  Cloud evolution for various metallicities is investigated by
three-dimensional nested grid simulations, in which the initial ratio of
rotational to gravitational energy of the host cloud \beta_0 (=10^-1 - 10^-6)
and cloud metallicity Z (=0 - Z_\odot) are parameters. Starting from a central
number density of n = 10^4 cm^-3, cloud evolution for 48 models is calculated
until the protostar is formed (n \simeq 10^23 cm^-3) or fragmentation occurs.
The fragmentation condition depends both on the initial rotational energy and
cloud metallicity. Cloud rotation promotes fragmentation, while fragmentation
tends to be suppressed in clouds with higher metallicity. Fragmentation occurs
when \beta_0 > 10^-3 in clouds with solar metallicity, while fragmentation
occurs when \beta_0 > 10^-5 in the primordial gas cloud. Clouds with lower
metallicity have larger probability of fragmentation, which indicates that the
binary frequency is a decreasing function of cloud metallicity. Thus, the
binary frequency at the early universe (or lower metallicity environment) is
higher than at present day (or higher metallicity environment). In addition,
binary stars born from low-metallicity clouds have shorter orbital periods than
those from high-metallicity clouds. These trends are explained in terms of the
thermal history of the collapsing cloud.
