Flat-plane based double-counting free and parameter free many-body DFT+U

Abstract

Burgess et al. have recently introduced the BLOR corrective exchange-correlation functional that is, by construction, the unique simplified rotationally-invariant DFT+U functional that enforces the flat-plane condition separately on each effective orbital of a localized subspace. Detached from the Hubbard model, functionals of this type are both double-counting correction free and, when optimized in situ using appropriate error quantifiers, effectively parameter free. In this work, the extension of the BLOR functional to address many-body errors (mBLOR) is derived. The mBLOR functional is built to enforce the flat-plane condition on the entire subspace, rather than on each orbital individually. In this way inter-orbital errors are corrected on the same footing as the single-particle ones. Focusing on exact test cases with strong inter-orbital interactions, the BLOR and mBLOR functionals were benchmarked against contemporary DFT+U functionals using the total energy extensivity condition on stretched homo-nuclear p-block dimers that represent various self-interaction and static-correlation error regimes. The BLOR functional outperformed all other DFT+$U$ functionals tested, which often act to increase total-energy errors, yet it still yielded large errors in some systems. mBLOR instead yielded low energy errors across all four strongly-correlated dimers, while being constructed using only semi-local approximation ingredients. As mBLOR would not otherwise introduce a band-gap correction in the manner that is a desirable feature of DFT+U, we developed a cost-free technique to reintroduce it automatically by moving the functional's unusual explicit derivative discontinuity into the potential. With this in place, mBLOR is the only known DFT$+U$ functional that opens the bandgap of stretched neutral homo-nuclear dimers without the aid of unphysical spin-symmetry breaking.

As accepted for publication in Phys. Rev. B. 22 pages, 9 figures, and 4 tables

References in corpus (39)

• Restoring the density-gradient expansion for exchange in solids and surfaces
• Generalized gradient approximation for solids and their surfaces
• Climbing the Density Functional Ladder: Non-Empirical Meta-Generalized Gradient Approximation Designed for Molecules and Solids
• A linear response approach to the calculation of the effective interaction parameters in the LDA+U method
• Correlated metals and the LDA+U method
• Hubbard parameters from density-functional perturbation theory
• Fractional spins and static correlation error in density functional theory
• Koopmans' condition for density-functional theory
• The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems
• Extended DFT+U+V method with on-site and inter-site electronic interactions
• Anisotropy and Magnetism in the LSDA+U Method
• Localized Orbital Scaling Correction for Systematic Elimination of Delocalization Error in Density Functional Approximations
• First principles study of electronic and structural properties of CuO
• The derivative discontinuity of the exchange-correlation functional
• Koopmans-compliant functionals and their performance against reference molecular data
• Exchange-Correlation Energy from Pairing Matrix Fluctuation and the Particle-Particle Random Phase Approximation
• High-throughput determination of Hubbard U and Hund J values for transition metal oxides via linear response formalism
• Electronic Structure Trends Across the Rare-Earth Series in Superconducting Infinite Layer Nickelates
• Predictive Power of the Exact Constraints and Appropriate Norms in Density Functional Theory
• Density Functional Model for Nondynamic and Strong Correlation
• The role of spin in the calculation of Hubbard $U$ and Hund's $J$ parameters from first principles
• Kohn-Sham potentials in exact density-functional theory at non-integer electron numbers
• Energetics and cathode voltages of LiMPO${}_4$ olivines (M = Fe, Mn) from extended Hubbard functionals
• Recovering the flat-plane condition in electronic structure theory at semi-local DFT cost
• First-principles Hubbard U and Hund's J corrected approximate density-functional theory predicts an accurate fundamental gap in rutile and anatase TiO2
• The effect of double counting, spin density, and Hund interaction in the different DFT+$U$ functionals
• Parametrization of LSDA+$U$ for noncollinear magnetic configurations: Multipolar magnetism in UO${}_2$
• Ensemble Density Functional Theory of Neutral and Charged Excitations
• DFT+U+J with linear response parameters predicts non-magnetic oxide band gaps with hybrid-functional accuracy
• Orbital-resolved DFT+U for molecules and solids
• Fragment-based Treatment of Delocalization and Static Correlation Errors in Density-Functional Theory
• Linear-scaling DFT+U with full local orbital optimization
• Local density approximations from finite systems
• A DFT+U type functional derived to explicitly address the flat plane condition
• Self-interaction correction in the LDA+U method
• Optimization strategies developed on NiO for Heisenberg exchange coupling calculations using projector augmented wave based first-principles DFT+U+J
• The Convexity Condition of Density-Functional Theory
• Reconciling the theoretical and experimental electronic structure of NbO2
• The tilted-plane structure of the energy of finite quantum systems

Cited by in corpus (2)

• First-principles Hubbard parameters with automated and reproducible workflows
• Foundations of the ionization potential condition for localized electron removal in density functional theory