I want to figure out if I can find the energy levels of the materials from a specific source for research purpose. Or should I extract these levels from various articles? The same question is also for band gaps.
Both answers are absolutely right. There several databases for calculated material properties with DFT. For the calculation of HOMO and LUMO for the respective material use DFT software as it is supported by many Quantum chemistry and solid state physics software packages, often along with other methods.