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The Lieb–Oxford lower bounds on the Coulomb energy, their importance to electron density functional theory, and a conjectured tight bound on exchange

The Lieb–Oxford lower bounds on the Coulomb energy, their importance to electron density functional theory, and a conjectured tight bound on exchange

Lieb and Oxford (1981) derived rigorous lower bounds, in the form of local functionals of the electron density, on the indirect part of the Coulomb repulsion energy. The greatest lower bound for a given electron number $N$ depends monotonically upon $N$, and the $N\to\infty$ limit is a bound for all …