UV-driven chemistry in simulations of the interstellar medium. I.
  Post-processed chemistry with the Meudon PDR code
  Our main purpose is to estimate the effect of assuming uniform density on the
line-of-sight in PDR chemistry models, compared to a more realistic
distribution for which total gas densities may well vary by several orders of
magnitude. A secondary goal of this paper is to estimate the amount of
molecular hydrogen which is not properly traced by the CO (J = 1 -> 0) line,
the so-called "dark molecular gas". We use results from a magnetohydrodynamical
(MHD) simulation as a model for the density structures found in a turbulent
diffuse ISM with no star-formation activity. The Meudon PDR code is then
applied to a number of lines of sight through this model, to derive their
chemical structures. It is found that, compared to the uniform density
assumption, maximal chemical abundances for H2, CO, CH and CN are increased by
a factor 2 to 4 when taking into account density fluctuations on the line of
sight. The correlations between column densities of CO, CH and CN with respect
to those of H2 are also found to be in better overall agreement with
observations. For instance, at N(H2) > 2.10^{20} cm-2, while observations
suggest that d[log N(CO)]=d[log N(H2)] = 3.07 +/- 0.73, we find d[log
N(CO)]=d[log N(H2)] =14 when assuming uniform density, and d[log N(CO)]=d[log
N(H2)] = 5.2 when including density fluctuations.
