We discuss, simplify, and improve the spin-dependent correction of Constantin et al. [Phys. Rev. B 84, 233103 (2011) https://doi.org/10.1103/PhysRevB.84.233103] for atomization energies, and develop a density parameter of the form v∝|∇n|/n10/9, 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.
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