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The energy transfer among the components in a gas determines its fate.Especially at low temperatures, inelastic collisions drive the cooling and theheating mechanisms. In the early Universe as well as in zero- or low-metallicity environments the major contribution comes from the collisions amongatomic and molecular hydrogen, also in its deuterated version. The present workshows some updated calculations of the H$_2$ cooling function based on novelcollisional data which explicitely take into account the reactive pathway atlow temperatures. Deviations from previous calculations are discussed and amultivariate data analysis is performed to provide a fit depending on both thegas temperature and the density of the gas.

Temperature and density dependent cooling function for H$_2$ with updated H$_2$/H collisional rates