Atomic ground states are usually degenerate. It is demonstrated that t
he density functionals for the exchange-correlation energy that are co
mmonly used are not invariant over the set of ground state densities.
This leads to uncertainties of the order of 3 to 5 kcal/mol in the ato
mic ground state energy of second and third period main group elements
and the first transition series. A much larger spread in energies is
obtained for transition elements if symmetry and equivalence restricti
ons for the Kohn-Sham orbitals are abandoned. It is recommended that a
tomic ground states that are actually used to calculate heats of atomi
zation are made explicit, and tables with one choice of atomic ground
state energies for the first rows of the periodic system are provided
for the local density approximation and for a few generalized gradient
approximations.