Simulations of ligated semiconductor quantum dots (QDs) and their physical properties, such as morphologies, QDÀligand interactions, electronic structures, and optical transitions, are expected to be very sensitive to computational methodology. We utilize Density Functional Theory (DFT) and systematically study how the choice of density functional, atom-localized basis set, and a solvent affects the physical properties of the Cd 33 Se 33 cluster ligated with a trimethylphosphine oxide ligand. We have found that qualitative performance of all exchange-correlation (XC) functionals is relatively similar in predicting strong QDÀligand binding energy (∼1 eV). Additionally, all functionals predict shorter CdÀSe bond lengths on the QD surface than in its core, revealing the nature and degree of QD surface reconstruction. For proper modeling of geometries and QDÀligand interactions, however, augmentation of even a moderately sized basis set with polarization functions (e.g., LANL2DZ* and 6-31G*) is very important. A polar solvent has very significant implications for the ligand binding energy, decreasing it to 0.2À0.5 eV. However, the solvent model has a minor effect on the optoelectronic properties, resulting in persistent blue shifts up to ∼0.3 eV of the low-energy optical transitions. For obtaining reasonable energy gaps and optical transition energies, hybrid XC functionals augmented by a long-range HartreeÀFock orbital exchange have to be applied.