ALCHEMI: an ALMA Comprehensive High-resolution Extragalactic Molecular Inventory. Survey presentation and first results from the ACA array

We used the Atacama Large Millimeter/submillimeter Array (ALMA), covering a nearly contiguous 289 GHz frequency range between 84.2 and 373.2 GHz, to image the continuum and spectral line emission at 1.6\arcsec ($\sim 28$ pc) resolution down to a sensitivity of $30-50$ mK. This article describes the ALMA Comprehensive High-resolution Extragalactic Molecular Inventory (ALCHEMI) Large Program. We focus on the analysis of the spectra extracted from the $15''$ ($\sim255$ pc) resolution ALMA Compact Array data. We model the molecular emission assuming local thermodynamic equilibrium with 78 species detected. Additionally, multiple hydrogen and helium recombination lines are identified. Spectral lines contribute 5 to 36\% of the total emission in frequency bins of 50 GHz. We report the first extragalactic detections of C$_2$H$_5$OH, HOCN, HC$_3$HO, and several rare isotopologues. Isotopic ratios of carbon, oxygen, sulfur, nitrogen and silicon were measure with multiple species. Infrared pumped vibrationaly excited HCN, HNC, and HC$_3$N emission, originating in massive star formation locations, is clearly detected at low resolution, while we do not detect it for HCO$^+$. We suggest high temperature conditions in these regions driving a seemingly "carbon-rich" chemistry which may also explain the observed high abundance of organic species close to those in Galactic hot cores. The $L_{vib}/L_{IR}$ ratio is used as a proxy to estimate a $3\%$ contribution from proto super star cluster to the global infrared emission. Measured isotopic ratios with high dipole moment species agree with those within the central kiloparsec of the Galaxy, while those derived from $\rm^{13}C^{18}O$ are a factor of 5 larger, confirming the existence of multiple ISM components within NGC 253 with different degrees of nucleosynthesis enrichment. ALCHEMI provides a template for early Universe galaxies.