Metal tips decorated with CO molecules have paved the way for an impressively high resolution in atomic force microscopy (AFM). Although Pauli repulsion and the associated CO tilting play a dominant role at short distances, experiments on polar and metallic systems show that electrostatic interactions are necessary to understand the complex contrast observed and its distance evolution. Attempts to describe those interactions in terms of a single electrostatic dipole replacing the tip have led to contradictory statements about its nature and strength. Here, we solve this puzzle with a comprehensive experimental and theoretical characterization of the AFM contrast on Cl vacancies. Our model, based on density functional theory (DFT) calculations, reproduces the complex evolution of the contrast between both the Na cation and Cl anion sites, and the positively charged vacancy as a function of tip height, and highlights the key contribution of electrostatic interactions for tip-sample distances larger than 500 pm. For smaller separations, Pauli repulsion and the associated CO tilting start to dominate the contrast. The electrostatic field of the CO-metal tip can be represented by the superposition of the fields from the metal tip and the CO molecule. The long-range behavior is defined by the metal tip that contributes the field of a dipole with its positive pole at the apex. At short-range, the CO exhibits an opposite field that prevails. The interplay of these fields, with opposite sign and rather different spatial extension, is crucial to describe the contrast evolution as a function of the tip height.

We introduce an efficient method to simulate high-resolution atomic force microscopy (HR-AFM) images with CO probes. Our model explicitly takes into account the charge densities of the sample and the probe for the calculation of the short-range (SR) interaction and retains ab initio accuracy with only two parameters, that are essentially universal, independent of the number of chemical species and the complexity of the bonding topology. The application to molecular images shows a strong dependence on the stoichiometry and bonding configuration that precludes the chemical identification of individual atoms based on local force–distance curves. However, we have identified features in the 2D images and 3D force maps that reflect the highly anisotropic spatial decay of the molecular charge density and provide a way toward molecular identification. The model treats SR and electrostatics interactions on an equal footing and correctly pinpoints the Pauli repulsion as the underlying interaction responsible for the bond order discrimination in C60. Finally, we settle the controversy regarding the origin of the intermolecular features, discarding the effect of the charge redistribution associated with the H bonds, and linking them with the overlap of the wave functions of the atoms that constitute the bond. This overlap creates saddle regions in the potential energy landscape that are sensed by the probe.

The interplay of van der Waals (vdW), electrostatic (ES), and short-range (SR) interactions on both the intraand intermolecular contrast observed in high-resolution atomic force microscopy (HR-AFM) is explored in a hydrogen-bonded monolayer of triazine molecules. Our efficient model to simulate AFM images uses the three-dimensional (3D) charge distribution of both tip and sample to calculate the ES interaction, takes into account the tilting of the CO molecule, and reproduces with high accuracy density functional theory calculations. In spite of triazine's hexagonal structure, the intramolecular contrast has triangular symmetry, reflecting the charge density of the molecule. Stripelike intermolecular features, which join the molecules in the H-bond directions, originate from the overlap of the charge density of the atoms in neighboring molecules and are sharpened by the CO tilt. We demonstrate the existence of different potential energy surface minima for the CO tilt and discuss its influence on imaging. Our results clearly show that the ES interaction maps represent a local 3D average of the ES potential of the sample weighted by the tip's charge density, while the SR interaction resembles a local 3D average of the charge density of the sample. However, the strong cancellation of both contributions results in a net interaction dominated by the ES and vdW far from the molecules, and by the SR at short distance. This cancellation, which essentially removes the dependence on the detailed charge distribution of the tip, explains why AFM images can be reproduced using only sample properties such as the z component of the electric field and the charge density of the molecule, and the success of simple models that only incorporate pairwise, point-charge interactions.

We show that noncontact atomic force microscopy (AFM) is sensitive to the local stiffness in the atomicscale limit on weakly coupled 2D materials, as graphene on metals. Our large amplitude AFM topography and dissipation images under ultrahigh vacuum and low temperature resolve the atomic and moiré patterns in graphene on Pt(111), despite its extremely low geometric corrugation. The imaging mechanisms are identified with a multiscale model based on density-functional theory calculations, where the energy cost of global and local deformations of graphene competes with short-range chemical and long-range van der Waals interactions. Atomic contrast is related with short-range tip-sample interactions, while the dissipation can be understood in terms of global deformations in the weakly coupled graphene layer. Remarkably, the observed moiré modulation is linked with the subtle variations of the local interplanar graphene-substrate interaction, opening a new route to explore the local mechanical properties of 2D materials at the atomic scale. DOI: 10.1103/PhysRevLett.116.245502 Atomic force microscopy (AFM) and scanning tunneling microscopy (STM) are tools of choice for characterizing the unique mechanical and electronic properties of graphene (G) and other 2D materials. Dynamic AFM [1] in the frequency modulation (FM) mode [2] has resolved the true geometric structure of a broad range of materials [3][4][5]. FM AFM experiments on carbon-based materials [6][7][8][9][10][11][12][13] show atomic contrast in Δf images and, depending on the setup, in the dissipation channel. While the origin of the dissipation is not well understood, the Δf contrast has been linked with the nature of the tip-sample interaction [14].G properties can be efficiently tuned by the interaction with metals [15,16]. The interaction strength varies widely from the strong coupling with Rh [17,18] and Ru [19] to the weak limit (Ir [20], Pt [21]), where G retains its unique electronic properties [22]. The different lattice parameters of G and the metal underneath are accommodated through the formation of commensurate structures known as moiré patterns, where C atoms become inequivalent due to their different bonding configuration with the metal. The resulting "true" topographic corrugation of G-the difference in height among the topmost and the bottom C atom-varies widely, even in the weakly interacting cases, where it ranges from ≈50 pm on Ir [23,24] to practically flat (≤ 3 pm) on Pt [21].While STM can easily resolve these moiré patterns, even in the G=Pt case [21,25], AFM experiments have only been reported in highly corrugated cases as Ru [26], Rh [27], and Ir [12,28]. Focusing on the most challenging case, G=Ir, experiments with a Kolibri sensor using a W tip clearly resolved the moiré in constant height (CH) AFM images [28]. Measurements with a tuning fork using both inert (CO-terminated) and reactive (Ir-terminated) tips [12] were able to identify the atoms with both tips at any tip-sample distance. This atomic-scale resolution allowed the ...

meso-Dibenzoporphycene molecules adsorbed on the Ag(111) surface and on 2-monolayer-thick NaCl films were studied using submolecular resolution atomic force microscopy (AFM), scanning tunneling microscopy (STM), and first-principles calculations to clarify their stability and tautomerization behavior. We have found that the bonding of the molecules with the surface is determined by the interplay of different contributions, including the interaction of the π-aromatic orbitals of the benzene rings and the metal-coordination bond of the lone-pair electrons of the imine nitrogen atoms with the metal atoms (Ag, Na) on each substrate. The strength of the latter ultimately governs the molecular adsorption configuration and determines the nature and energy barriers for tautomerization. On Ag(111), the interaction of the imine nitrogen atoms with the Ag atoms deforms the macrocycle of porphycene, leading to a distinct AFM contrast that allows a clear identification of the molecule in its cis tautomeric form. In contrast, on NaCl films, the weaker interaction with the Na atoms leads to a flatter geometry and very similar adsorption configurations for the cis-and trans-forms, which cannot be distinguished in AFM experiments. Although weak, the dominant role of this local N−Na interaction, compared to the essentially nondirectional dispersive interactions, results in a new type of tautomerization process. In this case, the transfer of hydrogen atoms within the porphycene cavity is accompanied by a significant displacement of the whole molecule to a new site to reach a new minimum energy adsorption configuration. Our theoretical calculations indicate that this lateral translation, rather than the intramolecular H transfer, dominates the activation energy on NaCl. This novel tautomerization behavior, which we have identified on a rather inert ionic surface, might also be present on other weakly interacting substrates.