  We have investigated the evolution and distribution of molecules in
collapsing prestellar cores via numerical chemical models, adopting the
Larson-Penston solution and its delayed analogues to study collapse. Molecular
abundances and distributions in a collapsing core are determined by the balance
among the dynamical, chemical and adsorption time scales. When the central
density n_H of a prestellar core with the Larson-Penston flow rises to 3 10^6
cm^{-3}, the CCS and CO column densities are calculated to show central holes
of radius 7000 AU and 4000 AU, respectively, while the column density of N2H+
is centrally peaked. These predictions are consistent with observations of
L1544. If the dynamical time scale of the core is larger than that of the
Larson-Penston solution owing to magnetic fields, rotation, or turbulence, the
column densities of CO and CCS are smaller, and their holes are larger than in
the Larson-Penston core with the same central gas density. On the other hand,
N2H+ and NH3 are more abundant in the more slowly collapsing core. Therefore,
molecular distributions can probe the collapse time scale of prestellar cores.
Deuterium fractionation has also been studied via numerical calculations. The
deuterium fraction in molecules increases as a core evolves and molecular
depletion onto grains proceeds. When the central density of the core is n_H=3
10^6 cm^{-3}, the ratio DCO+/HCO+ at the center is in the range 0.06-0.27,
depending on the collapse time scale and adsorption energy; this range is in
reasonable agreement with the observed value in L1544.
