The XYG3 type of doubly hybrid density functionals

Doubly hybrid ( DH ) functionals have emerged as a new class of density functional approximations ( DFAs ), which not only have a nonlocal orbital‐dependent component in the exchange part, but also incorporate the information of unoccupied orbitals in the correlation part, being at the top rung of Perdew's view of Jacob's ladder in DFAs . This review article focuses on the XYG3 type of DH ( xDH ) functionals, which use a low rung functional to perform the self‐consistent‐field calculation to generate orbitals and densities, with which a top rung DH functional is used for final energy evaluation. We will discuss the theoretical background of the xDH functionals, briefly reviewing the adiabatic connection formalism, coordinate scaling relations, and Görling–Levy perturbation theory. General performance of the xDH functionals will be presented for both energies and structures. In particular, we will present the fractional charge behaviors of the xDH functionals, examining the self‐interaction errors, the delocalization errors and the deviation from the linearity condition, as well as their effects on the predicted ionization potentials, electron affinities and fundamental gaps. This provides a theoretical rationale for the observed good performance of the xDH functionals. WIREs Comput Mol Sci 2016, 6:721–747. doi: 10.1002/wcms.1274 This article is categorized under: Electronic Structure Theory > Density Functional Theory