[en] Highlights: • New theoretical interpretation of the conversion of hydrogen observed in various silicon compounds. • Gives important estimates of H₂-Si spin-orbit couplings and electron repulsion in the cages. • Contribute to unifies various experimental observations of hydrogen conversion on non magnetic solids. • First account of the influence of the solid electronic structure on the nuclear conversion. The ortho-para conversion of hydrogen molecules oscillating inside tetrahedral cages of silicon compounds relies on the interaction of the nuclear protons with the silicon electrons. At each collision against the cage hard walls, the electron repulsion changes the molecular rotation while projecting a valence electron in the antibonding molecular state dressed by a group of conduction ones. That «bridge» facilitates the hyperfine contact of the electrons with the protons. At room temperature, the angular momentum transfer is enhanced by electron fluctuations that overcome the silicon gap and accelerate the nuclear rates by more than one order of magnitude.