High-resolution model for noncontact atomic force microscopy with a flexible molecule on the tip apex

Experiments using noncontact atomic force microscopy (NC-AFM) with CO-molecule-functionalized tips have distinctly imaged chemical structures within conjugated molecules. Here we describe a detailed model based on an ab initio approach of the interaction force between the AFM tip and the sample molecule that yields atomic-scale images, which agree very well with the experimental images we considered. The key ingredient of our model is to explicitly include the effect on the image due to the tilt of the CO molecule at the tip apex resulting from the lateral force exerted by the sample. On the basis of this model, we specifically discuss the distortion seen in AFM images. As reported very recently, the distortion in AFM images originates from an intrinsic effect, namely, different extents of π-electron orbitals, as well as from an extrinsic effect, specifically CO tilt. We find that intrinsic distortion is scanning height dependent, attributing to the integrated electron density in the tip-sample overlapping region moving away from (the vertical projection of) the atom or bond positions. This intrinsic distortion is dominant in AFM images, although the atomic positions could be displaced even more by the extrinsic distortion due to CO tilt.