For semiconductor nanocrystals (quantum dots), luminescent mechanisms are originated from both of the quantum confinement size effect and the radiative centers associated to surface states /defects. If the quantum confinement effect is the dominant mechanism for Photoluminescent (PL) then the carriers are confined in the nanocrystals and the wave function of an electron and a hole can partially overlap even in an indirect bandgap semiconductor such as silicon, giving rise to quasi-direct transitions and thus increasing the probability of a radiative recombination of the pair of carriers. In fact, the size related changes in the band gap energy of semiconductor nanocrystals cause to observing PL emission peak shift with changing the excitation wavelength about the bandgap energy. In this case, excitation energy can help to determine the bandgap energy value of the semiconductor nanocrystals approximately.
Yes you can do that. By measuring the PL spectra and absorbance spectra you can predict the triplet and singlet level of any ligand which will give you the the band gap of material.
Yes. It is possible. Band gap energy has been calculated for lead nanopowder (metal) - The details are in the paper - "Lead Nanopowder as Advanced Semi-Conductor, An Insight " Research and Application of Material 07/2013; 1(4):36. DOI:10.12966/ram.07.02.2013
Yess Eg values can be calculated using the formula Eg= 1240/λ where (λ in nanometer scale). in this case just provide the absorption data obtained from UV-Vis no need to include nm.