The local projection in the density functional theory plus U approach: A critical assessment

Abstract

Density-functional theory plus the Hubbard U correction (DFT + U) method is widely used in first-principles studies of strongly correlated systems, as it can give qualitatively (and sometimes, semi-quantitatively) correct description of energetic and structural properties of many strongly correlated systems with similar computational cost as local density approximation or generalized gradient approximation. On the other hand, the DFT + U approach is limited both theoretically and practically in several important aspects. In particular, the results of DFT + U often depend on the choice of local orbitals (the local projection) defining the subspace in which the Hubbard U correction is applied. In this work we have systematically investigated the issue of the local projection by considering typical transition metal oxides, β-MnO2 and MnO, and comparing the results obtained from different implementations of DFT + U. We found that the choice of the local projection has significant effects on the DFT + U results, which are more significant for systems with stronger covalent bonding (e.g., MnO2) than those with more ionic bonding (e.g., MnO). These findings can help to clarify some confusion arising from the practical use of DFT + U and may also provide insights for the development of new first-principles approaches beyond DFT + U.

DFT+ U study of self-trapping, trapping, and mobility of oxygen-type hole polarons in barium stannate

“…(C4) gives the correct number of electrons (see also is thus equivalent to the "ATOMIC" scheme in Ref. [53]. An important point is indeed that this formulation can recover the maximum number of electrons in oxygen orbitals, in contrary to other schemes, as can be seen in Table V …”

“…An important aspect of DFT+U calculations is the definition of correlated orbitals. Indeed, DFT+U , as well as the DFT+DMFT method, is dependent on their definition: it was recently highlighted [52,53] that using different definitions and different implementations lead to important differences in transition-metal oxides. Importantly, the number of correlated electrons is very sensitive to this choice, and thus the total energy, and thus the effect of DFT+U to restore the piecewise linearity of the total energy as a function of the number of electrons [15] (see discussion in Sec.…”

“…This is the scheme called "PAW" in Ref. [53]. A nearly identical formulation in terms of occupation matrix can be obtained by defining correlated orbitals as truncated renormalized atomic orbitals.…”

A biodegradable hybrid inorganic nanoscaffold for advanced stem cell therapy

“…This is because conventional DFT functionals are unable to describe the strong correlation effect among the partially filled d states in Mn 61 . The Hubbard parameter ‘ U’ , is introduced for the Mn 3d electrons to describe the on-site Coulomb interaction, as given in the well-known GGA + U method 62 . The values of U = 4 eV and J = 0 eV for MnO 2 were adopted 63 .…”

Improved pseudopotential transferability for magnetic and electronic properties of binary manganese oxides from DFT+U+J calculations

“…The magnetic and electronic structures of the manganese oxides are calculated with firstprinciples DFT using the PBEsol [85] parametrization of the generalized gradient approximation with on-site Coloumb repulsion and exchange parameters U and J, treated separately and explicitly defined within the rotationally invariant, fully anisotropic scheme (DFT+U +J ) [81,82], using the atomic orbital projection scheme [86] as implemented in the Quantum Espresso [87] package. It has been demonstrated that the fully anisotropic J parameter plays an important role in describing strongly correlated noncollinear antiferromagnetic systems [76].…”