Terminating the tip of an atomic force microscope with a CO molecule allows data to be acquired with a well-known and inert apex. Previous studies have shown conflicting results regarding the electrostatic interaction, indicating in some cases that the negative charge at the apex of the CO dominates, whereas in other cases the positive charge at the end of the metal tip dominates. To clarify this, we investigated CaF2(111). CaF2 is an ionic crystal and the (111) surface does not possess charge inversion symmetry. Far from the surface, the interaction is dominated by electrostatics via the negative charge at the apex. Closer to the surface, Pauli repulsion and CO bending dominate, which leads to an unexpected appearance of the complex 3-atom unit cell. We compare simulated data in which the electrostatics are modeled by point particles versus a charge density calculated by DFT. We also compare modeling Pauli repulsion via individual Lennard-Jones potentials versus a total charge density overlap. In doing so, we determine forcefield parameters useful for future investigations of biochemical processes.