Optimized Lieb-Oxford bound for the exchange-correlation energy

Abstract

Using the ideas of Lieb and Oxford [Int. J. Quantum Chem. $19,$ 427 (1981)], we show that the exchange-correlation energy, and indirect part of the Coulomb energy, are bounded from below by $-1.6358\int {\rho }^{4/3}\mathrm{}\left(x\right)dx,$ where $\rho \mathrm{}\left(x\right)\mathrm{}$ is the single-particle density.