Calculation of the gap in Ce$_{1/3}$NbO$_{3}$

With experimental measurements, \textit{Ce}$_{1/3}$\textit{ NbO}$_{3}$ was found to have a small gap of \textit{0.25-0.78eV}. In order to find whether this gap is due to electronic origin \textit{ab-initio DFT} (\textit{WIEN2k}) calculations were done. To find the correct gap, the calculations were done using a modified Becke-Johnson (\textit{mBJ}) potential. A 'conducting' \textit{Nb-O} gap with a \textit{Ce:4f} peak in the middle was found. In the convergence process, due to the nature of the \textit{mBJ} potential, this \textit{Ce:4f} interfered with the Fermi energy $E_{F}$. To avoid this problem a Hubbard $U_{H}$ was added to the \textit{Ce} atom, then it was possible to extrapolate back and obtain the correct 'conducting' \textit{Nb-O} gap of \textit{2eV} with the \textit{Ce:4f} peak at \textit{1.3eV} from the lower end of the gap. With this it can be confirmed that the conduction is not of electronic nature.