The abundance of interstellar ice constituents is usually expressed with respect to the water ice because, in denser regions, a significant portion of the interstellar grain surface would be covered by water ice. The binding energy (BE), or adsorption energy of the interstellar species regulates the chemical complexity of the interstellar grain mantle. Due to the high abundance of water ice, the BE of surface species with the water is usually provided and widely used in astrochemical modeling. However, the hydrogen molecules would cover some part of the grain mantle in the denser and colder part of the interstellar medium. Even at around ~ 10K, few atoms and simple molecules with lower adsorption energies can migrate through the surface. The BE of the surface species with H2 substrate would be very different from that of a water substrate. However, adequate information regarding these differences is lacking. Here, we employ the quantum chemical calculation to provide the BE of 95 interstellar species with H2 substrate. These are representative of the BEs of species to a H2 overlayer on a grain surface. On average, we notice that the BE with the H2 monomer substrate is almost ten times lower than the BE of these species reported earlier with the H2 O c-tetramer configuration. The encounter desorption of H and H2 was introduced (with ED (H, H2 ) =45 K and ED (H2 , H2 ) =23 K) to have a realistic estimation of the abundances of the surface species in the colder and denser region. Our quantum chemical calculations yield higher adsorption energy of H2 than that of H (ED (H, H2 ) = 23 - 25 K and ED (H2, H2 ) =67 - 79 K). We further implement an astrochemical model to study the effect of encounter desorption with the resent realistic estimation. The encounter desorption of the N atom (calculations yield ED (N, H2 ) =83 K) is introduced to study the differences with its inclusion.
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