number of Jeans masses is given by ($E_{\rm therm}/|E_{\rm grav}|)^{-3/2}$, so these clouds have roughly 3 Jeans masses in the initial configuration. All else being equal, if these clouds were to evolve isothermally from this point on, they would have the same propensity to fragment as the Pop. III.1 clouds, since this is directly related to the initial ratio of gravitational to thermal energy. Note that we have chosen a slightly subvirial configuration for our initial setup, to ensure that the clouds are still able to collapse when the turbulent motions are included. In addition to these simulations, we also performed a second set of Pop. III.2 simulations that start with the same gas mass as in the Pop. III.1 case (1000 M$_{\odot}$). In this case, the Pop.  III.2 simulations are initially more Jeans unstable than their Pop.  III.1 counterparts, and therefore might be expected to fragment significantly more.

In our Pop. III.1 simulations, we set the initial fractional abundances of H$_{2}$, H$^{+}$, HD and D$^{+}$ to $x_{\rm H_{2}} = 10^{-3}$, $x_{\rm H^{+}} = 10^{-7}$, $x_{\rm HD} = 3 \times 10^{-7}$ and $x_{\rm D^{+}} = 2.6 \times 10^{-12}$, respectively. Our values for $x_{\rm H_{2}}$, $x_{\rm H^{+}}$ and $x_{\rm HD}$ are 