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

Abstract

In this work we reexamine the LDA+U method of Anisimov and coworkers 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.

Magnetic MAX phases from theory and experiments; a review

“…For such materials the many electrons in partially filled d or f orbitals are inherently localized on each metal atom and by introducing the on-site Coulomb repulsion U, applied to localized electrons such as 3d or 4f , i.e., a DFT+U approach, results are improved [55][56][57][58]. Two commonly used methods for treating strongly correlated electron materials, are through empirical fitting or constrained DFT calculations [59][60][61][62]. The former method lacks a theoretical basis and is influenced by a limited or non-existing amount of experimental data, whereas the latter approach is motivated from first-principles but of questionable accuracy due to the artificial nature of the constrained system [54].…”

Synergy of van der Waals and self-interaction corrections in transition metal monoxides

“…Comparing the DOS at the bottom of the conduction band from SCAN+U and PBE+U to that from the more-sophisticated HSE06, one can see that SCAN needs a smaller SIC correction than PBE. The U parameter can be determined by using the linear-response approach [13] with self consistency [54,55]. The actual procedure in Ref.…”

“…Of greater concern is the fact that PBE wrongly predicts the zincblende (ZB) phase as the ground state for MnO and CoO [5,7,8]. Self-interaction correction (SIC) [9,10], approximated by DFT+U [11][12][13] with an appropriate on-site Hubbard U to the d-orbit, or via the more computationally-demanding hybrid functional [14,15] with a fraction of exact exchange, improves the band gap [1,2,5,[16][17][18][19][20][21], but cannot fully recover the polymorphism energetics [5,22]. Peng and Lany [22] first tackled this problem for MnO by the high-level adiabatic connection fluctuation-dissipation theorem random phase approximation to the correlation energy (RPA) [23][24][25].…”

The DFT+U: Approaches, Accuracy, and Applications

“…The U is self-consistently determined, which is fully consistent with the definition of the DFT+U Hamiltonian, making this approach for the potential calculations fully ab initio. The value of U implemented by Cococcioni et al is U eff = U−J, where J is indirectly assumed to be zero in order to obtain a simplified expression [17]. Nonetheless, J can add some additional flexibility to the DFT+U calculations, but it may yield surprising results including reversing the trends previously obtained in the implemented DFT+U calculations [18].…”

“…where the values of U can be determined through a linear response method [17], in which the response of the occupation of localized states to a small perturbation of the local potential is calculated. The U is self-consistently determined, which is fully consistent with the definition of the DFT+U Hamiltonian, making this approach for the potential calculations fully ab initio.…”