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Extragalactic observations allow the study of molecular chemistry and excitation under physical conditions which may differ greatly from those found in the Milky Way. The compact, obscured nuclei (CON) of luminous infrared galaxies (LIRG) combine large molecular columns with intense infrared (IR), ultra-violet (UV), and X- radiation and represent ideal laboratories for the study of the chemistry of the interstellar medium (ISM) under extreme conditions. Our aim was to obtain for the first time a multi-band spectral scan of a LIRG, and to derive molecular abundances and excitation to be compared to other Galactic and extragalactic environments. We obtained an ALMA Cycle 0 spectral scan of the dusty LIRG NGC 4418, spanning a total of 70.7GHz in bands 3, 6, and 7. We use a combined local thermal equilibrium (LTE) and non-LTE (NLTE) fit of the spectrum in order to identify the molecular species and to derive column densities and excitation temperatures. We derive molecular abundances and compare them with other Galactic and extragalactic sources by means of a principal component analysis. We detect 317 emission lines from a total of 45 molecular species, including 15 isotopic substitutions and 6 vibrationally excited variants. Our LTE/NLTE fit find kinetic temperatures from 20 to 350K, and densities between 10⁵ and 10⁷cm^–3. The spectrum is dominated by vibrationally excited HC₃N, HCN, and HNC, with vibrational temperatures from 300 to 450K. We find that the chemistry of NCG 4418 is characterized by high abundances of HC₃N, SiO, H₂S, and c-HCCCH but a low CH₃OH abundance. A principal component analysis shows that NGC 4418 and Arp 220 share very similar molecular abundances and excitation, which clearly set them apart from other Galactic and extragalactic environments. Our spectral scan confirms that the chemical complexity in the nucleus of NGC 4418 is one of the highest ever observed outside our Galaxy. The similar molecular abundances observed toward NCG 4418 and Arp 220 are consistent with a hot gas-phase chemistry, with the relative abundances of SiO and CH₃OH being regulated by shocks and X-ray driven dissociation. The bright emission from vibrationally excited species confirms the presence of a compact IR source, with an effective diameter smaller than 5pc and brightness temperatures higher than 350K. The molecular abundances and the vibrationally excited spectrum are consistent with a young AGN/starburst system. We suggest that NGC 4418 may be a template for a new kind of chemistry and excitation, typical of CON. Because of the narrow line widths and bright molecular emission, NGC 4418 is the ideal target for further studies of the chemistry in CONs.