  The reliable prediction of optical and fundamental gaps of finite size
systems using density functional theory requires to account for the potential
self-interaction error, which is notorious for degrading the description of
charge transfer transitions. One solution is provided by parameterized
long-range corrected functionals such as LC-BLYP, which can be tuned such as to
describe certain properties of the particular system at hand. Here, bare and
3-mercaptoprotionic acid covered \ce{Cd33Se33} quantum dots are investigated
using the optimally tuned LC-BLYP functional. The range separation parameter,
which determines the switching on of the exact exchange contribution is found
to be 0.12 bohr$^{-1}$ and 0.09 bohr$^{-1}$ for the bare and covered quantum
dot, respectively. It is shown that density functional optimization indeed
yields optical and fundamental gaps and thus exciton binding energies,
considerably different compared with standard functionals such as the popular
PBE and B3LYP ones. This holds true, despite the fact that the leading
transitions are localized on the quantum dot and do not show pronounced
long-range charge transfer character.
