In a recent paper, the chemical structure of a molecule was resolved by means of atomic force microscopy (AFM): using a metal tip terminated in a CO molecule, the authors could image the internal bonding arrangement of a pentacene molecule with remarkable spatial resolution (notably better than with other tip terminations), as verified by their first-principles calculations. Here we further explore with first-principles calculations the mechanisms, applicability, and capabilities of this approach for a wider range of situations, by varying the imaged molecule and the tip beyond the experimental cases. In our simulations, a high atomic resolution is found to be dominated by the electronic structure of the last two atoms on the tip apex which are set perpendicularly to the sample molecule. For example, tips terminated in CH4 or pentacene itself (both having a C-H apex) yield similar images, while tips terminated in O-2 or CO give quite different images. While using a CO-terminated tip successfully resolves the chemical structure of pentacene and of other extended planar networks based on C-6 rings, this tip fails to resolve the structures of benzene (with its single C-6 ring) or nonplanar C-6 networks, such as C-60 or small-diameter carbon nanotubes. Defects (such as N substitution for a C-H group) were also found to significantly influence the image resolution. Our findings indicate that further application of this approach requires, for each sample, careful selection of a suitable "imaging" molecule as tip termination.