A quantum mechanical analysis of the motion of two hydrogenic species (hydrogen atoms or protons) inside a planar array of other atoms uses model potentials to explore the effect of delocalization and exchange on the hydrogen bonds in DNA. The assembly of base pairs in DNA may allow further delocalization of hydrogen along the chain to form conduction bands. Possible hydrogen exchange within base pairs together with migration along the chain axis suggests that some of the stability of DNA arises through hydrogen conduction to repair bonding defects.