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We use a non-equilibrium chemical network to revisit and study the effect ofH_{2}, HD and LiH molecular cooling on a primordial element of gas. We solveboth the thermal and chemical equations for a gas element with an initialtemperature T\approx 1000K and a gas number density in the rangen_{tot}=1-10^{4} cm^{-3}. At low densities, n_{tot}<10^{2} cm^{-3}, the gasreaches temperatures \sim 100K and the main coolant is H_{2}, but at higherdensities, n_{tot}>10^{2} cm^{-3}, the HD molecule dominates the gastemperature evolution. The effect of LiH is negligible in all cases. We studiedthe effect of D abundance on the gas cooling. The D abundance was set initiallyto be in the range n_{D}/n_{H}=10^{-7}-10^{-4.5}, withn_{HD}/n_{H}={D^{+}}/n_{H}=10^{-10}. The simulations show that atn_{tot}>10^{2} cm^{-3} the HD cooling dominates the temperature evolution for Dabundances greater than 10^{-5}n_{H}. This number decrease at higher densities.Furthermore, we studied the effect of electrons and ionized particules on thegas temperature. We followed the gas temperature evolution withn_{H_{+}}/n_{H}=10^{-4}-10^{-1} and n_{D^{+}}/n_{H^{+}}=10^{-5}. The gastemperature reached lower values at high ionization degree because electrons,H^{+} and D^{+} are catalizers in the formation paths of the H_{2} and HDmolecules, which are the main coolers at low temperatures. Finaly, we studiedthe effect of an OB star, with T_{eff}=4\times 10^{4}K, would have on gascooling. It is very difficult for a gas with n_{tot} in the range between 1-100cm^{-3} to drop its temperature if the star is at a distance less than 100 pc.

Revisiting the effect of H2, HD and LiH molecules in the cooling of primordial gas