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Integral equation techniques are used to study scanning motions of a single-atom tip of the atomic force microscope (AFM) over a rigid, hydrophobic monolayer substrate in water. The calculated force curve is found to be oscillatory, in agreement with recent AFM experiments, which can lead to multiple scanning trajectories for the tip under a constant load. The unique trajectory along which the system is thermodynamically stable is revealed. This study shows that the tip may take a hopping motion over a defect-free substrate due to layering of water molecules between the tip and substrate.