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Hybrid functionals mixing the exact exchange with (semi)local functionals to reinstall the missing derivative discontinuity have been successfully employed to predict band gaps $({E}_{\mathrm{g}})$ in bulk semiconductors. Here we show that traditional hybrid functionals with fixed fractions of exact exchange do not perform significantly better than the most popular semilocal PBE-GGA functional for ${E}_{\mathrm{g}}$ of semiconductor nanostructures, since their band-gap corrections are essentially size independent. This is because they cannot respond properly to the variation in screening when size changes. They merely predict constant band-gap corrections to the PBE gaps in silicon nanowires (Si NWs) when wire diameter reduces, instead of the dramatic increase predicted by many-body $GW$ calculations. Moreover, these hybrid functionals generate almost identical wave functions compared with PBE for both bulk Si and Si NWs, whose overlaps with corresponding quasiparticle wave functions become much smaller than 1 for narrow NWs.

Hybrid functionals with fixed mixing parameter perform no better than PBE for fundamental band gaps of nanoscale materials