  We investigate the water deuteration ratio and ortho-to-para nuclear spin
ratio of H2 (OPR(H2)) during the formation and early evolution of a molecular
cloud, following the scenario that accretion flows sweep and accumulate HI gas
to form molecular clouds. We follow the physical evolution of post-shock
materials using a one-dimensional shock model, with post-processing gas-ice
chemistry simulations. This approach allows us to study the evolution of the
OPR(H2) and water deuteration ratio without an arbitrary assumption concerning
the initial molecular abundances, including the initial OPR(H2). When the
conversion of hydrogen into H2 is almost complete, the OPR(H2) is already much
smaller than the statistical value of three due to the spin conversion in the
gas phase. As the gas accumulates, the OPR(H2) decreases in a non-equilibrium
manner. We find that water ice can be deuterium-poor at the end of its main
formation stage in the cloud, compared to water vapor observed in the vicinity
of low-mass protostars where water ice is likely sublimated. If this is the
case, the enrichment of deuterium in water should mostly occur at somewhat
later evolutionary stages of star formation, i.e., cold prestellar/protostellar
cores. The main mechanism to suppress water ice deuteration in the cloud is the
cycle of photodissociation and reformation of water ice, which efficiently
removes deuterium from water ice chemistry. The removal efficiency depends on
the main formation pathway of water ice. The OPR(H2) plays a minor role in
water ice deuteration at the main formation stage of water ice.
