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Molecular hydrogen is the most abundant molecular species in the Universe.While no doubts exist that it is mainly formed on the interstellar dust grainsurfaces, many details of this process remain poorly known. In this work, wefocus on the fate of the energy released by the H$_2$ formation on the dust icymantles, how it is partitioned between the substrate and the newly formedH$_2$, a process that has a profound impact on the interstellar medium. Wecarried out state-of-art \textit{ab-initio} molecular dynamics simulations ofH$_2$ formation on periodic crystalline and amorphous ice surface models. Ourcalculations show that up to two thirds of the energy liberated in the reaction($\sim$300 kJ/mol $\sim$3.1 eV) is absorbed by the ice in less than 1 ps. Theremaining energy ($\sim$140 kJ/mol $\sim$1.5 eV) is kept by the newly bornH$_2$. Since it is ten times larger than the H$_2$ binding energy on the ice,the new H$_2$ molecule will eventually be released into the gas-phase. The icewater molecules within $\sim$4 \AA ~from the reaction site acquire enoughenergy, between 3 and 14 kJ/mol (360--1560 K), to potentially liberate otherfrozen H$_2$ and, perhaps, frozen CO molecules. If confirmed, the latterprocess would solve the long standing conundrum of the presence of gaseous COin molecular clouds. Finally, the vibrational state of the newly formed H$_2$drops from highly excited states ($\nu = 6$) to low ($\nu \leq 2$) vibrationallevels in a timescale of the order of ps.

H2 formation on interstellar grains and the fate of reaction energy