We have shown that the descent of the nanocrystal symmetry from spherical to point group Cs,
which is characterized by just one mirror plane symmetry element, leads step by step to activation
of all five F =2, Fz= 2,1, 0 excitons. Even the ground exciton becomes optically active,
which should be observable in low-temperature photoluminescence measurements. For several
intermediate symmetries the band edge exciton fine structure consists of sets of three linearly
polarized mutually orthogonal dipoles plus a dark exciton, one of which is always the ground state.
We quantify the effect of symmetry descent on the exciton fine structure by introducing a charged
Coulomb impurity in the nanocrystals. The calculations show that the nanocrystal symmetry
breaking by a Coulomb impurity, particularly a positively charged center, shortens the radiative
decay of nanocrystals even at room temperatures in qualitative agreement with the increase in PL
efficiency observed in nanocrystals doped with positive Ag charge centers.