You might fiind the formula and information for calculate the bandgap of nanoparticles :
The Brus Equation
L. E. Brus, “Electron-Electron and Electron-Hole Interactions in Small Semiconductor Crystallites: The Size Dependence of the Lowest Excited Electronic State,” Journal of Chemical Physics, Vol. 80, No. 9, 1984, p. 4403. doi:10.1063/1.447218
Brus gave the first theoretical calculation for semiconductor nanoparticles (using CdS and CdSe as examples) based on “effective mass approximation” (EMA).
Kayanuma accounted for the electron-hole spatial correlation effect and modified the Brus Equation.
Y. Kayanuma, “Quantum-Size Effects of Interacting Electrons and Holes in Semiconductor Microcrystals with Spherical Shape,” Physical Review B, Vol. 38, No. 14, 1988, pp. 9797-9805. doi:10.1103/PhysRevB.38.9797