We extend previous studies of nonlinear hydrodynamical effects on the fragmentation of cosmological. sheets in a dark matter dominated universe by allowing for the formation of hydrogen molecules. This is accomplished by solving a reaction flow system in nonequilibrium for the baryonic fluid that includes 27 chemical reactions and nine separate species: H, H+, He, He+, He++, H-, H-2(+), H-2, and e(-), Several one-dimensional calculations are performed for different initial data parameterized by the perturbation wavelength lambda(1), along the collapsing direction. Initial wavelengths in the range 1-10 Mpc corresponding to average shock velocities of 9-110 km s(-1) are considered. The higher velocity shocks produce higher concentrations of molecular hydrogen ranging from n(H2) = 5.8 x 10(-2) cm(-3) with a mass fraction n(H2)/n = 2.8 x 10(-3) for the 10 Mpc case to 2.5 x 10(-7) cm(-3) and 1.5 x 10(-5) for lambda(1) = 1 Mpc. The gas for those shocks (namely lambda(1) > 1 Mpc) that produces large concentrations of H-2 then cools further through the vibrational/rotational excitation of the molecules. For the lambda(1) = 10 Mpc case, the temperature drops to 4.3 x 10(-3) eV at redshift z = 4.4, where H, peaks in concentration. This is compared to 0.19 eV in a six species model for which H-, H-2(+), and H-2 are neglected. However, as the shock speed is decreased, the H, formation time increases and for the 1 Mpc case H, does not form rapidly enough to compensate for the decrease in the density because of the cosmological expansion and hence cannot affect the cooling of the gas. Because the cooling is isobaric, the accompanying increase in density together with the drop in temperature combine to collapse the gas to smaller volumes and to reduce the Jeans mass by factors ranging from 10(3) for lambda(1) = 10 Mpc (dropping from 9 x 10(6) M. when H-2 is neglected to 9 x 10(3) M.) to nearly unity for lambda(1) = 1 Mpc. Hence, the faster moving shocks are likely to fragment into smaller units that may be associated with massive stars. The fragmentation process is investigated with two-dimensional simulations for the case lambda(1) = 4 Mpc. We confirm predictions from the one-dimensional studies regarding the size and mass estimates of fragments.
