Journal
MOLECULAR PHYSICS
Volume 114, Issue 7-8, Pages 1076-1085Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/00268976.2015.1136440
Keywords
Density functional theory; Lieb-Oxford bound; exchange-correlation functionals; electronic correlation
Funding
- European Research Council [648932]
- Netherlands Organization for Scientific Research (NWO) [717.013.004]
- European Research Council (ERC) [648932] Funding Source: European Research Council (ERC)
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The Lieb-Oxford bound, a nontrivial inequality for the indirect part of the many-body Coulomb repulsion in an electronic system, plays an important role in the construction of approximations in density functional theory. Using the wave function for strictly correlated electrons of a given density, we turn the search over wave functions appearing in the original bound into a more manageable search over electron densities. This allows us to challenge the bound in a systematic way. We find that a maximising density for the bound, if it exists, must have compact support. We also find that, at least for particle numbers N 60, a uniform density profile is not the most challenging for the bound. With our construction, we improve the bound for N = 2 electrons that was originally found by Lieb and Oxford, we give a new lower bound to the constant appearing in the Lieb-Oxford inequality valid for any N, and we provide an improved upper bound for the low-density uniform electron gas indirect energy. [GRAPHICS] .
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