tokens: model is able to replicate the spread in the CRIR. There are two main controlling factors for the CRIR in the clouds: the number of embedded sources and the cloud environment. Embedded sources create a natural dispersion in ζ for different molecular cloud masses and star formation efficiencies. Without internal sources, there is no spread in our modeled CRIR as a function of column density. In order to represent the observations, the external CRIR must be increased instead for different regions. Local sources of CRs, such as nearby OB associations or supernova, contribute significantly to the CR flux at the cloud boundary. As the external CR flux is increased, the impact of attenuation also increases due to the rapid reduction in low-energy CRs. Figure 11 shows that the impact of attenuation is different between the HNI and LNI models. For the LNI model, ζ changes by less than an order of magnitude across four orders of magnitude in A V . Conversely, the HNI model CRIR decreases by two orders of magnitude due to an overall reduction in MeV-scale CRs. The HNI model overpredicts the CRIRs measured in diffuse gas to CRIRs measured near high-mass protostars, excluding the galactic center sightlines. However, the spectrum is the maximal CR spectrum from Voyager -1 observations (Stone et al. 2013 ; Ivlev et al. 2015 ). The LNI and LNA models underpredict the observed CRIR for all but a few sightlines. Thus, Figure 11 demonstrates that it is essential to consider the cloud environment and properly treat the CR physics and cloud density distributions. Models without attenuation only represent the CRIR within narrow ranges of A V and not in the cloud interiors. Figure 11 also underscores that the low = energy CR spectrum, which, if often adopted in astrochemical modeling, is a poor fit to the majority of the observations. 4.3. Challenges for Deriving the CRIR from Chemical Diagnostics There have been numerous attempts to find chemical diagnostics that are strong tracers of the CRIR (Caselli et al. 1998 ; Indriolo et al. 2007 , 2015 ; Neufeld et al. 2010 ; Indriolo McCall 2012 ; Neufeld Wolfire 2017 ; Albertsson et al. 2018 ). Some of these, such as [DCO + ]/[HCO + ], cannot be modeled with the current 3 d-pdr version due to the lack of deuterium and isotopic chemistry. Most probes of the CRIR are based on the local abundance, which is difficult to directly ascertain from observations. The use of column density ratios typically assumes the line emission observed between species is cospatial. Figures 8 and 9 examine effects of CR physics on the , and column density ratio diagnostics. However, we find that none of these ratios are monotonically sensitive to the average CRIR, shown for the LDI model in Figure 5 . The [CO/C + ] column density ratio is anti-correlated with the density-averaged CRIR because the amount of CO declines while the amount of C + increases in large, massive clusters. Local abundance ratios are used for fitting observations with
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