We provide a new method to derive heavy element abundances based on the unique suite of nebular lines in the mid- to far-infrared (IR) range. Using grids of photo-ionisation models that cover a wide range in O/H and N/O abundances, and ionisation parameter, our code HII-Chi-mistry-IR (HCm-IR) provides model-based abundances based on extinction free and temperature insensitive tracers, two significant advantages over optical diagnostics. The code is probed using a sample of 56 galaxies observed with $Spitzer$ and $Herschel$ covering a wide range in metallicity, $7.2 lesssim 12+log(O/H) lesssim 8.9$. The IR model-based metallicities obtained are robust within a scatter of 0.03 dex when the hydrogen recombination lines, which are typically faint transitions in the IR range, are not available. When compared to the optical abundances obtained with the direct method, model-based methods, and strong-line calibrations, HCm-IR estimates show a typical dispersion of ~0.2 dex, in line with previous studies comparing IR and optical abundances, a do not introduce a noticeable systematic above $12+log(O/H) gtrsim 7.6$. This accuracy can be achieved using the lines [SIV]$_{10.5 mu m}$, [SIII]$_{18.7,33.5 mu m}$, [NeIII]$_{15.6 mu m}$ and [NeII]$_{12.8 mu m}$. Additionally, HCm-IR provides an independent N/O measurement when the [OIII]$_{52,88 mu m}$ and [NIII]$_{57 mu m}$ transitions are measured, and therefore the derived abundances in this case do not rely on particular assumptions in the N/O ratio. Large uncertainties (~0.4 dex) may affect the abundance determinations of galaxies at sub- or over-solar metallicities when a solar-like N/O ratio is adopted. Finally, the code has been applied to 8 galaxies located at $1.8 < z < 7.5$ with ground-based detections of far-IR lines redshifted in the submm range, revealing solar-like N/O and O/H abundances in agreement with recent studies.
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