Are High Resolution Atomic Force Microscopy images proportional to the force gradient or the force maps?

Frequency modulation Atomic Force Microscopy using tips functionalized with carbon monoxide (also known as High Resolution AFM) shows an extraordinary resolution on molecules and it can disclose their inner structure on the frequency shift maps. When operating the microscope at low amplitudes, <1 Å, these frequency shift measurements have been traditionally interpreted as the force gradient between the probe and the sample. Here, we show that, for CO-terminated tips, this interpretation fails even for amplitudes as small as 0.2–0.3 Å. The main reason behind this failure is the very rapid variation in tip-sample interaction upon tip approach associated with the mobility of the CO probe, which deflects to reduce the Pauli repulsion with the sample. Besides, we propose a new and very simple approach for the frequency shift in terms of the force at the closest tip-sample separation. This force approximation reproduces the real frequency maps for amplitudes larger than ∼0.3 Å, independent of CO deflection.