We perform density-functional theory calculations on model surfaces to investigate the interplay between the morphology, electronic structure, and chemistry of oxygen-and hydroxyl-rich surfaces of InP(001) and GaP(001). Four dominant local oxygen topologies are identified based on the coordination environment: M -O-M and M -O-P bridges for the oxygen-decorated surface; and M -[OH]-M bridges and atop M -OH structures for the hydroxyl-decorated surface (M =In,Ga). Unique signatures in the electronic structure are linked to each of the bond topologies, defining a map to structural models that can be used to aid the interpretation of experimental probes of native oxide morphology. The M -O-M bridge can create a trap for hole carriers upon imposition of strain or chemical modification of the bonding environment of the M atoms, which may contribute to the observed photocorrosion of GaP/InP-based electrodes in photoelectrochemical cells. Our results suggest that a simplified model incorporating the dominant local bond topologies within an oxygen adlayer should reproduce the essential chemistry of complex oxygen-rich InP(001) or GaP(001) surfaces, representing a significant advantage from a modeling standpoint.