X_CO-factor (left panel) and the X_CI-factor (right panel) for all models (solid blue lines). The dashed black lines illustrate the best-fit expressions (Eqs. (7) and (8) for X_Co and X_CI, respectively). We show in the left panel the observations of Israel (1997); Leroy et al. (2011); Elmegreen et al. (2013); Shi et al. (2015, 2016), including the average MW value (shown as the large blue star (Bolatto et al. 2013)) and the best-fit relations of Genzel et al. (2012) and Madden et al. (2020). We show in the right panel the observations of Heintz & Watson (2020) and their best-fit relation together with that of Ramambason et al. (2024). For all scattered observational data, we plot the reported error bars, which may be smaller than the symbol size. In all cases, the PDFCHEM best-fit expressions match the observations well. In both panels, the case of [C/O] = 0 is shown as the dotted gray line, which further assumes the linear relation of $\mathcal{D}$ with [O/H] (dotted lines in the panels of Fig. 1). The cyan lines show the conversion factors when we account for an observational sensitivity limit (0.1 K for the CO (1−0) and [CI] (1–0) lines). The shaded areas in the PDFCHEM models represent the 1σ standard deviation.