The origin of life on Earth would benefit from a prebiotic atmosphere that produced nitriles, like HCN, which enable ribonucleotide synthesis. However, geochemical evidence suggests that Hadean air was relatively oxidizing with negligible photochemical production of prebiotic molecules. These paradoxes are resolved by iron-rich asteroid impacts that transiently reduced the entire atmosphere, allowing nitriles to form in subsequent photochemistry. Here, we investigate impact-generated reducing atmospheres using new time-dependent, coupled atmospheric chemistry and climate models, which account for gas-phase reactions and surface-catalysis. The resulting H$_2$-, CH$_4$- and NH$_3$-rich atmospheres persist for millions of years, until hydrogen escapes to space. HCN and HCCCN production and rainout to the surface can reach $10^9$ molecules cm$^{-2}$ 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 produce HCN 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 to 1330 km diameter), depending on how efficiently iron reacts with a steam atmosphere, the extent of atmospheric equilibration with an impact-induced melt pond, and the surface area of nickel that catalyzes CH$_4$ production. Alternatively, if steam permeates and deeply oxidizes crust, impactors $\sim 10^{20}$ kg could be effective. Atmospheres with copious nitriles have $> 360$ K surface temperatures, perhaps posing a challenge for RNA longevity, although cloud albedo can produce cooler climates. Regardless, post-impact cyanide can be stockpiled and used in prebiotic schemes after hydrogen has escaped to space.
Comment: Accepted by Planetary Science Journal on 7/4/23