Anyone can calculate band gap in 2D or bulk material but I have observed some paper where in cluster they did not use band gap. Is it possible to calculate band gap in cluster using software?
As clusters are finite systems and lack periodicity, the 'HOMO-LUMO gap' is more appropriate. You can calculate the HOMO-LUMO gap using QE or VASP by performing a single-point energy calculation and analyzing the orbital energies.