I still have a doubt regarding the theoretical values? Is energy difference between HOMO and LUMO is the optical band energy on compared with Tauc plot?
The bandgap not only corresponds to the HOMO-LUMO difference but to more orbitals. In bandgap there are many additional orbitals to consider which, together with HOMO and LUMO, are responsible for all transitions of the material.
To get more insights, you may find theories related to optical bandgap and photonic bandgap. I hope this answer will help you. Best luck with your research !!