  The formation of compact dusty clouds in diffuse interstellar medium (ISM)
has been recently proposed and studied by Tsytovich et al. (2014). In the
present paper, an effect of the clouds on the rate of H$\to$H$_2$ transition in
the ISM is examined. We discuss the mechanisms leading to the formation of the
clouds and the creation of gaseous clumps around them, analyze the main
processes determining the efficiency of the recombination of atomic hydrogen on
dust grains, and estimate the expected enhancement of the global H$_2$
formation due to the presence of the clouds. In conclusion, we argue that the
compact dusty clouds provide optimum conditions for the atomic recombination in
diffuse ISM, and point out some astrophysical implications of the resulting
H$_2$ formation enhancement.

Astrophysics of Galaxies