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

Spin-dependent gradient correction for more accurate atomization energies of molecules