For good photocatalyst band gap should be also in range for light absorption. I want to know relation between bulk and nanostructure bandgap for choosing photocatalyst.
Nanostructures have the spatial dimension of visible light wavelengths (or smaller). Size effects are the dominant component in the formation of their electronic structure over other properties and that's actually what actually makes the nanostructures interesting in the first place.
Quantum dots have received additional focus after the recent nobel prizes and are a perfect demonstration of this: bulk CdSe has a band gap of 1.74eV, but for each size of the dot you have a different band gap.
You can calculate the bandgap using Tauc method from the solid UV analysis of the material. Then you find the particle size or crystallite size using TEM or XRD respectively. Then you can analyse the Andre relation where the corelation between the bandgap and the particle size has been discussed clearly.