We discuss the possibility of a Kondo like effect associated with H in metals resulting from the strong dependence of the H1s orbital radius on the occupation number. We demonstrate that such a strong breathing property of the orbital radius, which translates directly into a strong occupation dependent hopping, results in the formation of local singlet-like bound states involving one electron on H and one on the surrounding metal orbitals. We also show that already at a mean field level an occupation dependent hopping integral leads to a substantial potential energy correction on hydrogen, and that the failure of LDA to incorporate this correction is probably responsible for the incorrect prediction of a metallic ground state for the YH3 switchable mirror compounds.