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At low temperatures, the main coolant in primordial gas is molecular hydrogen, H 2 . Recent work has shown that primordial gas that is not collapsing gravitationally but is cooling from an initially ionized state forms hydrogen deuteride, HD, in sufficient amounts to cool the gas to the temperature of the cosmic microwave background. This extra cooling can reduce the characteristic mass for gravitational fragmentation and may cause a shift in the characteristic masses of Population III stars. Motivated by the importance of the atomic and molecular data for the cosmological question, we assess several chemical and radiative processes that have hitherto been neglected: the sensitivity of the low‐temperature H 2  cooling rate to the ratio of ortho‐H 2  to para‐H 2 , the uncertainty in the low‐temperature cooling rate of H 2  excited by collisions with atomic hydrogen, the effects of cooling from H 2  excited by collisions with protons and electrons, and the large uncertainties in the rates of several of the reactions responsible for determining the H 2  fraction in the gas.  It is shown that the most important of neglected processes is the excitation of H 2  by collisions with protons and electrons. Their effect is to cool the gas more rapidly at early times, and consequently to form less H 2  and HD at late times. This fact, as well as several of the chemical uncertainties presented here, significantly affects the thermal evolution of the gas. We anticipate that this may lead to clear differences in future detailed three‐dimensional studies of first structure formation. In such calculations it has previously been shown that the details of the timing between cooling and merger events decide between immediate runaway gravitational collapse and a slower collapse delayed by turbulent heating.  Finally, we show that although the thermal evolution of the gas is in principle sensitive to the ortho–para ratio, in practice the standard assumption of a 3:1 ratio produces results that are almost indistinguishable from those produced by a more detailed treatment.

Uncertainties in H 2 and HD chemistry and cooling and their role in early structure formation