Hubbard parameters from density-functional perturbation theory

Abstract

We present a transparent and computationally efficient approach for the first-principles calculation of Hubbard parameters from linear-response theory. This approach is based on density-functional perturbation theory and the use of monochromatic perturbations. In addition to delivering much improved efficiency, the present approach makes it straightforward to calculate automatically these Hubbard parameters for any given system, with tight numerical control on convergence and precision. The effectiveness of the method is showcased in three case studies -Cu2O, NiO, and LiCoO2 -and by the direct comparison with finite differences in supercell calculations. I. INTRODUCTIONThe development of density-functional theory (DFT) [1,2] has allowed modeling of a broad spectrum of properties for a large variety of systems. In practical applications DFT relies on approximations to the exchange-correlation (xc) electronic interactions, among which the local-density approximation (LDA) and the generalized-gradient approximation (GGA) are the most popular ones. Both approximations suffer from self-interaction errors (SIE), which limit the accuracy only to systems with weak and moderate electronic correlations. In systems with strongly localized electrons of d and f types, SIE in LDA and GGA are much larger, which leads to overdelocalization of these electrons and quantitative and sometimes even qualitative failures in the description of complex materials (e.g. metallic instead of insulating ground states).Various corrective methods have been devised to deal with SIE. In particular, in DFT with hybrid functionals -such as e.g. B3LYP [3][4][5][6][7] or HSE06 [8,9] -a fraction of the non-local Fock exchange is used for all (strongly localized and non-strongly localized) electrons with a fraction of (semi-)local exchange and a fully (semi-)local correlation. This approach is computationally more expensive than DFT with (semi-)local functionals, because the Fock exchange is a non-local integral operator which acts on Kohn-Sham (KS) wave functions. However, there has been recent progress in the development of very efficient techniques, such as the adaptively compressed exchange [10], to speed up such calculations. Another recent suggestion is the meta-GGA functional SCAN (strongly constrained and appropriately normed semilocal density functional) [11], which has shown promising results for many systems [12,13]. Having a marginal increase in the computational cost, DFT with the SCAN functional uses a xc potential which depends on KS wave functions via a kinetic energy density. However, SCAN still contains significant SIE [12]. arXiv:1805.01805v2 [cond-mat.str-el]

Self-consistent site-dependent DFT+ U study of stoichiometric and defective SrMnO3

“…In periodic systems without defects, this approach allows to use primitive cells rather than computationally expensive supercells 64 . When supercells are needed, for example for systems with defects as in this work, the DFPT calculation of the Hubbard parameters, using coarser q-point grids than for primitive cells, still offer a higher level of accuracy, automation, and a better scaling than the linear response approach of Ref.…”

“…To highlight that U is a Hubbard-manifold and material-dependent property, we have computed the selfconsistent Hubbard U for stoichiometric bulk SMO (U SC ) using the DFPT approach of Ref. 64 (see also Sec. III).…”

Reinventing solid state electronics: Harnessing quantum confinement in bismuth thin films

“…These approximations typically result in a large and systematic underestimation of band gaps in semiconductors. The semimetallic band structure of bulk Bi found using DFT predicts a much larger band overlap of ~160 meV (16,17) compared to the experimental value. To provide an improved description of the confinement effect in bismuth thin films, particularly with respect to determining band gap energies, the GW (G: Green's function, W: screened Coulomb interaction) method in conjunction with a many body perturbation theory (MBPT) correction is used (18).…”

Hubbard-corrected density functional perturbation theory with ultrasoft pseudopotentials

“…We stress that this overall very good agreement with the experiments is obtained without any fitting parameter. Our Hubbard U value (4.55 eV) was determined ab initio and self-consistently using a recentlydeveloped DFPT-based linear-response technique [66]. Table II reports the computed high-frequency dielectric tensor and Born effective charges, in comparison with the experimental values.…”