Interstellar Dust-Catalyzed Molecular Hydrogen Formation Enabled by Nuclear Quantum Effects

Molecular hydrogen (H$_2$) plays a critical role in astrophysical processes from galaxy evolution to the formation of planets. While the dominant formation channel in the interstellar medium is considered as dust-catalyzed H$_2$ formation, this process could become inefficient at low temperatures suppressed by the Boltzmann factor. This work demonstrates that quantum tunneling can dominate the formation of H$_2$, resolving the long-standing problem of formation efficiency. Path integral Monte Carlo simulations reveals that the quantum tunneling of hydrogen atoms maintains stable reaction rates at temperatures below 50 K on both graphitic and silicate grain surfaces. Kinetic Monte Carlo calculations further indicate that the actual H$_2$ formation efficiency is governed not by atomic diffusion, but rather by the energy barriers associated with chemisorption, desorption, and the association of two hydrogen atoms. These findings establish a robust physical basis for dust-catalyzed H$_2$ formation, offer quantitative reaction rates for refining astrophysical models, and provide a framework for interpreting observations of interstellar molecular materials.