Inapplicability of exact constraints and a minimal two-parameter generalization to the DFT+$U$ based correction of self-interaction error

Abstract

In approximate density functional theory (DFT), the self-interaction error is an electron delocalization anomaly associated with underestimated insulating gaps. It exhibits a predominantly quadratic energy-density curve that is amenable to correction using efficient, constraint-resembling methods such as DFT + Hubbard $U$ (DFT+$U$). Constrained DFT (cDFT) enforces conditions on DFT exactly, by means of self-consistently optimized Lagrange multipliers, and while its use to automate error corrections is a compelling possibility, we show that it is limited by a fundamental incompatibility with constraints beyond linear order. We circumvent this problem by utilizing separate linear and quadratic correction terms, which may be interpreted either as distinct constraints, each with its own Hubbard $U$ type Lagrange multiplier, or as the components of a generalized DFT+$U$ functional. The latter approach prevails in our tests on a model one-electron system, $H_2^{+}$, in that it readily recovers the exact total-energy while symmetry-preserving pure constraints fail to do so. The generalized DFT+$U$ functional moreover enables the simultaneous correction of the total-energy and ionization potential or the correction of either together with the enforcement of Koopmans condition. For the latter case, we outline a practical, approximate scheme by which the required pair of Hubbard parameters, denoted as U1 and U2, may be calculated from first-principles.

arXiv comment7 pages, 5 figures. Accepted for Physical Review B Rapid Communications on 30th November 2016

References in corpus (17)

• A linear response approach to the calculation of the effective interaction parameters in the LDA+U method
• Hubbard-corrected DFT energy functionals: the LDA+U description of correlated systems
• Density functional theory in transition-metal chemistry: a self-consistent Hubbard U approach
• A direct view at excess electrons in TiO${}_2$ rutile and anatase
• Koopmans' condition for density-functional theory
• Koopmans-compliant functionals and their performance against reference molecular data
• The effect of the Perdew-Zunger self-interaction correction to density functionals on the energetics of small molecules
• First-principles Calculation of Effective Onsite Coulomb Interaction of 3d Transition Metals: Constrained Local Density Functional Approach with Maximally Localized Wannier Function
• Realistic, quantitative descriptions of electron-transfer reactions: diabatic free-energy surfaces from first-principles molecular dynamics
• Projector self-consistent DFT+U using non-orthogonal generalized Wannier functions
• Static correlation beyond the random phase approximation: Dissociating H2 with the Bethe-Salpeter equation and time-dependent GW
• Piecewise linearity in the $GW$ approximation for accurate quasiparticle energy predictions
• Linear-scaling DFT+U with full local orbital optimization
• Optimization of constrained density functional theory
• Ligand Discrimination in Myoglobin from Linear-Scaling DFT+U
• Self-interaction correction in the LDA+U method
• Towards First-principles Electrochemistry

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• 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
• TDDFT+$U$: Hubbard corrected approximate density-functional theory in the excited-state regime