-1cm
\label{chemistry} We employ the chemistry network described in detail by \citet{Greifetal2009b}, which follows the abundance evolution of \({\mathrm{H}}\), \({\mathrm{H}^+}\), \({\mathrm{H}^-}\), \({\mathrm{H}_2}\), \({\mathrm{H}_2}^+\), \({\mathrm{He}}\), \({\mathrm{He}^+}\), \({\mathrm{He}}^{++}\), \({\mathrm{D}}\), \({\mathrm{D}}^+\), \({\mathrm{HD}}\) and e\(^-\). All relevant cooling mechanisms are accounted for, including \({\mathrm{H}}\) and \({\mathrm{He}}\) collisional excitation and ionisation, recombination, bremsstrahlung and inverse Compton scattering.
In order to properly model the chemical evolution at high densities, \({\mathrm{H}_2}\) cooling induced by collisions with \({\mathrm{H}}\) and \({\mathrm{He}}\) atoms and other \({\mathrm{H}_2}\) molecules is also included. Three-body reactions involving \({\mathrm{H}_2}\) become important above \(n \gtrsim 10^8{\,{\rm cm}^{-3}}\); we employ the intermediate rate from \citet{PallaSalpeterStahler1983}, but see \citet{Turketal2011} for a discussion of the uncertainty of these rates. In addition, the efficiency of \({\mathrm{H}_2}\) cooling is reduced above \(\sim\)\(10^9{\,{\rm cm}^{-3}}\) as the ro-vibrational lines of \({\mathrm{H}_2}\) become optically thick above this density. To account for this we employ the Sobolev approximation together with an escape probability formalism (see \citealt{Yoshidaetal2006, Greifetal2011} for details).