Currently, I am interested to calculate the band gap of divalent metal cations like Pb2+, Sn2+, Ge2+ and some anions like I-, Br-, Cl-. Please tell me, will it be efficient to calculate the band gap energy of these using DFT calculations?
Yes. You have to do single point calculations with proper inputs using DFT. Then you can look into the orbital energies to get the HOMO-LUMO energy gap.
For cation, basis set with polarization function is good. while for anion, basis set with diffuse function need to be used. You can go through ORCA software manual regarding the choice of basis sets.