Rotationally invariant ab initio evaluation of Coulomb and exchange parameters for DFT+U calculations

Abstract

Conventional density functional theory (DFT) fails for strongly correlated electron systems due to large intra-atomic self-interaction errors. The DFT+U method provides a means of overcoming these errors through the use of a parametrized potential that employs an exact treatment of quantum mechanical exchange interactions. The parameters that enter into this potential correspond to the spherically averaged intra-atomic Coulomb (U) and exchange (J) interactions. Recently, we developed an ab initio approach for evaluating these parameters on the basis of unrestricted Hartree-Fock (UHF) theory, which has the advantage of being free of self-interaction errors and does not require experimental input [Mosey and Carter, Phys. Rev. B 76, 155123 (2007)]. In this work, we build on that method to develop a more robust and convenient ab initio approach for evaluating U and J. The new technique employs a relationship between U and J and the Coulomb and exchange integrals evaluated using the entire set of UHF molecular orbitals (MOs) for the system. Employing the entire set of UHF MOs renders the method rotationally invariant and eliminates the difficulty in selecting unambiguously the MOs that correspond to localized states. These aspects overcome two significant deficiencies of our earlier method. The new technique is used to evaluate U and J for Cr(2)O(3), FeO, and Fe(2)O(3). The resulting values of U-J are close to empirical estimates of this quantity for each of these materials and are also similar to results of constrained DFT calculations. DFT+U calculations using the ab initio parameters yield results that are in good agreement with experiment. As such, this method offers a means of performing accurate and fully predictive DFT+U calculations of strongly correlated electron materials.

First-principles modeling of localizeddstates with theGW@LDA+Uapproach

“…They are significantly smaller than AZA's but very close to the linear response and constrained RPA ones. 84,85,92 The difference between our and AZA's constrained DFT results can be attributed to the different basis used in the calculations, i.e., full-potential vs atomic sphere approximation, and LAPW vs LMTO.…”

“…The determination of U from first principles has attracted growing interest in recent years. 67,74,[84][85][86][87][88][89][90][91][92] The most widely used approach is the constrained DFT formalism, which was developed in a general form by Dederichs et al 86 and later widely used to calculate parameters for effective Hamiltonians ͑Hubbard or Anderson͒. 93…”

Twin formation in hematite during dehydration of goethite

“…We applied a 600 eV cutoff to limit the plane-wave basis set without compromising the computational accuracy. In this study, for comparison, we considered two different twin boundaries, which are called prismatic (100) and basal Dudarev et al [27], with an effective on-site Coulomb interaction parameter of 4.3 eV [28]. The calculated lattice constants of hematite were a = 5.068 Å and c = 13.876 Å, obtained by using a 5 × 5 × 3 k-mesh on the rhombohedral unit cell with 12 Fe atoms.…”

Stability and Polaronic Motion of Self-Trapped Holes in Silver Halides: Insight through DFT+UCalculations

“…The DFT+ method has been described in depth in the literature [54][55][56] . It has been extensively used in the study of transition-metal oxides where the correction 57 is typically applied to the d orbitals of the transition metal [54][55][56][58][59][60] . In other systems in which the localization of electrons or holes involves s and/or p orbitals, the corrections are applied on these orbitals 9, 61-63 .…”