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We report first-principles theoretical investigations of possible metal contacts to monolayer black phosphorus (BP). By analyzing lattice geometry, five metal surfaces are found to have minimal lattice mismatch with BP: Cu(111), Zn(0001), In(110), Ta(110), and Nb(110). Further studies indicate Ta and Nb bond strongly with monolayer BP causing substantial bond distortions, but the combined Ta-BP and Nb-BP form good metal surfaces to contact a second layer BP. By analyzing the geometry, bonding, electronic structure, charge transfer, potential, and band bending, it is concluded that Cu(111) is the best candidate to form excellent Ohmic contact to monolayer BP. The other four metal surfaces or combined surfaces also provide viable structures to form metal/BP contacts, but they have Schottky character. Finally, the band bending property in the current-in-plane (CIP) structure where metal/BP is connected to a freestanding monolayer BP, is investigated. By both work function estimates and direct calculations of the two-probe CIP structure, we find that the freestanding BP channel is n type. [ABSTRACT FROM AUTHOR]