  The chemistry of H2O, CO and other small molecular species in an isolated
pre-stellar core, L1544, has been assessed in the context of a comprehensive
gas-grain chemical model, coupled to an empirically constrained
physical/dynamical model. Our main findings are (i) that the chemical network
remains in near equilibrium as the core evolves towards star formation and the
molecular abundances change in response to the evolving physical conditions.
The gas-phase abundances at any time can be calculated accurately with
equilibrium chemistry, and the concept of chemical clocks is meaningless in
molecular clouds with similar conditions and dynamical time scales, and (ii) A
comparison of the results of complex and simple chemical networks indicates
that the abundances of the dominant oxygen and carbon species, H2O, CO, C, and
C+ are reasonably approximated by simple networks. In chemical equilibrium, the
time-dependent differential terms vanish and a simple network reduces to a few
algebraic equations. This allows rapid calculation of the abundances most
responsible for spectral line radiative cooling in molecular clouds with long
dynamical time scales. The dust ice mantles are highly structured and the ice
layers retain a memory of the gas-phase abundances at the time of their
deposition. A complex (gas-phase and gas-grain) chemical structure therefore
exists, with cosmic-ray induced processes dominating in the inner regions. The
inferred H2O abundance profiles for L1544 require that the outer parts of the
core and also any medium exterior to the core are essentially transparent to
the interstellar radiation field.
