Dresden 2017 – scientific programme
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HL: Fachverband Halbleiterphysik
HL 40: Electronic-Structure Theory: New Concepts and Developments in Density Functional Theory and Beyond - III
HL 40.7: Talk
Tuesday, March 21, 2017, 12:15–12:30, GER 38
An optimisability proof for self-consistent constrained DFT, and its implications for constraint-based self-interaction error correction — Glenn Moynihan1, Gilberto Teobaldi2,3, and •David D. O’Regan1 — 1School of Physics, CRANN and AMBER, Trinity College Dublin, Ireland. — 2Stephenson Institute for Renewable Energy and Department of Chemistry, The University of Liverpool, U.K. — 3Beijing Computational Science Research Center, China.
We develop the connection between constrained DFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening [1]. In particular, we provide a non-perturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers, generalizing the proof of Ref. [2]. We demonstrate that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT, and we provide necessary conditions for the optimizability of multi-constraint cDFT. We show that the applicability of cDFT in automating symmetry-preserving self-interaction error corrections is limited by a fundamental incompatibility with non-linear constraints. We circumvent this 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, two-parameter DFT+U functional [3]. [1] Phys. Rev. B 94, 035159 (2016). [2] Phys. Rev. A 72, 024502 (2005). [3] Phys. Rev. B Rapid Comms., Accepted (2016), arXiv:1608.07320.