  We present a detailed theoretical analysis of a non-thermal escape of
molecular hydrogen from Mars induced by collisions with hot atomic oxygen from
martian corona. To accurately describe the energy transfer in O + H$_2(v,j)$
collisions, we performed extensive quantum-mechanical calculations of
state-to-state elastic, inelastic, and reactive cross sections. The escape flux
of H$_2$ molecules was evaluated using a simplified 1D column model of the
martian atmosphere with realistic densities of atmospheric gases and hot oxygen
production rates for the low solar activity conditions. An average density of
the non-thermal escape flux of H$_2$ of $1.9\times10^5$ cm$^{-2}$s$^{-1}$ was
obtained considering energetic O atoms produced in dissociative recombinations
of O$_{2}^{+}$ ions. Predicted rovibrational distribution of the escaping H$_2$
was found to contain a significant fraction of higher rotational states. While
the non-thermal escape rate was found to be lower than Jeans flux for H$_2$
molecules, the non-thermal escape rates of HD and D$_2$ are significantly
higher than their respective Jeans rates. The accurate values of non-thermal
escape fluxes of different molecular isotopes of H$_2$ may be important in
analyses of evolution of the martian atmosphere. The described molecular
ejection mechanism is general and expected to contribute to atmospheric escape
of H$_2$ and other light molecules from planets, satellites, and exoplanetary
bodies.
