  The fragmentation process in collapsing clouds with various metallicities is
studied using three-dimensional nested-grid hydrodynamics. Initial clouds are
specified by three parameters: cloud metallicity, initial rotation energy and
initial cloud shape. For different combinations of these parameters, we
calculate 480 models in total and study cloud evolution, fragmentation
conditions, orbital separation and binary frequency. For the cloud to fragment
during collapse, the initial angular momentum must be higher than a threshold
value, which decreases with decreasing metallicity. Although the exact
fragmentation conditions depend also on the initial cloud shape, this
dependence is only modest. Our results indicate a higher binary frequency in
lower-metallicity gas. In particular, with the same median rotation parameter
as in the solar neighbourhood, a majority of stars are born as members of
binary/multiple systems for < 10^-4 Z_sun. With initial mass < 0.1 M_sun, if
fragments are ejected in embryo from the host clouds by multi-body interaction,
they evolve to substellar-mass objects. This provides a formation channel for
low-mass stars in zero- or low-metallicity environments.
