As you know, LDA or GGA often underestimate the width of band gap, and this is a well-known issue[1]. You can crosscheck the width of band gap with hybrid functional calculations.

[1] Perdew, John P., et al. "Accurate density functional with correct formal properties: A step beyond the generalized gradient approximation." Physical review letters 82.12 (1999): 2544.

Dear Dr. Zhao,

Thanks for sharing your experience here with me. But it seems that you gave the easiest explanation. I recently found in literature that CuAl2O4 nanoparticles has a band gap of about 3.7 eV ( A Green Protocol for Synthesis of MAl2O4, [M = Cu and Co] Spinels Under Microwave Irradiation Method ). The authors confirm that " The optical band gap increases, while size of the nanoparticles decreases, because band gap energy exhibits an increasing trend as the crystal size decreases, due to the quantum confinement". It seems that the problem is not the GGA-PBE because this type of function deal with perfect crystal. It obvious that many authors do not consider the crystal defects in Lab. I think that these defect shift the UV spectra toward visible region. Thanks you once again

Dear Obeid,

I think you have to be more careful in your conclusion, I agree with Dr Zhao, it is well known that LDA & GGA do not accurate depict the valence band position because of the loose treatment of correlation.

It may be a mixture between the error in the methodology and the error in the experimental measurements. Also consider that the gap you calculate is for a solid, an infinite repetition of cells. While the nanoparticles could behave more like a molecule, so you will have quantum sized effects.

1) Nanoparticles are not bulk materials

2) Experiments can induce different modification of the band-gap

3) You ignored all the magnetic properties, which could be of influence.

Thank you Federico Brivio and Julio Cesar Gonzalez-Torres for your kind response. Spin polarized was also taken into consideration during the optimization of the CuAl2O4 spinel structure, but the band gap still overestimated. Spinel structure is further complicated. I believe that cations distributions within tetrahedral and octahedral sites may not take into consideration in experiment along with cation/anion vacancies or other defects which may effect the band gap measurement using UV-Vis spectrometer.

you should check the effect of Spin-orbit coupling on the band gap of CuAl2O4 .

javaria