  In the framework of density-functional theory, several popular density
functionals for exchange and correlation have been constructed to satisfy a
local form of the Lieb-Oxford bound. In its original global expression, the
bound represents a rigorous lower limit for the indirect Coulomb interaction
energy. Here we employ exact-exchange calculations for the G2 test set to show
that the local form of the bound is violated in an extensive range of both the
dimensionless gradient and the average electron density. Hence, the results
demonstrate the severity in the usage of the local form of the bound in
functional development. On the other hand, our results suggest alternative ways
to construct accurate density functionals for the exchange energy.
