Local density approximation combined with Gutzwiller method for correlated electron systems*

We introduce in detail our newly developed \textit{ab initio} LDA+Gutzwiller (local density approximation plus Gutzwiller) method, in which the Gutzwiller variational approach is naturally incorporated with the density functional theory (DFT) through the ``Gutzwiller density functional theory (GDFT)'' (which is a generalization of original Kohn-Sham formalism). This method can be used for ground state determination of electron systems ranging from weakly correlated metal to strongly correlated insulators with long-range ordering. The method is fully variational, the charge-density self-consistency can be naturally achieved, and the quantities, such as total energy, linear response, can be accurately obtained similar to LDA-type calculations. We will present some applications on typical correlated systems including d-electron systems (iron, nickel, $Na_xCoO_2$ and so on) and f-electron systems (delta plutonium). The obtained results using LDA+Gutzwiller are in good agreement with existing experiments.