Linear response approach to the calculation of the effective interaction parameters in theLDA+Umethod

In this work we reexamine the $\mathrm{LDA}+\mathrm{U}$ method of Anisimov and co-workers in the framework of a plane-wave pseudopotential approach. A simplified rotational-invariant formulation is adopted. The calculation of the Hubbard $U$ entering the expression of the functional is discussed and a linear response approach is proposed that is internally consistent with the chosen definition for the occupation matrix of the relevant localized orbitals. In this way we obtain a scheme whose functionality should not depend strongly on the particular implementation of the model in ab initio calculations. We demonstrate the accuracy of the method, computing structural and electronic properties of a few systems including transition and rare-earth correlated metals, transition metal monoxides, and iron silicate.