Calculations of Hubbard<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>U</mml:mi></mml:math>from first-principles

Aryasetiawan, Ferdi; Karlsson, K.; Jepsen, O.; Schönberger, U.

doi:10.1103/physrevb.74.125106

Cited by 465 publications

(371 citation statements)

References 21 publications

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“…Since it inherently preserves the spatial localization of Hubbard projector duals, it is also less computationally expensive and simpler to implement in linear-scaling methods, in practice, than the "on-site" or "dual" representations which employ delocalized dual projectors. In order to alleviate the remaining arbitrariness in DFT+U and related methods in the nonorthogonal case, the tensorial formalism may be combined with both a projector self-consistency algorithm 15 or any one of a number of available first-principles methods for the U parameter 13,18,[21][22][23][24] ; the latter remains as an avenue for future investigation.…”

Section: Discussionmentioning

confidence: 99%

“…Here,Û (σ) (r, r ′ ) is the Coulomb interaction screened according to mechanisms described by an appropriate theory such as linear-response 13,18,21 , constrained LDA 22 , constrained RPA 23 or constrained adiabatic LDA 24 . Coulomb repulsion is represented by those terms for which m = m ′′ ; m ′ = m ′′′ , while direct exchange is given by those elements with m = m ′′′ ; m ′ = m ′′ .…”

Section: Application To the Dft+u Methodsmentioning

confidence: 99%

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Subspace Representations in Ab Initio Methods for Strongly Correlated Systems

O’Regan

Payne²,

Mostofi³

2011

Optimised Projections for the Ab Initio Simulation of Large and Strongly Correlated Systems

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We present a generalized definition of subspace occupancy matrices in ab initio methods for strongly correlated materials, such as DFT+U and DFT+DMFT, which is appropriate to the case of nonorthogonal projector functions. By enforcing the tensorial consistency of all matrix operations, we are led to a subspace projection operator for which the occupancy matrix is tensorial and accumulates only contributions which are local to the correlated subspace at hand. For DFT+U in particular, the resulting contributions to the potential and ionic forces are automatically Hermitian, without resort to symmetrization, and localized to their corresponding correlated subspace. The tensorial invariance of the occupancies, energies and ionic forces is preserved. We illustrate the effect of this formalism in a DFT+U study using self-consistently determined projectors.

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Section: Discussionmentioning

confidence: 99%

Section: Application To the Dft+u Methodsmentioning

confidence: 99%

Subspace Representations in Ab Initio Methods for Strongly Correlated Systems

O’Regan

Payne²,

Mostofi³

2011

Optimised Projections for the Ab Initio Simulation of Large and Strongly Correlated Systems

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“…A complicated many-electron problem is made of electrons living in these localized orbitals, where they experience strong correlations among each other and with a subtle coupling with the extended states. Isolating a few degrees of freedom relevant to the correlation is the idea in the Hubbard model, where screened or renormalized Coulomb interaction (U) is kept among the localized orbitals' electrons [13]. In other word, the localized orbitals in the bandgap, which are present as localized states (d-and f-states), are too close to the Fermi energy.…”

Section: Practical Implementations Of the Hubbard Correctionmentioning

confidence: 99%

“…However, the semiempirical way of evaluating the U parameter fails to capture its dependence on the volume, structure, or the magnetic phase of the crystal, and also does not permit the capturing of changes in the on-site electronic interaction under changing physical conditions, such as chemical reactions. In order to get full advantage of this method, different procedures have been addressed to determine the Hubbard U from first principles [13]. In these procedures, the U parameter can generally be calculated using a self-consistent and basis set in an independent way.…”

Section: Optimizing the U Valuementioning

confidence: 99%

The DFT+U: Approaches, Accuracy, and Applications

Tolba¹,

Gameel²,

Ali³

et al. 2018

Density Functional Calculations - Recent Progresses of Theory and Application

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This chapter introduces the Hubbard model and its applicability as a corrective tool for accurate modeling of the electronic properties of various classes of systems. The attainment of a correct description of electronic structure is critical for predicting further electronic-related properties, including intermolecular interactions and formation energies. The chapter begins with an introduction to the formulation of density functional theory (DFT) functionals, while addressing the origin of bandgap problem with correlated materials. Then, the corrective approaches proposed to solve the DFT bandgap problem are reviewed, while comparing them in terms of accuracy and computational cost. The Hubbard model will then offer a simple approach to correctly describe the behavior of highly correlated materials, known as the Mott insulators. Based on Hubbard model, DFT+U scheme is built, which is computationally convenient for accurate calculations of electronic structures. Later in this chapter, the computational and semiempirical methods of optimizing the value of the Coulomb interaction potential (U) are discussed, while evaluating the conditions under which it can be most predictive. The chapter focuses on highlighting the use of U to correct the description of the physical properties, by reviewing the results of case studies presented in literature for various classes of materials.

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“…Aryasetiawan et al have discussed in great details the difference between these two approaches (i.e., cLDA and cRPA) and the advantages of the cRPA approach. 12,13 For example, the cRPA approach allows the evaluation of the full Hubbard U and exchange J matrices and their energy dependence. Inter-site interaction can be calculated easily within the cRPA approach, especially when the MLWF are used, without the need of using large unit cells.…”

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confidence: 99%

Screened Coulomb interaction of localized electrons in solids from first principles

Shih

Zhang

et al. 2012

Phys. Rev. B

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We report the implementation of a first-principles approach for calculating the screened Coulomb and exchange energies for localized electrons in solids. Our method is based on the pseudopotential plane wave formalism. The localized orbitals are represented by maximally localized Wannier functions (MLWF), and the screening effects are calculated within the constrained random phase approximation (cRPA). As first applications of this new development, we investigate the on-site Coulomb U and exchange J for the 3d electrons in ZnO, NiO, and CuGaS2. Both the bare (unscreened) and the screened U and J matrices are presented. We find that it is very important for these parameters to be calculated self-consistently. Intra-channel (i.e., d-d) and energy-dependent screening effects are also discussed.

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Calculations of HubbardUfrom first-principles

Cited by 465 publications

References 21 publications

Subspace Representations in Ab Initio Methods for Strongly Correlated Systems

Subspace Representations in Ab Initio Methods for Strongly Correlated Systems

The DFT+U: Approaches, Accuracy, and Applications

Screened Coulomb interaction of localized electrons in solids from first principles

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