  Atomistically detailed computational studies of nanocrystals, such as those
derived from the promising lead-halide perovskites, are challenging due to the
large number of atoms and lack of symmetries to exploit. Here, focusing on
methylammonium lead iodide nanocrystals, we combine a real-space tight binding
model with the GW approximation to the self-energy and obtain exciton
wavefunctions and absorption spectra via solutions of the associated
Bethe-Salpeter equation. We find that the size dependence of carrier
confinement, dielectric contrast, electron-hole exchange, and exciton binding
energies has a strong impact on the lowest excitation energy, which can be
tuned by almost 1 eV over the diameter range of 2-6 nm. Our calculated
excitation energies are about 0.2 eV higher than experimentally measured
photoluminescence, and they display the same qualitative size dependence.
Focusing on the fine structure of the band-edge excitons, we find that the
lowest-lying exciton is spectroscopically dark and about 20-30 meV lower in
energy than the higher-lying triplet of bright states, whose degeneracy is
slightly broken by crystal field effects.
