  Magnetic fields play such essential roles in star formation as transporting
angular momentum and driving outflows from a star-forming cloud, thereby
controlling the formation efficiency of a circumstellar disc and also multiple
stellar systems. The coupling of magnetic fields to the gas depends on its
ionization degree. We calculate the temperature evolution and ionization degree
of a cloud for various metallicities of Z/Zsun = 1e-6, 1e-5, 1e-4, 1e-3, 1e-2,
1e-1, and 1. We update the chemical network by reversing all the gas-phase
processes and by considering grain-surface chemistry, including grain
evaporation, thermal ionization of alkali metals, and thermionic emission from
grains. The ionization degree at nH ~ 1e15-1e19 /cm^3 becomes up to eight
orders of magnitude higher than that obtained in the previous model, owing to
the thermionic emission and thermal ionization of K and Na, which have been
neglected so far. Although magnetic fields dissipate owing to ambipolar
diffusion or Ohmic loss at nH < 1e15 /cm^3, the fields recover strong coupling
to the gas at nH ~ 1e15 /cm^3, which is lower by a few orders of magnitude
compared to the previous work. We develop a reduced chemical network by
choosing processes relevant to major coolants and charged species. The reduced
network consists of 104 (161) reactions among 28 (38) species in the absence
(presence, respectively) of ionization sources. The reduced model includes H2
and HD formation on grain surfaces as well as the depletion of O, C, OH, CO,
and H2O on grain surfaces.
