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.

In this work we reexamine the LDA+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.

The electronic structure and properties of cerium oxides (CeO2 and Ce2O3) have been studied in the framework of the LDA+U and GGA(PW91)+U implementations of density functional theory. The dependence of selected observables of these materials on the effective U parameter has been investigated in detail. The examined properties include lattice constants, bulk moduli, density of states, and formation energies of CeO2 and Ce2O3. For CeO2, the LDA+U results are in better agreement with experiment than the GGA+U results whereas for the computationally more demanding Ce2O3 both approaches give comparable accuracy. Furthermore, as expected, Ce2O3 is much more sensitive to the choice of the U value. Generally, the PW91 functional provides an optimal agreement with experiment at lower U energies than LDA does. In order to achieve a balanced description of both kinds of materials, and also of nonstoichiometric CeO2−x phases, an appropriate choice of U is suggested for LDA+U and GGA+U schemes. Nevertheless, an optimum value appears to be property dependent, especially for Ce2O3. Optimum U values are found to be, in general, larger than values determined previously in a self-consistent way.

We investigate the effect of transition metal (TM) substitution in cuprous oxide Cu2O on the basis of ab initio calculations employing density-functional theory (GGA+U). By using the supercell approach, we study the effect of substituting Cu by Mn, Fe, Co, and Ni, assuming both low TM concentrations (3.2%) in a cubic geometry and higher TM concentrations (9.1%) in a trigonal setup. For the elements Mn and Co, magnetic exchange constants up to the fifth nearest neighbor are calculated, assuming both cases, perfect Mn/Co:Cu2O as well as defects in the host such as single copper and oxygen vacancies. Our results clearly show the importance of defects in these materials and thus offer an explanation for various, seemingly opposed, experimental results.

The electronic structures of delafossite-type oxide AgFeO2 have been calculated by using the full potential linearlized augmented plane wave (FP-LAPW) method within the generalized gradient approximation (GGA) and GGA + U. It was found that the GGA calculations lead to a metallic state for AgFeO2 which is in contradiction with the experiment that AgFeO2 is a semiconductor. By taking into account the Hubbard interaction parameter U, the GGA + U calculations produce a semiconducting state for AgFeO2 when U > 0.68 eV. An energy band gap which is the gap between the highest occupied valance band of Ag-3d and the lowest upper Hubbard band of Fe-3d was predicted to be 1.15 eV with an effective Ueff = 7.86 eV.

We present an ab initio method for calculating effective onsite Coulomb interactions of solid. The method is based on constrained local density functional theory formulated in terms of maximally localized Wannier functions. This scheme can be implemented with any basis, and thus allows us to perform the constrained calculation with plane-wave-based electronic-structure codes. We apply the developed method to the evaluation of the onsite interaction of 3d transition-metal series. The results are discussed using a heuristic formula for screened Coulomb interactions.

Transition-metal centers are the active sites for a broad variety of biological and inorganic chemical reactions. Notwithstanding this central importance, density-functional theory calculations based on generalized-gradient approximations often fail to describe energetics, multiplet structures, reaction barriers, and geometries around the active sites. We suggest here an alternative approach, derived from the Hubbard U correction to solid-state problems, that provides an excellent agreement with correlated-electron quantum chemistry calculations in test cases that range from the ground state of Fe2 and Fe₂^- to the addition elimination of molecular hydrogen on FeO+. The Hubbard U is determined with a novel self-consistent procedure based on a linear-response approach.

Ricardo Grau-Crespo, Ibério de P. R. Moreira, Francesc Illas, Nora H. de Leeuw and C. Richard A. Catlow

Paul Erhart, Karsten Albe, and Andreas Klein