Pop III.2 clouds, where $k_{\rm B}$ is the Boltzmann constant. These confining pressures are similar to the internal pressure of the clouds in each case (see the temperatures and densities in §\[sec:ics\] below).

Finally, we have added a treatment of primordial gas chemistry and cooling to the code. To model the thermal evolution of the gas, we use an operator-split formalism, which treats the effects of radiative and chemical heating and cooling separately from compressional heating. The influence of radiative and chemical heating and cooling on the thermal energy of each particle can thus be formulated as an ordinary differential equation (ODE), which can then be solved simultaneously with the chemical rate equations (also ODEs) that describe the chemical evolution of the gas. As @tao09 have previously discussed, the strong coupling between the chemical and thermal evolution of high density primordial gas that results from the importance of three-body H$_{2}$ formation heating and H$_{2}$ collisional dissociation cooling renders it vital to treat cooling and chemistry simultaneously; treatments that do not do so will produce numerically stable results only with great difficulty. Full details of our chemical model and cooling function are given in the Appendix.

![image](fig01a){height="3.0in"} ![image](fig01b){height="3.0in"}

![image](fig01c){height="3.0in"} ![image](fig01d){height="3.0in"}

![\[fig:sinkmf\] 