Ω_H2 evolution (upper panel) and maximum H₂ mass fractions (lower panel) reached in the no-catalysis simulation (black solid lines; HM-HISSmed) are compared to runs including H₂ grain catalysis at T_gr = 75 K. Gas Z is either forced to constant values of Z = Z_⊙ (blue dot-dot-dot-dashed lines; HM-HISS-cat-75-Zsun) and 0.01 Z_⊙ (orange dashed lines; HM-HISS-cat-75-0.01Zsun), or consistently computed from temporal evolution of SN II, AGB, and SN Ia metal spreading and cooling from both resonant and fine-structure lines (magenta dot-dashed lines; HM-HISS-cat-75-Zt). Photoelectric heating on dust grains is tested, as well (green dotted lines; HM-HISSmed-cat-75-pe).