tokens: reduced mass of the collision system. The collisional coefficients for N 2 H + are taken from Lique et al. (2015) , who computed them for the N 2 H + /p-H 2 system. The rates for the DCO + /p-H 2 system were computed by Pagani et al. (2012) , who take into account the hyperfine structure given by the deuterium nucleus. Finally, the collisions of HCO + with p-H 2 were published by Flower (1999) , from which we scaled the coefficients for HC 18 O + . In all cases, the o-H 2 is neglected,which is a reasonable assumption given that the ortho-to-para ratio (OPR) in L1544 is found to be as low as OPR = 10 −3 ( Kong et al. 2015 ). Fig. 4 Profiles of dust temperature (green), gas temperature (red), H 2 volume density (black, in logarithmic scale), and velocity (blue, in units of 0.1 km s −1 ) for the L1544 model developed in Keto et al. (2015) . The velocity in the model is negative (it represents contraction motions), but it is shown here as positive for improved readability. We tested all the 15 models described in Sect. 3.1 . The abundance profiles produced by the chemical model often systematically overestimate or underestimate the observed fluxes, and need to be multiplied by a numerical factor to find a good agreement with the observations. However, MOLLIE requires too much computational time to allow a full sampling of the parameter space. For each molecule, we therefore proceeded as follows: first, we test all the original models, varying the evolutionarystage and the thickness of the surrounding cloud, and we select the one that best reproduces the trend of the different transitions (e.g. the ratio between the peak temperatures of the brightest component of each line). We then multiply the whole profile by a numerical factor, testing approximately five values until the observed fluxes are matched. This is considered the best fit to the observations. We want to highlight that our goal is to obtain a simultaneous fit for all molecules that is roughly consistent with the observations, and a full parameter-space search for the best possible fit within the model uncertainties is beyond the scope of the present paper. In the following text, we focus on the abundance profiles that provide the best-fit solution for each molecule. As an example, wepresent in Sect. 3.2.2 the resulting spectra from several of the 15 abundance profiles for N 2 D + . 3.2.1 Best-fit solution for the observed molecules at the dust peak The best-fit solutions for each molecule are shown in red in Figs. 1 and 2 overlaying the observations. We also include here the analysis of a single-pointing observation of HCO + (1–0) performed at the dust peak (see Sect. 2 for details). Despite the fact that a map for this transition is not available, it is important to check the behaviour of the chemical model for HCO + , the main isotopologue of its family. The observed spectrum of HCO + , together with the best fit from MOLLIE, is shown in the bottom-right panel of Fig. 2 .
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