Multicenter bonding is shown to be able to dramatically reduce atomic transport barriers in solids. Theoretical analysis of H atoms in a nanoporous polymorph of ZnO (SOD-ZnO) shows intercage hopping to be aided by four-center bonds which: (i) radically reduce the sterically hindered H-transport barrier to be close to that found in Pd membranes, and (ii) induce p doping. SOD-ZnO is also shown to be thermodynamically favored under triaxial tension and selective for encapsulating weakly perturbed H atoms. Such materials have potential use in atomic transport, control, and purification.