  We propose hybrid schemes incorporating exact exchange into
thermally-assisted-occupation density functional theory (TAO-DFT) [J.-D. Chai,
J. Chem. Phys. 136, 154104 (2012)] for an improved description of nonlocal
exchange effects. With a few simple modifications, global and range-separated
hybrid functionals in Kohn-Sham density functional theory (KS-DFT) can be
combined seamlessly with TAO-DFT. In comparison with global hybrid functionals
in KS-DFT, the resulting global hybrid functionals in TAO-DFT yield promising
performance for systems with strong static correlation effects (e.g., the
dissociation of H2 and N2, twisted ethylene, and electronic properties of
linear acenes), while maintaining similar performance for systems without
strong static correlation effects. Besides, a reasonably accurate description
of noncovalent interactions can be efficiently achieved through the inclusion
of dispersion corrections in hybrid TAO-DFT. Relative to semilocal density
functionals in TAO-DFT, global hybrid functionals in TAO-DFT are generally
superior in performance for a wide range of applications, such as
thermochemistry, kinetics, reaction energies, and optimized geometries.
