  The molecular evolution that occurs in collapsing prestellar cores is
investigated. To model the dynamics, we adopt the Larson-Penston (L-P) solution
and analogues with slower rates of collapse. For the chemistry, we utilize the
new standard model (NSM) with the addition of deuterium fractionation and
grain-surface reactions treated via the modified rate approach. The use of
surface reactions distinguishes the present work from our previous model. We
find that these reactions efficiently produce H2O, H2CO, CH3OH, N2, and NH3
ices. In addition, the surface chemistry influences the gas-phase abundances in
a variety of ways. The current reaction network along with the L-P solution
allows us to reproduce satisfactorily most of the molecular column densities
and their radial distributions observed in L1544. The agreement tends to worsen
with models that include strongly delayed collapse rates. Inferred radial
distributions in terms of fractional abundances are somewhat harder to
reproduce. In addition to our standard chemical model, we have also run a model
with the UMIST gas-phase chemical network. The abundances of gas-phase
S-bearing molecules such as CS and CCS are significantly affected by
uncertainties in the gas-phase chemical network. In all of our models, the
column density of N2H+ monotonically increases as the central density of the
core increases during collapse from 3 10^4 cm-3 to 3 10^7 cm-3. Thus, the
abundance of this ion can be a probe of evolutionary stage. Molecular D/H
ratios in assorted cores are best reproduced in the L-P picture with the
conventional rate coefficients for fractionation reactions. If we adopt the
newly measured and calculated rate coefficients, the D/H ratios, especially
N2D+/N2H+, become significantly lower than the observed values.
