  We discuss, simplify, and improve the spin-dependent correction of L.A.
Constantin et al., Phys. Rev. B 84, 233103, for atomization energies, and
develop a density parameter of the form $v\propto |\nabla n|/n^{10/9}$, found
from the statistical ensemble of one-electron densities. The here constructed
exchange-correlation generalized gradient approximations (GGAs), named zvPBEsol
and zvPBEint, show a broad applicability, and a good accuracy for many
applications, because these corrected functionals significantly improve the
atomization and binding energies of molecular systems, without worsening the
behavior of the original functionals (PBEsol and PBEint) for other properties.
This spin-dependent correction is also applied to meta-GGA dynamical
correlation functionals combined with exact-exchange; in this case a
significant (about 30%) improvement in atomization energies of small molecules
is found.
