The experimentally observed enhancement of hydrogen adsorption in Cu-2-tetracarboxylate paddle-wheel frameworks is investigated by ab initio density-functional theory calculations. We reveal that the puzzling enhancement is due to the effective orbital coupling between the occupied H-2 sigma and the unoccupied Cu 4s-derived states. The nontrivial dihydrogen-metal sigma-s interaction is enabled by a strong localization of the Cu 4s orbital after hybridizing with the neighboring oxygen 2p orbitals. Based on this understanding, we predict that the dihydrogen-metal interaction can be further increased by alloying Cu with s-orbital element Zn or Mg.