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arXiv · 2203.12473

Improved Lieb-Oxford bound on the indirect and exchange energies

Mathieu Lewin·Elliott H. Lieb·Robert Seiringer
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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.

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Mathieu Lewin, Elliott H. Lieb, Robert Seiringer. 2022-03-23. Improved Lieb-Oxford bound on the indirect and exchange energies. https://doi.org/10.1007/s11005-022-01584-5

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