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Our main purpose is to estimate the effect of assuming uniform density on theline-of-sight in PDR chemistry models, compared to a more realisticdistribution for which total gas densities may well vary by several orders ofmagnitude. A secondary goal of this paper is to estimate the amount ofmolecular 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 turbulentdiffuse ISM with no star-formation activity. The Meudon PDR code is thenapplied to a number of lines of sight through this model, to derive theirchemical structures. It is found that, compared to the uniform densityassumption, maximal chemical abundances for H2, CO, CH and CN are increased bya factor 2 to 4 when taking into account density fluctuations on the line ofsight. The correlations between column densities of CO, CH and CN with respectto those of H2 are also found to be in better overall agreement withobservations. For instance, at N(H2) > 2.10^{20} cm-2, while observationssuggest that d[log N(CO)]=d[log N(H2)] = 3.07 +/- 0.73, we find d[logN(CO)]=d[log N(H2)] =14 when assuming uniform density, and d[log N(CO)]=d[logN(H2)] = 5.2 when including density fluctuations.

UV-driven chemistry in simulations of the interstellar medium. I. Post-processed chemistry with the Meudon PDR code