Hubbard U parameters for transition metals from first principles

Physical review. B./Physical review. B, vol. 105

Abstract

Using the linear response-based constrained local density approximation (cLDA) approach we systematically computed the Hubbard $U$ parameters for series of $3d, 4d,$ and $5d$ transition metals. We compare the results with estimations by the constrained random phase approximation (cRPA) method and discuss the performance of the self-consistent density functional theory + $U$ ($\mathrm{DFT}+U$) method for prediction of lattice parameters, work functions, $d$-bandwidths and $d$-band centers. Interestingly, we found that blindly applied the standard, fully localized limit (FLL) version of the $\mathrm{DFT}+U$ approach heavily overestimates the positions of $d$-band centers with respect to the Fermi level, but much better agreement with experiment is obtained when applying a more realistic, Wannier-type representation of $d$ orbitals for projection of $d$ states occupancies. We present another, independent estimate of the Hubbard $U$ parameter based on the comparison of Hartree-Fock and DFT eigenvalues, and positions of $d$-band centers. The so-derived estimates are surprisingly well consistent with the ones derived from the above-mentioned first principles approaches, and allow for validation of cRPA or cLDA results for the disputed cases, including Cu, Ag, and Au for which large $U$ parameters are obtained from the cLDA method.

Authors 2

1. Rebekka Tesch Aachen Chair of Theory and Computation of Energy Materials Faculty of Georesources and Materials Engineering

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   Institute of Energy and Climate Research, Theory and Computation of Energy Materials (IEK-13), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany; Chair of Theory and Computation of Energy Materials, Faculty of Georesources and Materials Engineering, RWTH Aachen University, 52062 Aachen, Germany; and Jülich Aachen Research Alliance, JARA-CSD and JARA-ENERGY, 52425 Jülich, Germany

   Chair of Theory and Computation of Energy Materials, Faculty of Georesources and Materials Engineering, RWTH Aachen University, 52062 Aachen, Germany

   Institute of Energy and Climate Research, Theory and Computation of Energy Materials (IEK-13), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany

   Jülich Aachen Research Alliance, JARA-CSD and JARA-ENERGY, 52425 Jülich, Germany

2. Piotr M. Kowalski Aachen Chair of Theory and Computation of Energy Materials Faculty of Georesources and Materials Engineering

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Aachen Research Alliance

   Affiliation as printed

   Institute of Energy and Climate Research, Theory and Computation of Energy Materials (IEK-13), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany; Chair of Theory and Computation of Energy Materials, Faculty of Georesources and Materials Engineering, RWTH Aachen University, 52062 Aachen, Germany; and Jülich Aachen Research Alliance, JARA-CSD and JARA-ENERGY, 52425 Jülich, Germany

   Chair of Theory and Computation of Energy Materials, Faculty of Georesources and Materials Engineering, RWTH Aachen University, 52062 Aachen, Germany

   Institute of Energy and Climate Research, Theory and Computation of Energy Materials (IEK-13), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany

   Jülich Aachen Research Alliance, JARA-CSD and JARA-ENERGY, 52425 Jülich, Germany