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The origin of life on Earth would benefit from a prebiotic atmosphere thatproduced nitriles, like HCN, which enable ribonucleotide synthesis. However,geochemical evidence suggests that Hadean air was relatively oxidizing withnegligible photochemical production of prebiotic molecules. These paradoxes areresolved by iron-rich asteroid impacts that transiently reduced the entireatmosphere, allowing nitriles to form in subsequent photochemistry. Here, weinvestigate impact-generated reducing atmospheres using new time-dependent,coupled atmospheric chemistry and climate models, which account for gas-phasereactions and surface-catalysis. The resulting H$_2$-, CH$_4$- and NH$_3$-richatmospheres persist for millions of years, until hydrogen escapes to space. HCNand HCCCN production and rainout to the surface can reach $10^9$ moleculescm$^{-2}$ s$^{-1}$ in hazy atmospheres with a mole ratio of $\mathrm{CH_4} /\mathrm{CO_2} > 0.1$. Smaller $\mathrm{CH_4} / \mathrm{CO_2}$ ratios produceHCN rainout rates $< 10^5$ molecules cm$^{-2}$ s$^{-1}$, and negligible HCCCN.The minimum impactor mass that creates atmospheric $\mathrm{CH_4} /\mathrm{CO_2} > 0.1$ is $4 \times 10^{20}$ to $5 \times 10^{21}$ kg (570 to1330 km diameter), depending on how efficiently iron reacts with a steamatmosphere, the extent of atmospheric equilibration with an impact-induced meltpond, and the surface area of nickel that catalyzes CH$_4$ production.Alternatively, if steam permeates and deeply oxidizes crust, impactors $\sim10^{20}$ kg could be effective. Atmospheres with copious nitriles have $> 360$K surface temperatures, perhaps posing a challenge for RNA longevity, althoughcloud albedo can produce cooler climates. Regardless, post-impact cyanide canbe stockpiled and used in prebiotic schemes after hydrogen has escaped tospace.

Origin of Life Molecules in the Atmosphere After Big Impacts on the Early Earth