  We propose global hybrid approximations of the exchange-correlation (XC)
energy functional which reproduce well the modified fourth-order gradient
expansion of the exchange energy in the semiclassical limit of many-electron
neutral atoms and recover the full local density approximation (LDA) linear
response. These XC functionals represent the hybrid versions of the APBE
functional [Phys. Rev. Lett. 106, 186406, (2011)] yet employing an additional
correlation functional which uses the localization concept of the correlation
energy density to improve the compatibility with the Hartree-Fock exchange as
well as the coupling-constant-resolved XC potential energy. Broad energetical
and structural testings, including thermochemistry and geometry, transition
metal complexes, non-covalent interactions, gold clusters and small
gold-molecule interfaces, as well as an analysis of the hybrid parameters, show
that our construction is quite robust. In particular, our testing shows that
the resulting hybrid, including 20\% of Hartree-Fock exchange and named hAPBE,
performs remarkably well for a broad palette of systems and properties, being
generally better than popular hybrids (PBE0 and B3LYP). Semi-empirical
dispersion corrections are also provided.
