Self-interaction correction in the LDA+U method

We present one critical aspect of the LDA+U method regarding its self-interaction correction of the local density approximation (LDA). By re-examining the mean-field approximation on the Hubbard energy in the Hartree-Fock form, we have derived an LDA "double-counting" energy expression which led to a more reasonable self-interaction correction in an alternative LDA+U scheme. For the bulk Gd metal, the alternative scheme resulted in electronic properties more consistent with experiments in comparison to the LDA and the existing LDA+U schemes.