  Combining the co-evolving chemistry, hydrodynamics and radiative transfer is
an important step for star formation studies. It allows both a better link to
observations and a self-consistent monitoring of the magnetic dissipation in
the collapsing core. Our aim is to follow a chemo-dynamical evolution of
collapsing dense cores with a reduced gas-grain chemical network. We present
the results of radiative hydrodynamic (RHD) simulations of 1 M$_\odot$ isolated
dense core collapse. The physical setup includes RHD and dynamical evolution of
a chemical network. To perform those simulations, we merged the
multi-dimensional adaptive-mesh-refinement code RAMSES and the thermo-chemistry
Paris-Durham shock code. We simulate the formation of the first hydro-static
core (FHSC) and the co-evolution of 56 species describing mainly H-C-O
chemistry. Accurate benchmarking is performed, testing the reduced chemical
network against a well-establiched complex network. We show that by using a
compact set of reactions, one can match closely the CO abundances with results
of a much more complex network. Our main results are: (a) We find that
gas-grain chemistry post-processing can lead to one order of magnitude lower CO
gas-phase abundances compared to the dynamical chemistry, with strongest effect
during the isothermal phase of collapse. (b) The free-fall time has little
effect on the chemical abundances for our choice of the parameters. (c)
Dynamical chemical evolution is required to describe the CO gas phase abundance
as well as the CO ice formation for the mean grain size larger then 1$\mu{}$m.
(d) Furthermore, dust mean size and size distribution have a strong effect on
chemical abundances and hence on the ionization degree and magnetic
dissipation. We conclude that dust grain growth in the collapse simulations can
be as important as coupling the collapse with chemistry.
