Previous calculations of the pregalactic chemistry have found that a small amount of H _ { 2 } , x [ { { { H } _ { 2 } } } ] \equiv n [ { H } _ { 2 } ] / n [ { H } ] \approx 2.6 \times 10 ^ { -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 } } } ] \approx 6 \times 10 ^ { -7 } for the standard cosmology .
This production is due almost entirely to the H ^ { - } mechanism , with \sim 1 per cent coming from HeH ^ { + } and \sim 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 .