Inapplicability of exact constraints and a minimal twoparameter generalization to the DFT+U based correction of selfinteraction error
Abstract
In approximate densityfunctional theory (DFT), the selfinteraction error is an electron delocalization anomaly associated with underestimated insulating gaps. It exhibits a predominantly quadratic energydensity curve that is amenable to correction using efficient, constraintresembling methods such as DFT + Hubbard U (DFT+U ). Constrained DFT (cDFT) enforces conditions on DFT exactly, by means of selfconsistently 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 oneelectron system, H_{2}^{+} , in that it readily recovers the exact total energy while symmetrypreserving 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 U_{1} and U_{2}, may be calculated from first principles.
 Publication:

Physical Review B
 Pub Date:
 December 2016
 DOI:
 10.1103/PhysRevB.94.220104
 arXiv:
 arXiv:1608.07320
 Bibcode:
 2016PhRvB..94v0104M
 Keywords:

 Physics  Chemical Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Physics  Computational Physics;
 Quantum Physics
 EPrint:
 7 pages, 5 figures. Accepted for Physical Review B Rapid Communications on 30th November 2016