Explicit demonstration of the equivalence between DFT+U and the Hartree-Fock limit of DFT+DMFT

Abstract

Several methods have been developed to improve the predictions of density functional theory (DFT) in the case of strongly correlated electron systems. Out of these approaches, DFT+$U$, which corresponds to a static treatment of the local interaction, and DFT combined with dynamical mean field theory (DFT+DMFT), which considers local fluctuations, have both proven incredibly valuable in tackling the description of materials with strong local electron-electron interactions. While it is in principle known that the Hartree-Fock (HF) limit of the DFT+DMFT approach should recover DFT+$U$, demonstrating this equivalence in practice is challenging, due to the very different ways in which the two approaches are generally implemented. In this work, we introduce a way to perform DFT+$U$ calculations in Quantum ESPRESSO using Wannier functions as calculated by Wannier90, which allows us to use the same Hubbard projector functions both in DFT+$U$ and in DFT+DMFT. We benchmark these DFT+$U$ calculations against DFT+DMFT calculations where the DMFT impurity problem is solved within the HF approximation. Considering a number of prototypical materials including NiO, MnO, LaMnO${}_3$, and LuNiO${}_3$, we establish the sameness of the two approaches. Finally, we showcase the versatility of our approach by going beyond the commonly used atomic orbital-like projectors by performing DFT+$U$ calculations for VO${}_2$ using a special set of bond-centered Wannier functions.

References in corpus (64)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• A linear response approach to the calculation of the effective interaction parameters in the LDA+U method
• Maximally localized Wannier functions: Theory and applications
• Electronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
• Maximally-localized Wannier functions for entangled energy bands
• Quantum ESPRESSO toward the exascale
• Wannier90 as a community code: new features and applications
• Hubbard-corrected DFT energy functionals: the LDA+U description of correlated systems
• Strong electronic correlations from Hund's coupling
• Dynamical singlets and correlation-assisted Peierls transition in VO2
• Dynamical Mean-Field Theory within the Full-Potential Methods: Electronic structure of Ce-115 materials
• First-principles Calculations of the Electronic Structure and Spectra of Strongly Correlated Systems: Dynamical Mean-field Theory
• Implementation of the Projector Augmented Wave LDA+U Method: Application to the Electronic Structure of NiO
• TRIQS: A Toolbox for Research on Interacting Quantum Systems
• Hubbard U and Hund's Exchange J in Transition Metal Oxides: Screening vs. Localization Trends from Constrained Random Phase Approximation
• Full orbital calculation scheme for materials with strongly correlated electrons
• Implementation of the LDA+U method using the full potential linearized augmented plane wave basis
• Charge disproportionation without charge transfer in the rare-earth nickelates as a possible mechanism for the metal-insulator transition
• Plane-wave based electronic structure calculations for correlated materials using dynamical mean-field theory and projected local orbitals
• Extended DFT+U+V method with on-site and inter-site electronic interactions
• Spin and charge ordering in self-doped Mott insulators
• Dynamical mean-field theory using Wannier functions: a flexible route to electronic structure calculations of strongly correlated materials
• Vanadium dioxide : A Peierls-Mott insulator stable against disorder
• Self-consistency over the charge-density in dynamical mean-field theory: a linear muffin-tin implementation and some physical implications
• Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps
• NiO: Correlated Bandstructure of a Charge-Transfer Insulator
• Reconciling the ionic and covalent pictures in rare-earth nickelates
• A polymorphous band structure model of gapping in the anti-ferromagnetic and paramagnetic phases of the Mott insulators MnO, FeO, CoO, and NiO
• Origin of Jahn-Teller distortion and orbital-order in LaMnO3
• Metal-insulator Transition in VO2: a DFT+DMFT perspective
• Double Counting in LDA+DMFT - The Example of NiO
• LDA+DMFT implemented with the pseudopotential plane-wave approach
• Computing total energies in complex materials using charge self-consistent DFT+DMFT
• Insulating gap in FeO: correlations and covalency
• Resolving the VO${}_2$ controversy: Mott mechanism dominates the insulator-to-metal transition
• Effective band-structure in the insulating phase versus strong dynamical correlations in metallic VO2
• Interplay of octahedral rotations and breathing distortions in charge ordering perovskite oxides
• Symmetry-adapted Wannier functions in the maximal localization procedure
• Applications of DFT+DMFT in Materials Science
• Unraveling the Mott-Peierls intrigue in Vanadium dioxide
• The effect of double counting, spin density, and Hund interaction in the different DFT+$U$ functionals
• Interplay between breathing mode distortion and magnetic order in rare-earth nickelates $R$NiO${}_3$ within DFT+$U$
• Pulay forces in density-functional theory with extended Hubbard functionals: From nonorthogonalized to orthogonalized manifolds
• Dynamical mean-field approach to materials with strong electronic correlations
• Density functional plus dynamical mean field theory of the metal-insulator transition in early transition metal oxides
• Spin-density functional theories and their $+U$ and $+J$ extensions: a comparative study of transition metals and transition metal oxides
• Fingerprints of Spin-Orbital Physics in Crystalline O${}_2$
• Effective crystal field and Fermi surface topology: a comparison of d- and dp-orbital models
• Electronic correlations and crystal structure distortions in BaBiO3
• Selectively Localized Wannier Functions
• Orbital-resolved DFT+U for molecules and solids
• The origin of the vanadium dioxide transition entropy
• Charge self-consistent electronic structure calculations with dynamical mean-field theory using Quantum ESPRESSO, Wannier90 and TRIQS
• Rubidium superoxide: a p-electron Mott insulator
• Oxygen Vacancies in Strontium Titanate: a DFT+DMFT study
• On the calculation of crystal field parameters using Wannier functions
• Hellmann-Feynman Forces within the DFT+U in Wannier functions basis
• Effect of Hubbard U on the construction of low energy Hamiltonians for LaMnO_3 via maximally localized Wannier functions
• Hybridization driving distortions and multiferroicity in rare-earth nickelates
• DFT+DMFT study of oxygen vacancies in a Mott Insulator
• Magnetostriction-Driven Muon Localization in an Antiferromagnetic Oxide
• Single-site DFT+DMFT for vanadium dioxide using bond-centered orbitals
• Incorporating static intersite correlation effects in vanadium dioxide through DFT$+V$

Cited by in corpus (8)

• First-principles Hubbard parameters with automated and reproducible workflows
• Comparative analysis of methods for calculating Hubbard parameters using cRPA
• Comparative study of magnetic exchange parameters and magnon dispersions in NiO and MnO from first principles
• Impact of strong electronic correlations on altermagnets: the case of NiS2
• Pairing Symmetry Crossover from $d$-wave to $s_{\pm }$-wave in a Bilayer Nickelate Driven by Hund's Coupling and Crystal Field Splitting
• Electronic correlations and spin-charge-density stripes in double-layer La${}_3$Ni${}_2$O${}_7$
• Getting the manifold right: The crucial role of orbital resolution in DFT+U for mixed d-f electron compounds
• Bridging constrained random-phase approximation and linear response theory for computing Hubbard parameters