from experimental measurements48.

Next, we consider a more general case where the van der Waals contribution for the two tips is signicantly different but one of the tips is neutral, that is, QBE0. This would correspond to the situation where macroscopically different tips, possibly with different tip termination, are used. In this case, we obtain the following relation for the surface electrostatic eld ES (for details see Supplementary Note 3):

ES

kA dx dxvdW

QA ; 6

where dxvdW F

vdW,A/kA F

vdW,B/kB. The differences of the van der Waals deformation eld components (dxvdW) can be

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From the correlation analysis of the experimental and theoretical AFM images of PTCDA (Supplementary Fig. 5), we can estimate the uncertainties in Q and k. For the neutral tip, the maximum correlation is well dened within 0.05e and 0.08 Nm 1. However, for the positively charged tip there are multiple Q-k combinations that provide a similar correlation between experiment and theory. As the scaling term of the vector eld is the ratio Q/k, we can estimate the systematic

error from its variation. By selecting the different favourable Q,k pairs, we nd a systematic error of approximately 20%. It is important to note that this uncertainty only affects the absolute values, that is, the relative variation of the electrostatic potential is correct.

Single TOAT molecule on Cu(111). As the second example, we studied individual TOAT molecules, since they have a highly non-homogeneous charge distribution. The central N atom donates an electron to the delocalized p-system and is thus positively charged. In contrast, the three ketone groups at the edge of the molecule withdraw electron density from the ring system and therefore have a partial negative charge. High-pass ltered constant-height AFM images of a TOAT molecule on Cu(111) acquired with CO and Xe tips are shown in Fig. 4a,b, respectively. There are signicant differences between images acquired with the two different tip terminations. The central region of the molecule appears smaller while the peripheral benzene rings are elongated for images acquired with a Xe-terminated tip compared to images obtained with a CO tip. Again, this effect is attributed to a repulsive interaction between the positively charged Xe tip and the positively charged central area

a b

Hz

Hz

+0.36

0.11

0.91

0.15+0.151.74

c d

Hz

Hz

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+1.85

a b

eV0.61

0.38

0.04

0.04

e

f

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Es from DFT

CO-tip

CO-tip

1.0 nm

c

d

g h

Es from exp.

Es from exp.

eV

Es from DFT

e

f

+

+

+0.5 eV

0.3 eV+0.5 eV

0.3 eV

Vs from DFT

Vs from DFT Vs from exp.

Vs from exp.

Figure 3 | Determining the electrostatic eld above a close-packed PTCDA layer. (a,b) experimental high-resolution AFM images of a self-assembled monolayer of PTCDA deposited on Ag(111) obtained with two different Xe tips. (c) simulated AFM image using an effective chargeQ 0.0e and the effective lateral stiffness k 0.16 Nm 1. (d) same as c

but with Q 0.3e and k 0.20 Nm 1. (e,f) the experimental images

superimposed with a deformation grid dened by comparing the corresponding sharp features between the two images in a and b.(g) electrostatic potential calculated from the deformation eld (grey arrows). (h) calculated Hartree potential from DFT simulations 3.0 above the molecular layer.

Xe-tip

Figure 4 | Determining the electrostatic eld above an individual molecule. (a) High-pass ltered constant-height AFM images of a TOAT molecule on Cu(111) acquired with a Xe tip. Crosses indicate characteristic vertices. (b) Same as a but measured with a CO tip. (c) electrostatic force eld calculated from DFT. (d) experimentally determined electrostatic force eld obtained after subtraction of the van der Waals component from the deformation eld obtained from the images shown in a and b. (e) calculated Hartree potential; (f) electrostatic potential calculated from the experimental deformation eld shown in d.

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of the molecule. This effect is reproduced by our simulations for a Xe tip with an effective charge Q 0.3 e and lateral stiffness

k 0.24 Nm 1. Similarly, we found the best match between

experimental and theoretical AFM images acquired with the CO tip with an effective charge Q 0.0e and lateral stiffness

k 0.24 Nm 1 (details can be found in Supplementary Fig. 5).

For individual molecules, positions of vertices were determined manually (blue and red markers in Fig. 4a,b). The deformation eld can be obtained by alignment of corresponding vertices (dx)

in the two AFM images using interpolation by radial basis functions and exploiting the threefold rotational symmetry of the TOAT molecule (see Supplementary Method: estimation of the image distortion from high-resolution AFM images of TOAT molecule and Supplementary Fig. 6). The obtained deformation eld shown in Supplementary Fig. 7 is directly proportional to total lateral force eld.

Here, the estimated lateral force eld also contains the van der Waals force component, which can be determined with the help of numerical modelling34. Thus the electrostatic eld ES can be reconstructed from equation (6) using the tted lateral stiffness (kA, kB) and differential van der Waals deformation eld dxvdW (details of how dxvdW was subtracted are provided in the Supplementary Method: subtraction of van der Waals component from distortion eld on TOAT). Figure 4d shows the as determined electrostatic eld while its calculated counterpart is given in Fig. 4c. The agreement between theory and experiment above the molecule is again very good. Note that the method cannot provide resolution outside of the molecule (green area in Fig. 4c,d), due to the lack of sharp features in this region. Hence we nullied the obtained electrostatic eld in this area.

For the TOAT molecules, we obtained the experimental electrostatic potential VS by determining the derivative of the electrostatic eld ES. The resulting electrostatic potential, shown in Fig. 4f, matches the calculated electrostatic eld over the molecule including a complex charge distribution on the benzene lobes. The charge distribution near the oxygen atoms can not be described properly due to the lack of sharp features in this area. In the TOAT case, our method cannot reliably quantify the absolute magnitude of the electrostatic potential due to uncertainties associated with subtraction of the vdW force eld and the absence of sharp features outside the molecule. We decided not to provide a quantitative comparison of the electrostatic potential VS to

avoid an over-interpretation of our method.

DiscussionWe will now discuss several important aspects of the method to facilitate its assessment. The resolution of our method is directly connected to the requirement of having sharp edges in images originating from a saddle point of the potential energy surface. Therefore, the method can only be used to determine the electrostatic eld at close tip-sample distances where such features are present.

As discussed above, the position of the sharp edges remains practically constant in the close distance regime. This has two important consequences. First, the position of sharp edges is determined by a bifurcation (cusp) in the probe particle trajectories upon tip approach. The deection of the probe particle beyond this branching point does not further affect the apparent position of the edges in the images. Consequently, only the value of the lateral spring constant k at the tip-sample distance where the branching occurs will inuence the results. Therefore, variations of the lateral stiffness k with tip-sample distance39 do not affect the analysis. Second, our method can only map the electrostatic eld at the height where the trajectory of the probe particle branches.

It is important to note that sharp edges are visible in both simultaneously acquired AFM and STM channels, as shown in Supplementary Fig. 8. In addition, sharp features are also present in high-resolution STM (ref. 3) and IETS-STM (ref. 4) images. Hence, in principle, our method can also be applied to such data.

The possibility to extract quantitative information depends critically on several factors. First, uncertainties in the values of k and Q could potentially be eliminated by acquiring two images with the same functionalized tip, the charge of which can be effectively modied by other means (for example, by some oxidation/reduction process of the moiety attached to the tip). A search for new functionalized tips with the possibility to modulate an effective charge without loosing its mechanical stability is the subject of current investigations. Alternatively, one can try to reduce the uncertainties in k and Q by, for example, using more sophisticated algorithms for image analysis. The simulation of the electrostatic interaction can be further improved by implementation of a more realistic charge distribution on the probe particle using dipole/quadrupole or even the charge distribution obtained directly from ab initio calculations50.

In conclusion, we showed that the electrostatic interaction between the probe and a molecule on the surface affects distortions in high-resolution images. In particular, the electro-static eld originating from polar molecules can be mapped with high resolution by analysing the differences in the distortions in images acquired with differently charged tips. The arguments and results presented above demonstrate the background, advantages and limitations of the method to probe the electrostatic potential of molecules with submolecular spatial resolution. The main advantages of this method are the clear relation between the physical observables and the electrostatic eld, the high spatial resolution and its applicability to STM and AFM images. In addition, it offers the prospect of extracting quantitative information. Here, we applied the method for molecules, but it can be easily extended to surfaces and surface defects (for example, impurities, vacancies, subsurface defects and so on). As such, it constitutes a valuable complementary tool to existing techniques.

Finally we would like to stress that the general idea behind the technique can be applied to any lateral force acting on the last atom of the tip (the probe particle). Consequently, new potential applications can be envisaged, such as imaging the electrostatic eld of the probe itself or that of excited molecules. In addition, it may be possible to map molecular magnetic eld as well.

Methods

AFM/STM measurements of PTCDA/Ag(111). The PTCDA on Ag(111) experiments were carried out with a Specs LT STM/AFM with a commercially available Kolibri sensor, operating at B1.2 K in ultra-high vacuum. Kolibri sensor parameters used in experiment are: f0E985,387 Hz, QE230,000 and AE70 pm.

The Ag surface was cleaned by repeated cycles of sputtering (Ar , pArE5 10 6 mbar, 10 min) and annealing (E800 K, 5 min). PTCDA was

evaporated in ultra-high vacuum (Po1.5 10 9 mbar) for 4 min from a crucible

thermally heated to E673 K. Evaporation was performed E10 min after the nal annealing of the Ag sample with no post evaporation annealing. Xe (99.99% purity) was deposited on the cold sample (To10 K) by opening shutters for E14 s to pXe 5 10 7 mbar. The tip was functionalized in two steps. First, a metal

terminated tip was obtained by few nm dipping of the sensor into the clean Ag surface with a E2 V bias pulse. Second, Xe-terminated tip was obtained by spontaneous picking up a Xe atom from a Xe island by the metal terminated tip, while scanning in STM mode (0.1 V, 10 pA).

The acquisition of the three-dimensional (3D) force maps was done automatically, by measuring a sequence of constant-height images and changing the tip-sample separation in between the subsequent images. Apart from the frequency shift, tunnelling current, dissipation and also the amplitude channels have been recorded simultaneously. The step in z was chosen to be in the order of picometres and positive, that is, increasing the tip-sample distance.

Images acquired with different tips were aligned vertically using the following procedure. First, for each tip a data cube with simulated 3D frequency shift values is generated for a particular set of k and Q values. The offsets in z-distance of the

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experimental and theoretical data sets are then determined by aligning the z-position of the frequency shift minimum for the centres of the molecules. Once this information is available for each tip, images corresponding to approximately the same tip-sample distance can be selected.

AFM/STM measurements of TOAT/Cu(111). Individual TOAT molecules on Cu(111) with a neutral CO terminated tip and a positively charged Xe tip were imaged using a Scienta-Omicron LT STM/AFM with a commercially available Qplus sensor, operating at B4.6 K in ultrahigh vacuum with an average pressure of 5 10 10 mbar. The baked qPlus sensor (3 h at 120 C) had a quality factor of

Q 30,000, a resonance frequency of f0 25,634 Hz and a peak-to-peak oscillation

amplitude of approximately 2 .

A Cu(111) crystal surface was cleaned with several sputter and anneal cycles before inserting it in the microscope head. The TOAT molecules were thermally evaporated onto the cold surface using an e-beam evaporator (Focus GmbH). For STM imaging, the bias voltage was applied to the sample. After approaching the tip to the surface, an atomically sharp metal tip was prepared by controlled crashes into the copper surface and bias pulses. Each chemically passivated tip was prepared by subsequent pick-up of either a Xe atom or CO molecule2,5153. After a free-lying TOAT molecule was located on the surface, the tip was left in tunnelling contact (I 10 pA at V 0.1 V) and allowed to relax for 12 h to minimize drift and

piezo-creep. All AFM images were acquired in constant-height mode. After each AFM image, the STM feedback loop was enabled for 2 s to further minimize tip-sample drift. A complete stack of images resulting in a 3D force grid took B13 h to acquire.

DFT calculation of PTCDA/Ag(111). We used a pre-optimized herringbone structure of PTCDA molecules on Ag(111) surface54 consisting of two molecules in the unit cell and a slab of 3 Ag layers (99 Ag atoms). The Hartree potential used for generating the theoretical electrostatic force eld35 was obtained from self-consistent total energy DFT using the Vienna ab initio simulation package55 with generalized gradient approximation based functional PW91 (ref. 56) and projector augmented-wave method57. Plane wave basis set was chosen with Ecut 396 eV.

DFTcalculation of TOAT/Cu(111). Total energy DFT calculations were performed using the FHI-aims code58. We used a 6 6 supercell made of four Cu layers to

describe the Cu(111) surface. The TOAT molecule was placed on the surface with the N atom in a top position. This position was chosen based on the experimental ndings. All the atoms except the two bottom Cu layers were relaxed until the remaining atomic forces and the total energy were below 10 2 eV 1 and10 5 eV, respectively. A Monkhorst-Pack grid of 2 2 1 was used for the

integration in the Brillouin zone. All the calculations were carried out at the GGA-PBE level59 including the Tkatchenko-Schefer treatment60 of the van der Waals interaction. The use of van der Waals interactions was necessary to correctly describe the interaction between the molecule and surface. The basis set, pseudo-potentials, integration grids and Hartree potential accuracy were specied using the tight settings. For species like H, O, N the basis set level was set to tier 2 while for Cu a rst tier was used. Note that a tier represents a single set of radial functions added to the minimal basis to effectively describe the chemical bond.

AFM simulations. To calculate high-resolution AFM images we used a home built AFM simulation toolkit34,35 (avaible opensource at https://github.com/ProkopHapala/ProbeParticleModel

Web End =https://github.com/ https://github.com/ProkopHapala/ProbeParticleModel

Web End =ProkopHapala/ProbeParticleModel ; see also webpage http://nanosurf.fzu.cz/ppr/

Web End =http://nanosurf.fzu.cz/ppr/ ). We used default parameters of pairwise LJ potentials34. The optimized structures and corresponding surface Hartree potentials were obtained from fully relaxed total energy DFT simulations of the system, see above. The effective tipcharge Q and lateral stiffness k of probe particle are a free input of the model. The positions of the Df(z) minima in the centres of the molecules were taken as the reference points in Z, for both the experiment and theory.

Processing of experimental data and matching to simulation. Iterative algorithm for registration of experimental AFM/STM images using linear correlation is described in the Supplementary Method: data set registration procedure and Supplementary Fig. 9. The estimation of the effective stiffness K and effective charge Q is described in the Supplementary Method: correlating the experimental and theoretical data sets to obtain the probe characteristics K and Q and Supplementary Fig. 4 for PTCDA and Supplementary Fig. 5 for TOAT. The evaluation of the electrostatic potential by tting its derivatives to image distortions is described in the Supplementary Method: evaluation of the electrostatic potential from the distortion vector eld.

Data availability. The data that support the ndings of this study are available from the corresponding authors on request.

References

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

2. Gross, L., Mohn, F., Moll, N., Liljeroth, P. & Meyer, G. The chemical structure of a molecule resolved by atomic force microscopy. Science 325, 11101114 (2009).

3. Temirov, R., Soubatch, S., Neucheva, O., Lassise, A. C. & Tautz, F. S. A novel method achieving ultra-high geometrical resolution in scanning tunnelling microscopy. New J. Phys. 10, 053012 (2008).

4. Chiang, C. l., Xu, C., Han, Z. & Ho, W. Real-space imaging of molecular structure and chemical bonding by single-molecule inelastic tunneling probe. Science 344, 885888 (2014).

5. Gross, L. et al. Bond-order discrimination by atomic force microscopy. Science 337, 13261329 (2012).

6. Gross, L. Recent advances in submolecular resolution with scanning probe microscopy. Nat. Chem. 3, 273278 (2011).

7. Emmrich, M. et al. Subatomic resolution force microscopy reveals internal structure and adsorption sites of small iron clusters. Science 348, 308311 (2015).

8. Sweetman, A. et al. Intramolecular bonds resolved on a semiconductor surface. Phys. Rev. B 90, 165425 (2014).

9. Iwata, K. et al. Chemical structure imaging of a single molecule by atomic force microscopy at room temperature. Nat. Commun. 6, 7766 (2015).

10. Moreno, C., Stetsovych, O., Shimizu, T. K. & Custance, O. Imaging three-dimensional surface objects with submolecular resolution by atomic force microscopy. Nano Lett. 15, 22572262 (2015).

11. Huber, F. et al. Intramolecular force contrast and dynamic current-distance measurements at room temperature. Phys. Rev. Lett. 115, 066101 (2015).

12. de Oteyza, D. G. et al. Direct imaging of covalent bond structure in single-molecule chemical reactions. Science 340, 14341437 (2013).

13. Pavlicek, N. et al. Atomic force microscopy reveals bistable congurations of dibenzo[a,h]thianthrene and their interconversion pathway. Phys. Rev. Lett. 108, 08610 (2012).

14. Kawai, S. et al. Obtaining detailed structural information about supramolecular systems on surfaces by combining high-resolution force microscopy with ab initio calculations. ACS Nano 7, 90989105 (2013).

15. Schuler, B., Meyer, G., Pena, D., Mullins, O. C. & Gross, L. Unraveling the molecular structures of asphaltenes by atomic force microscopy. J. Am. Chem. Soc. 137, 98709876 (2015).

16. Pavlicek, N. et al. On-surface generation and imaging of arynes by atomic force microscopy. Nat. Chem. 7, 623628 (2015).

17. Dienel, T. et al. Resolving atomic connectivity in graphene nanostructure junctions. Nano Lett. 15, 51855190 (2015).

18. Clayden, J., Greeves, N. & Warren, S. Organic Chemistry (Oxford University Press, 2001).

19. Nonnenmacher, M., OBoyle, M. P. & Wickramasinghe, H. K. Kelvin probe force microscopy. Appl. Phys. Lett. 58, 2921 (1991).

20. Mohn, F., Gross, L., Moll, N. & Meyer, G. Imaging the charge distribution within a single molecule. Nat. Nanotechnol. 7, 227231 (2012).

21. Baier, R., Leendertz, C., Lux-Steiner, M. C. & Sadewasser, S. Toward quantitative Kelvin probe force microscopy of nanoscale potential distributions. Phys. Rev. B 85, 165436 (2012).

22. Enevoldsen, G. H., Glatzel, T., Christensen, M. C., Lauritsen, J. V. & Besenbacher, F. Atomic scale kelvin probe force microscopy studies of the surface potential variations on the TiO2(110) surface. Phys. Rev. Lett. 100, 236104 (2008).

23. Sadewasser, S. et al. New insights on atomic-resolution frequency-modulation kelvin-probe force-microscopy imaging of semiconductors. Phys. Rev. Lett. 103, 266103 (2009).

24. Schuler, B. et al. Contrast formation in Kelvin probe force microscopy of single p-conjugated molecules. Nano Lett. 14, 33423346 (2014).

25. Neff, J. L. & Rahe, P. Insights into Kelvin probe force microscopy data of insulator-supported molecules. Phys. Rev. B 91, 085424 (2015).

26. Corso, M. et al. Charge redistribution and transport in molecular contacts. Phys. Rev. Lett. 115, 136101 (2015).

27. Weymouth, A., Wutscher, T., Welker, J., Hofmann, T. & Giessibl, F. Phantom force induced by tunneling current: a characterization on Si(111). Phys. Rev. Lett. 106, 226801 (2011).

28. Albrecht, F. et al. Probing charges on the atomic scale by means of atomic force microscopy. Phys. Rev. Lett. 115, 076101 (2015).

29. Wagner, C. et al. Scanning quantum dot microscopy. Phys. Rev. Lett. 115, 026101 (2015).

30. Bartels, L. et al. Dynamics of electron-induced manipulation of individual CO molecules on Cu(111). Phys. Rev. Lett. 80, 2004 (1998).

31. Welker, J. & Giessibl, F. J. Revealing the angular symmetry of chemical bonds by atomic force microscopy. Science 336, 444449 (2012).

32. Mohn, F., Schuler, B., Gross, L. & Meyer, G. Different tips for high-resolution atomic force microscopy and scanning tunneling microscopy of single molecules. Appl. Phys. Lett. 102, 073109 (2013).

NATURE COMMUNICATIONS | 7:11560 | DOI: 10.1038/ncomms11560 | http://www.nature.com/naturecommunications

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33. Moll, N., Gross, L., Mohn, F., Curioni, A. & Meyer, G. The mechanisms underlying the enhanced resolution of atomic force microscopy with functionalized tips. New J. Phys. 12, 125020 (2010).

34. Hapala, P. et al. The mechanism of high-resolution STM/AFM imaging with functionalized tips. Phys. Rev. B 90, 085421 (2014).

35. Hapala, P., Temirov, R., Tautz, F. S. & Jelinek, P. Origin of high-resolution IETS-STM images of organic molecules with functionalized tips. Phys. Rev. Lett. 113, 226101 (2014).

36. Guo, C., Xin, X., Van Hove, M. A., Ren, X. & Zhao, Y. Origin of the contrast interpreted as intermolecular and intramolecular bonds in atomic force microscopy images. J. Phys. Chem. C 119, 1419514200 (2015).

37. van der Lit, J., Di Cicco, F., Hapala, P., Jelinek, P. & Swart, I. Submolecular resolution imaging of molecules by atomic force microscopy: the inuence of the electrostatic force. Phys. Rev. Lett. 105, 096102 (2016).

38. Boneschanscher, M. P., Hamalainen, S. K., Liljeroth, P. & Swart, I. Sample corrugation affects the apparent bond lengths in atomic force microscopy. ACS Nano 8, 30063014 (2014).

39. Neu, M. et al. Image correction for atomic force microscopy images with functionalized tips. Phys. Rev. B 89, 205407 (2014).

40. Zhang, J. et al. Real-space identication of intermolecular bonding with atomic force microscopy. Science 342, 611614 (2013).

41. Sweetman, A. M. et al. Mapping the force eld of a hydrogen-bonded assembly. Nat. Commun. 5, 3931 (2014).

42. Moll, N. et al. Image distortions of a partially uorinated hydrocarbon molecule in atomic force microscopy with carbon monoxide terminated tips. Nano Lett. 14, 61276131 (2014).

43. Hamalainen, S. K. et al. Intermolecular contrast in atomic force microscopy images without intermolecular bonds. Phys. Rev. Lett. 113, 186102 (2014).44. Kawai, S. et al. Extended halogen bonding between fully uorinated aromatic molecules. ACS Nano 9, 25742583 (2015).

45. Jarvis, S. P. et al. Intermolecular artifacts in probe microscope images of C60 assemblies. Phys. Rev. B 92, 241405 (2015).

46. Gao, D. Z. et al. Using metallic noncontact atomic force microscope tips for imaging insulators and polar molecules: tip characterization and imaging mechanisms. ACS Nano 8, 53395351 (2014).

47. Sun, Z., Boneschanscher, M., Swart, I., Vanmaekelbergh, D. & Liljeroth, P. Quantitative atomic force microscopy with carbon monoxide terminated tips. Phys. Rev. Lett. 106, 046104 (2011).

48. Weymouth, A. J., Hofmann, T. & Giessibl, F. J. Quantifying molecular stiffness and interaction with lateral force microscopy. Science 343, 11201122 (2014).

49. Gross, L. et al. Investigating atomic contrast in atomic force microscopy and Kelvin probe force microscopy on ionic systems using functionalized tips. Phys. Rev. B 90, 155455 (2014).

50. Ellner, M. et al. The electric eld of CO tips and its relevance for atomic force microscopy. Nano Lett. 16, 19741980 (2016).

51. Eigler, D. M., Lutz, C. P. & Rudge, W. E. An atomic switch realized with the scanning tunnelling microscope. Nature 352, 600603 (1991).

52. Bartels, L., Meyer, G. & Rieder, K.-H. Controlled vertical manipulation of single CO molecules with the scanning tunneling microscope: a route to chemical contrast. Appl. Phys. Lett. 71, 213215 (1997).

53. Giessibl, F. Advances in atomic force microscopy. Rev. Mod. Phys. 75, 949 (2003).

54. Rohlng, M., Temirov, R. & Tautz, F. Adsorption structure and scanning tunneling data of a prototype organic-inorganic interface: PTCDA on Ag(111). Phys. Rev. B 76, 115421 (2007).

55. Kresse, G. & Furthmller, J. Efcient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169 (1996).

56. Perdew, J. P. et al. Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46, 66716687 (1992).

57. Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 17581775 (1999).

58. Blum, V. et al. Ab initio molecular simulations with numeric atom-centered orbitals. Comput. Phys. Commun. 180, 21752196 (2009).

59. Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 38653868 (1996).

60. Tkatchenko, A. & Schefer, M. Accurate molecular van der waals interactions from ground-state electron density and free-atom reference data. Phys. Rev. Lett. 102, 073005 (2009).

Acknowledgements

This work was nancially supported by grants from the Czech Science Foundation (grant no. 14-16963J), the Ministry of Education of the Czech Republic grant no. LM2015087 and the Netherlands Organization for Scientic Research (ECHO-STIP grantno. 717.013.003).

Author contributions

P.H., M. and P.J. conceived the method. I.S. and P.J. conceived the experiments. M., O.S., J.L, N.J.v.d.H. and I.S. carried out the experiments and analysed the experimental data. P.H., M.O., P.M. and P.J. performed and analysed the total energy DFT and AFM calculations. P.H., I.S., M. and P.J. wrote the paper. All coauthors provided feedback on the manuscript.

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How to cite this article: Hapala, P. et al. Mapping the electrostatic force eld of single molecules from high-resolution scanning probe images. Nat. Commun. 7:11560doi: 10.1038/ncomms11560 (2016).

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