  We investigate fundamental properties of meta-generalized-gradient
approximations (meta-GGAs) to the exchange-correlation energy functional, which
have an implicit density dependence via the Kohn-Sham kinetic-energy density.
To this purpose, we construct the most simple meta-GGA by expressing the local
exchange-correlation energy per particle as a function of a fictitious density,
which is obtained by inverting the Thomas-Fermi kinetic-energy functional. This
simple functional considerably improves the total energy of atoms as compared
to the standard local density approximation. The corresponding
exchange-correlation potentials are then determined exactly through a solution
of the optimized effective potential equation. These potentials support an
additional bound state and exhibit a derivative discontinuity at integer
particle numbers. We further demonstrate that through the kinetic-energy
density any meta-GGA incorporates a derivative discontinuity. However, we also
find that for commonly used meta-GGAs the discontinuity is largely
underestimated and in some cases even negative.
