  We quantify if the chemical abundance gradients given by a dynamical model of
core collapse including time-dependent changes in density and temperature
differ greatly from abundances derived from static models, where the density
and temperature structures of the core are kept fixed as the chemistry evolves.
For this study we developed a new one-dimensional spherically symmetric
hydrodynamics code that couples the hydrodynamics equations with a
comprehensive time-dependent gas-grain chemical model, including deuterium and
spin-state chemistry, and radiative transfer calculations to derive
self-consistent time-dependent chemical abundance gradients. We applied the
code to model the collapse of a starless core up to the point when the infall
flow becomes supersonic.
  The abundances predicted by the dynamical and static models are almost
identical during the quiescent phase of core evolution, but the results start
to diverge after the onset of core collapse, where the static model
underestimates abundances at high medium density (inner core) and
underestimates them at low density (outer core), and this is clearly reflected
in simulated lines. The static model generally overestimates deuteration, which
is increasingly evident the more D atoms are substituted in the molecule. We
also find that using a limited chemical network, or a limited set of cooling
molecules, may lead to an overestimate of the collapse timescale, and in some
cases may prevent the collapse altogether. In our model, most of the line
cooling near the center of the core is due to HCN, CO, and NO. In conclusion,
the use of a static physical model is not a reliable method of simulating
chemical abundances in starless cores after the onset of gravitational
collapse. The adoption of complex chemistry and a comprehensive set of cooling
molecules is necessary to model the collapse adequately.
