I'm calculating the band gap of an AlN sheet within two functional (B3LYP and B97D). With B3lyp the band gap is relatively higher than that for B97D. Does it make sense? Does anyone know a references for that?
The reason for the difference is the partial correction for the electronic self interaction provided by the Fock exchange that is included in the B3LYP functional. We pointed this out when we first introduced B3LYP into solid state calculations back in 2001 : On the prediction of band gaps from hybrid functional theory, J Muscat, A Wander, N M Harrison, Chem Phys Lett, 342, 397, (2001). The behaviour has been documented in many subsequent publications.
Both functionals cannot well present the band gap. I think if the band gap is so important to you, you must use other exchange correlation functional, such as HSE or PBE0.
As Nicholas reply, , the partial exchange energy of HF in B3LYP leads to better description of HOMO-LUMO gap. Because it prevents the self interaction of electron little bit. You can find composition of B3LYP functional in gaussian homepage or many papers.