We have developed a model for molecular hydrogen formation under astrophysically relevant conditions .
This model takes fully into account the presence of both physisorbed and chemisorbed sites on the surface , allows quantum mechanical diffusion as well as thermal hopping for absorbed H-atoms , and has been benchmarked versus recent laboratory experiments on H _ { 2 } formation on silicate surfaces .
The results show that H _ { 2 } formation on grain surface is efficient in the interstellar medium up to some 300K .
At low temperatures ( \leq 100K ) , H _ { 2 } formation is governed by the reaction of a physisorbed H with a chemisorbed H. At higher temperatures , H _ { 2 } formation proceeds through reaction between two chemisorbed H atoms .
We present simple analytical expressions for H _ { 2 } formation which can be adopted to a wide variety of surfaces once their surfaces characteristics have been determined experimentally .