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.
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