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Hydrogen has been the subject of intense research following the discovery ofhigh-temperature superconductivity in hydrides, and as a result of continuousefforts to produce solid hydrogen. The Born-Oppenheimer approximation is thecentral piece of the quantum mechanical description of molecules and solids andit is expected to have its weakest validity in hydrogen containing matter as itis the lightest element of all. The Born-Oppenheimer approximation is almostalways assumed in the description of solids. Some beyond Born-Oppenheimereffects are likely included in the state-of-art method used to describehydrogen-rich materials, but the effects on the electronic structure in solidshave not been considered before. Here we compute the beyond Born-Oppenheimercorrections to electron density and report a breakdown of the Born-Oppenheimerapproximation in experimentally known hydride superconductor YH6 and in Cs-IVstructure of solid hydrogen. In both of these materials, we find a significanttransfer of electron density from the volumes surrounding the expectedpositions of the hydrogen nuclei to volumes in between the nuclei. We expectthese results to be the starting point of the beyond Born-Oppenheimer studiesof electronic structure in solids, which is likely necessary to understandthese forms of hydrogen-containing materials, also having significanttechnological importance.

Breakdown of the Born-Oppenheimer approximation in solid hydrogen and hydrogen-rich solids