Doubly hybrid density functionals that correctly describe both density and energy for atoms

Significance It was commented that some modern density functional theory functionals may be giving the correct energies for the wrong reason and functionals that produce “right” energies from “wrong” densities fail twice. However, the route to the “heaven” of the “Jacob’s ladder” is incomplete in Medvedev et al. [Medvedev MG, et al. (2017)Science 355:49–52], as the authors did not provide any information on the top fifth-rung functionals. We fill the gap to show here that the XYG3 type of doubly hybrid density functionals (xDHs) can correctly describe both density and energy for the same atomic set used by Medvedev et al., such that electronic structure calculations for molecular sciences of the main group elements can be carried out reliably by using xDHs.