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Atomistically detailed computational studies of nanocrystals, such as thosederived from the promising lead-halide perovskites, are challenging due to thelarge number of atoms and lack of symmetries to exploit. Here, focusing onmethylammonium lead iodide nanocrystals, we combine a real-space tight bindingmodel with the GW approximation to the self-energy and obtain excitonwavefunctions and absorption spectra via solutions of the associatedBethe-Salpeter equation. We find that the size dependence of carrierconfinement, dielectric contrast, electron-hole exchange, and exciton bindingenergies has a strong impact on the lowest excitation energy, which can betuned by almost 1 eV over the diameter range of 2-6 nm. Our calculatedexcitation energies are about 0.2 eV higher than experimentally measuredphotoluminescence, and they display the same qualitative size dependence.Focusing on the fine structure of the band-edge excitons, we find that thelowest-lying exciton is spectroscopically dark and about 20-30 meV lower inenergy than the higher-lying triplet of bright states, whose degeneracy isslightly broken by crystal field effects.

Excitons and their Fine Structure in Lead Halide Perovskite Nanocrystals from Atomistic GW/BSE Calculations