  The addition of metals to any gas can significantly alter its evolution by
increasing the rate of radiative cooling. In star-forming environments,
enhanced cooling can potentially lead to fragmentation and the formation of
low-mass stars, where metal-free gas-clouds have been shown not to fragment.
Adding metal cooling to numerical simulations has traditionally required a
choice between speed and accuracy. We introduce a method that uses the
sophisticated chemical network of the photoionization software, Cloudy, to
include radiative cooling from a complete set of metals up to atomic number 30
(Zn) that can be used with large-scale three-dimensional hydrodynamic
simulations. Our method is valid over an extremely large temperature range (10
K < T < 10^8 K), up to hydrogen number densities of 10^12 cm^-3. At this
density, a sphere of 1 Msun has a radius of roughly 40 AU. We implement our
method in the adaptive mesh refinement (AMR) hydrodynamic/N-body code, Enzo.
Using cooling rates generated with this method, we study the physical
conditions that led to the transition from Population III to Population II star
formation. While C, O, Fe, and Si have been previously shown to make the
strongest contribution to the cooling in low-metallicity gas, we find that up
to 40% of the metal cooling comes from fine-structure emission by S, when solar
abundance patterns are present. At metallicities, Z > 10^-4 Zsun, regions of
density and temperature exist where gas is both thermally unstable and has a
cooling time less than its dynamical time. We identify these doubly unstable
regions as the most inducive to fragmentation. At high redshifts, the CMB
inhibits efficient cooling at low temperatures and, thus, reduces the size of
the doubly unstable regions, making fragmentation more difficult.
