We obtained an ALMA Cycle 0 spectral scan of the dusty LIRG NGC 4418, spanning a total of 70.7 GHz 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 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 six vibrationally excited variants. Our LTE/NLTE fit find kinetic temperatures from 20 to 350 K, and densities between 10$^5$ and 10$^7$ cm$^{-3}$. The spectrum is dominated by vibrationally excited HC$_3$N, HCN, and HNC, with vibrational temperatures from 300 to 450 K. We find high abundances of HC$_3$N, SiO, H$_2$S, and c-HCCCH and a low CH$_3$OH 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. The similar molecular abundances observed towards NCG 4418 and Arp 220 are consistent with a hot gas-phase chemistry, with the relative abundances of SiO and CH$_3$OH 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 $<$5 pc and brightness temperatures $>$350 K. 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 compact obscured nuclei (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.
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