The interplay of van der Waals (vdW), electrostatic (ES), and short-range (SR) interactions on both the intra- and 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.

• Received 6 June 2017

DOI:https://doi.org/10.1103/PhysRevB.96.075418