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This study aims to identify exemplary science cases for observing N$_2$O,CH$_3$Cl, and CH$_3$Br in exoplanet atmospheres at abundances consistent withbiogenic production using a space-based mid-infrared nulling interferometricobservatory, such as the LIFE (Large Interferometer For Exoplanets) missionconcept. We use a set of scenarios derived from chemical kinetics models thatsimulate the atmospheric response of varied levels of biogenic production ofN$_2$O, CH$_3$Cl and CH$_3$Br in O$_2$-rich terrestrial planet atmospheres toproduce forward models for our LIFEsim observation simulator software. Inaddition we demonstrate the connection to retrievals for selected cases. We usethe results to derive observation times needed for the detection of thesescenarios and apply them to define science requirements for the mission. Ouranalysis shows that in order to detect relevant abundances with a mission likeLIFE in it's current baseline setup, we require:  (i) only a few days of observation time for certain very near-by "GoldenTarget" scenarios, which also motivate future studies of "spectral-temporal"observations  (ii) $\sim$10 days in certain standard scenarios such as temperate,terrestrial planets around M star hosts at 5 pc,  (iii) $\sim$50 - 100 days in the most challenging but still feasible cases,such as an Earth twin at 5pc. A few cases for very low fluxes around specifichost stars are not detectable.  In summary, abundances of these capstone biosignatures are detectable atplausible biological production fluxes for most cases examined and for asignificant number of potential targets.

Large Interferometer For Exoplanets (LIFE): XII. The Detectability of  Capstone Biosignatures in the Mid-Infrared -- Sniffing Exoplanetary Laughing  Gas and Methylated Halogens