We have synthesized hydrogenated and deuterated amorphous carbon materials that have a density, 2.7 ± 0.1 g/cm3, consistent with almost entirely tetrahedral bonding. In hydrogen-free tetrahedral amorphous carbon, the presence of a minority of sp2 bonded atoms leads to localized states that could be passivated with hydrogen by analogy with hydrogenated amorphous silicon. Neutron diffraction analysis demonstrated that the local bonding environment is consistent with ab initio models of high density hydrogenated tetrahedral amorphous carbon and with the related tetrahedral molecular structure neopentane. The optical bandgap of our material, 4.5 eV, is close to the bandgap in the density of states determined by scanning tunneling spectroscopy (4.3 eV). This bandgap is considerably larger than that of hydrogen-free tetrahedral amorphous carbon, confirming that passivation of sp2 associated tail-states has occurred. Both the structural and electronic measurements are consistent with a model in which the tetrahedrally bonded carbon regions are terminated by hydrogen, causing hopping conductivity to dominate.