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 parametrized 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 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 well established fact that the leading transitions are localized on the quantum dot and do not show pronounced long-range charge transfer character.