systems. LDA+U method could not treat metallic phase near metal-insulator transition since it has been developed in order to discuss magnetic insulators. [@re:LDA+U2] Fluctuation of charge or/and spin densities plays an important role in low-energy excitations near the metal-insulator transition. To discuss realistic materials of strongly correlated electron systems, another method is needed for the “dynamical” electron correlation.

The dynamical mean field theory (DMFT) has been developed and applied to model systems of strongly correlated electrons, which led us to a unified picture of low- and high-energy excitations in anomalous metallic phase near metal-insulator transition. [@re:Rev-DMFT] DMFT is based on mapping of many electron systems in bulk onto single impurity atom embedded in effective medium, namely the single impurity problem. In this mapping procedure, the on-site dynamical correlation is included and the inter-atomic correlation is neglected. The combination of DMFT with LDA, called LDA+DMFT, has been developed in order to discuss realistic systems. [@re:Ans; @re:Lic] LDA or DFT meet their own new stage with the GW approximation, [@re:GW-Arya] which is based on the many body perturbation theory and the random phase approximation (RPA). The combination of DMFT with the GW approximation (GW+DMFT) was proposed to include both on-site and inter-atomic 