Nonempirical (double‐hybrid) density functionals applied to atomic excitation energies: A systematic basis set investigation

We investigate here the lowest‐energy (spin‐conserving) excitation energies for the set of He‐Ne atoms, with the family of nonempirical PBE, PBE0, PBE0‐1/3, PBE0‐DH, PBE‐CIDH, PBE‐QIDH, and PBE0‐2 functionals, after employing a wide variety of basis sets systematically approaching the basis set limit: def2‐nVP(D), cc‐pVnZ, aug‐cc‐pVnZ, and d‐aug‐cc‐pVnZ. We find that an accuracy (ie, mean unsigned error) of 0.3 to 0.4 eV for time‐dependent density functional theory (DFT) atomic excitation energies can be robustly achieved with modern double‐hybrid methods, which are also stable with respect to the addition of a double set of diffuse functions, contrarily to hybrid versions, in agreement with recent findings employing sophisticated multiconfigurational DFT methods. Atomic excitation energies calculated by time‐dependent density functional theory demands highly accurate basis sets with diffuse functions, together with modern double‐hybrid density functionals, to be competitive with CASPT2/CASSCF and multiconfigurational pair‐density functional theory methods.