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# Improved Lieb-Oxford bound on the indirect and exchange energies

Abstract : The Lieb-Oxford inequality provides a lower bound on the Coulomb energy of a classical system of $N$ identical charges only in terms of their one-particle density. We prove here a new estimate on the best constant in this inequality. Numerical evaluation provides the value 1.58, which is a significant improvement to the previously known value 1.64. The best constant has recently been shown to be larger than 1.44. In a second part, we prove that the constant can be reduced to 1.25 when the inequality is restricted to Hartree-Fock states. This is the first proof that the exchange term is always much lower than the full indirect Coulomb energy.
Document type :
Journal articles

https://hal.archives-ouvertes.fr/hal-03618116
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Submitted on : Thursday, March 24, 2022 - 9:15:28 AM
Last modification on : Monday, October 3, 2022 - 4:26:04 PM

### Citation

Mathieu Lewin, Elliott H. Lieb, Robert Seiringer. Improved Lieb-Oxford bound on the indirect and exchange energies. Letters in Mathematical Physics, 2022, 112, pp.92. ⟨10.1007/s11005-022-01584-5⟩. ⟨hal-03618116⟩

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