  Contemporary galactic star formation occurs predominantly within
gravitationally unstable, cold, dense molecular gas within supersonic,
turbulent, magnetized giant molecular clouds (GMCs). Significantly, because the
chemical evolution timescale and the turbulent eddy-turnover timescale are
comparable at typical GMC conditions, molecules evolve via inherently
non-equilibrium chemistry which is strongly coupled to the dynamical evolution
of the cloud.
  Current numerical simulation techniques, which include at most three decades
in length scale, can just begin to bridge the divide between the global
dynamical time of supersonic turbulent GMCs, and the thermal and chemical
evolution within the thin post-shock cooling layers of their background
turbulence. We address this GMC astrochemical scales problem using a solution
methodology, which permits both complex three-dimensional turbulent dynamics as
well as accurate treatment of non-equilibrium post-shock thermodynamics and
chemistry.
  We present the current methodology in the context of the larger scope of
physical processes important in understanding the chemical evolution of GMCs,
including gas-phase chemistry, dust grains and surface chemistry, and turbulent
heating. We present results of a new Lagrangian verification test for
supersonic turbulence. We characterize the evolution of these species according
to the dimensionless local post-shock Damk\"{o}hler number, which quantifies
the ratio of the dynamical time in the post-shock cooling flow to the chemical
reaction time of a given species.
  Lastly, we discuss implications of this work to the selection of GMC
molecular tracers, and the zeroing of chemical clocks of GMC cores.
