Previous calculations of the pregalactic chemistry have found that a small
amount of H_2, x[H_2]=n[H_2]/n[H] = 2.6e-6, is produced catalytically through
the H^-, H_2^+, and HeH^+ mechanisms. We revisit this standard calculation
taking into account the effects of the nonthermal radiation background produced
by cosmic hydrogen recombination, which is particularly effective at destroying
H^- via photodetachment. We also take into consideration the non-equilibrium
level populations of H_2^+, which occur since transitions among the
rotational-vibrational levels are slow compared to photodissociation. The new
calculation predicts a final H_2 abundance of x[H_2] = 6e-7 for the standard
cosmology. This production is due almost entirely to the H^- mechanism, with ~1
per cent coming from HeH^+ and ~0.004 per cent from H_2^+. We evaluate the
heating of the diffuse pregalactic gas from the chemical reactions that produce
H_2 and from rotational transitions in H_2, and find them to be negligible.Comment: 13 pages, 5 figures, MNRAS submitte