  The gravitational collapse of a spherical cloud core is investigated by
numerical calculations. The initial conditions of the core lie close to the
critical Bonnor-Ebert sphere with a central density of \sim 10^4 cm^{-3} in one
model (alpha=1.1), while gravity overwhelms pressure in the other (alpha=4.0),
where alpha is the internal gravity-to-pressure ratio. The alpha=1.1 model
shows reasonable agreement with the observed velocity field in prestellar
cores. Molecular distributions in cores are calculated by solving a chemical
reaction network that includes both gas-phase and grain-surface reactions. When
the central density of the core reaches 10^5 cm^{-3}, carbon-bearing species
are significantly depleted in the central region of the alpha=1.1 model, while
the depletion is only marginal in the other model. The two different approaches
encompass the observed variations of molecular distributions in different
prestellar cores, suggesting that molecular distributions can be probes of
contraction or accumulation time scales of cores. The central enhancement of
the NH3/N2H+ ratio, which is observed in some prestellar cores, can be
reproduced under certain conditions by adopting recently measured branching
fractions for N2H+ recombination. Various molecular species, such as CH3OH and
CO2, are produced by grain-surface reactions. The ice composition depends
sensitively on the assumed temperature. Multi-deuterated species are included
in our most recent gas-grain chemical network. The deuterated isotopomers of
H3+ are useful as probes of the central regions of evolved cores, in which
gas-phase species with heavy elements are strongly depleted. At 10 K, our model
can reproduce the observed abundance ratio of ND3/NH3, but underestimates the
isotopic ratios of deuterated to normal methanol.
