Top: The various components of the cooling function per hydrogen nucleus, L/n (erg s⁻³), Lyα, metal ([C II], [O I]), and H₂ cooling, as functions of temperature. We assume n = 1 cm⁻³, ﹩{x}_{{{\rm{H}}}^{+}}={x}_{{\rm{e}}}={10}^{-4}﹩ (solid) or 10⁻² (dashed), and ﹩{x}_{{{\rm{H}}}_{2}}={10}^{-6}﹩. Typically, for T ≪ 10⁴ K the density is high and x_e is small. For Lyα cooling we always assume ﹩{x}_{{\rm{e}}}={10}^{-2}﹩. The three sets of metal cooling curves are for Z′ = 1, 10⁻², and 10⁻⁴. Bottom: The H₂ cooling efficiency ﹩{{ \mathcal L }}_{{{\rm{H}}}_{2}}﹩ (erg cm³ s⁻³) by atomic hydrogen excitation (based on data from Lique 2015). Recall, for low densities, ﹩{L}_{{{\rm{H}}}_{2}}={x}_{{{\rm{H}}}_{2}}{n}^{2}{{ \mathcal L }}_{{{\rm{H}}}_{2}}﹩. The contributions from decays of individual ro-vibrationnal H₂ levels, (v, J), and their energies above ground (in Kelvin) are indicated.