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 NH _ { 3 } /N _ { 2 } H ^ { + } ratio , which is observed in some prestellar cores , can be reproduced under certain conditions by adopting recently measured branching fractions for N _ { 2 } H ^ { + } recombination .
Various molecular species , such as CH _ { 3 } OH and CO _ { 2 } , 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 H _ { 3 } ^ { + } 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 ND _ { 3 } /NH _ { 3 } , but underestimates the isotopic ratios of deuterated to normal methanol .