  Hydrogen has been the subject of intense research following the discovery of
high-temperature superconductivity in hydrides, and as a result of continuous
efforts to produce solid hydrogen. The Born-Oppenheimer approximation is the
central piece of the quantum mechanical description of molecules and solids and
it is expected to have its weakest validity in hydrogen containing matter as it
is the lightest element of all. The Born-Oppenheimer approximation is almost
always assumed in the description of solids. Some beyond Born-Oppenheimer
effects are likely included in the state-of-art method used to describe
hydrogen-rich materials, but the effects on the electronic structure in solids
have not been considered before. Here we compute the beyond Born-Oppenheimer
corrections to electron density and report a breakdown of the Born-Oppenheimer
approximation in experimentally known hydride superconductor YH6 and in Cs-IV
structure of solid hydrogen. In both of these materials, we find a significant
transfer of electron density from the volumes surrounding the expected
positions of the hydrogen nuclei to volumes in between the nuclei. We expect
these results to be the starting point of the beyond Born-Oppenheimer studies
of electronic structure in solids, which is likely necessary to understand
these forms of hydrogen-containing materials, also having significant
technological importance.
