Influence of size effect and electron correlation to the energy band gap of CuFeO$_{2}$ and AgFeO$_{2}$

We have calculated the electronic structure of delafossite type oxides CuFeO$_{2}$ and AgFeO$_{2}$ using the Full Potential Linearlized Augmented Plane Wave (FP-LAPW) method within Perdew-Burke-Ernzerhof Generalized-Gradient Approximation (PBE-GGA). A metallic state instead of true insulating state is obtained for CuFeO$_{2}$ and AgFeO$_{2}$. The insulating state is reproduced when electron correlations have been taken into account. An effective Hubbard parameter for Fe, U$_{eff}$=7.86eV, has been derived based on an ab initio constraint calculation. This value is an over estimation for the optical band gaps of CuFeO$_{2}$ and most probably for AgFeO$_{2}$ as well. One reasonable U$_{eff}$ has been derived by comparing between computational and experimental X-Ray emission spectra. The energy band gap of CuFeO$_{2}$ and AgFeO$_{2}$ within the PBE-GGA+U is found as charge transfer gap. Theoretical optical band gaps $\Delta _{0}$=1.30eV, $\Delta _{1}$=2.06eV, and $\Delta _{2}$=3.20eV for CuFeO$_{2}$ are quite compatible with experimental data. For AgFeO$_{2}$ an optical band gap $\Delta _{0}$=1.90eV has been predicted. The size effect is considered as the origin of the increase in optical and energy band gaps of AgFeO$_{2}$ in comparison with CuFeO$_{2}$.