Context. Future and ongoing infrared and radio observatories such as JWST, METIS, and ALMA will increase the amount of rest-frame IR spectroscopic data for galaxies by several orders of magnitude. While studies of the chemical composition of the interstellar medium (ISM) based on optical observations have been widely spread over decades for star-forming galaxies (SFGs) and, more recently, for active galactic nuclei (AGN), similar studies need to be performed using IR data. In the case of AGN, this regime can be especially useful given that it is less affected by temperature and dust extinction, traces higher ionic species, and can also provide robust estimations of the chemical abundance ratio N/O. Aims. We present a new tool based on a Bayesian-like methodology (HII-CHI-MISTRY-IR) to estimate chemical abundances from IR emission lines in AGN. We use a sample of 58 AGN with IR spectroscopic data retrieved from the literature, composed by 43 Seyferts, eight ultraluminous infrared galaxies (ULIRGs), four luminous infrared galaxies (LIRGs), and three low-ionization nuclear emission line regions (LINERs), to probe the validity of our method. The estimations of the chemical abundances based on IR lines in our sample are later compared with the corresponding abundances derived from the optical emission lines in the same objects. Methods. HII-CHI-MISTRY-IR takes advantage of photoionization models, characterized by the chemical abundance ratios O/H and N/O, and the ionization parameter U, to compare their predicted emission-line fluxes with a set of observed values. Instead of matching single emission lines, the code uses some specific emission-line ratios that are sensitive to the above free parameters. Results. We report mainly solar and also subsolar abundances for O/H in the nuclear region for our sample of AGN, whereas N/O clusters are around solar values. We find a discrepancy between the chemical abundances derived from IR and optical emission lines, the latter being higher than the former. This discrepancy, also reported by previous studies of the composition of the ISM in AGN from IR observations, is independent of the gas density or the incident radiation field to the gas, and it is likely associated with dust obscuration and/or temperature stratification within the gas nebula.
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