  Density-functional theory requires ever better exchange-correlation (xc)
functionals for the ever more precise description of many-body effects on
electronic structure. Universal constraints on the xc energy are important
ingredients in the construction of improved functionals. Here we investigate
one such universal property of xc functionals: the Lieb-Oxford lower bound on
the exchange-correlation energy, $E_{xc}[n] \ge -C \int d^3r n^{4/3}$, where
$C\leq C_{LO}=1.68$. To this end, we perform a survey of available exact or
near-exact data on xc energies of atoms, ions, molecules, solids, and some
model Hamiltonians (the electron liquid, Hooke's atom and the Hubbard model).
All physically realistic density distributions investigated are consistent with
the tighter limit $C \leq 1$. For large classes of systems one can obtain
class-specific (but not fully universal) similar bounds. The Lieb-Oxford bound
with $C_{LO}=1.68$ is a key ingredient in the construction of modern xc
functionals, and a substantial change in the prefactor $C$ will have
consequences for the performance of these functionals.
