Optical transitions and nature of Stokes shift in spherical CdS quantum   dots
  We study the structure of the energy spectra along with the character of the states participating in optical transitions in colloidal CdS quantum dots (QDs) using the {\sl ab initio} accuracy charge patching method combined with the %pseudopotential based folded spectrum calculations of electronic structure of thousand-atom nanostructures. In particular, attention is paid to the nature of the large resonant Stokes shift observed in CdS quantum dots. We find that the top of the valence band state is bright, in contrast with the results of numerous {\bf k$\cdot$p} calculations, and determine the limits of applicability of the {\bf k$\cdot$p} approach. The calculated electron-hole exchange splitting suggests the spin-forbidden valence state may explain the nature of the ``dark exciton'' in CdS quantum dots. 
D. O. Demchenko and Lin-Wang Wang