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One of the long-term goals of exoplanet science is the atmosphericcharacterization of dozens of small exoplanets in order to understand theirdiversity and search for habitable worlds and potential biosignatures.Achieving this goal requires a space mission of sufficient scale. We seek toquantify the exoplanet detection performance of a space-based mid-infrarednulling interferometer that measures the thermal emission of exoplanets. Forthis, we have developed an instrument simulator that considers all majorastrophysical noise sources and coupled it with Monte Carlo simulations of asynthetic exoplanet population around main-sequence stars within 20 pc. Thisallows us to quantify the number (and types) of exoplanets that our missionconcept could detect over a certain time period. Two different scenarios todistribute the observing time among the stellar targets are discussed anddifferent apertures sizes and wavelength ranges are considered. Within a2.5-year initial search phase, an interferometer consisting of four 2 mapertures with a total instrument throughput of 5% covering a wavelength rangebetween 4 and 18.5 $\mu$m could detect up to ~550 exoplanets with radii between0.5 and 6 R$_\oplus$ with an integrated SNR$\ge$7. At least ~160 of thedetected exoplanets have radii $\le$1.5 R$_\oplus$. Depending on the observingscenario, ~25-45 rocky exoplanets (objects with radii between 0.5 and 1.5$_{\oplus}$) orbiting within the empirical habitable zone (eHZ) of their hoststars are among the detections. With an aperture size of 3.5 m, the totalnumber of detections can increase to up to ~770, including ~60-80 rocky, eHZplanets. With 1 m aperture size, the maximum detection yield is ~315exoplanets, including $\le$20 rocky, eHZ planets. In terms of predicteddetection yield, such a mission can compete with large single-aperturereflected light missions. (abridged)

Large Interferometer For Exoplanets (LIFE): I. Improved exoplanet detection yield estimates for a large mid-infrared space-interferometer mission